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N77-295 INAS--Cl503S57) EFYECTS O- DAIPING ON MODE
SHApES-VOLUM E I FinalBepP~t (Boeing 322 pAerospace CoSeattleo-Wasb) UnclasCSCL 20K
HC A IAMl A01
AUG 1977 RECEIVED j
NASA STI FACIU1 1 INPUT BRANCIf 7
D180-20572-1 FINAL REPORT
CONTRACT NAS8-31369
EFFECTS OF DAMPING ON MODE SHAPES - VOLUME I
JUNE 271 1977
PREPARED BY
BOEING AEROSPACE COMPANY MISSILE AND ARMAMENT DIVISION
SEATTLEJ WASHINGTON 98124
ampL-A NiST- PROGRAM LEADER
PREPARED FOR
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION MARSHALL SPACE FLIGHT CENTERJ ALABAMA 35812
ABSTRACT
Displacement velocity and acceleration admittances were calshyculated for a realistic NASTRAN structural model of Space Shuttle
for three conditions liftoff maximum dynamic pressure and end
of Solid Rocket Booster burn The realistic model of the Orbiter
External Tank and Solid Rocket Motors included the representation
of structural joint transmissibilities by finite stiffness and
damping elements Data values for the finite damping elements
were assigned to duplicate overall low-frequency modal damping
values taken from tests of similar vehicles For comparison with the calculated admittances position and rate gains were computed
for a conventional Shuttle model for the liftoff condition
KEY WORDS
finite-element structural model
structural joints
damping
normal modes
Space Shuttle
admittances
ii
ACKNOWLEDGMENTS
The work described in this report was sponsored by the George C
Marshall Space Flight Center under NASA Contract NAS8-31369 The
work was performed under the technical direction of George L von
Pragenau and Richard W Schock of the MSFC Systems Dynamics Labshy
oratory A NASTRAN structural model of the Orbiter was provided
by C Thomas Modlin ofthe Structural Mechanics Divi~ion of the
Johnson Space Center The computer programming was performed by
Malcolm W Ice of Boeing Computer Services Inc The authors
gratefully acknowledge the contributions made by each of these
individuals toward the successful completion of this contract
iii
TABLE OF CONTENTS - VOLUME I
Section Page
ABSTRACT AND KEY WORDS ii
ACKNOWLEDGMENTS iii
ILLUSTRATIONS v
TABLES vii
10 INTRODUCTION 1
20 TECHNICAL APPROACH 3
21 Structural Joint Modeling 3
22 Joint Damping Prediction 18
23 Admittance Matrix Calculation 21
30 REALISTIC STRUCTURAL MODEL 26
31 Space Shuttle Structural Models 26
32 Structural Joints and Damping 72
33 Solid Rocket Motor Propellant Dynamics 94
34 Space Shuttle Modes and Modal Damping 104
40 CRITICAL RESONANCES FROM CONVENTIONAL MODEL (LIFTOFF) 108
50 CRITICAL RESONANCES FROM REALISTIC MODEL 162
51 Critical Modes 162
52 Critical Resonances 162
60 ADMITTANCE METHOD COMPARISON AND MODAL 164 EXCITABILITY CRITERIA
61 Comparison of Realistic and Conventional Approaches 164
62 Criteria for the Excitability of Modes 187
70 COMPUTER TIME ESTIMATES 188
71 Orbiter 188
72 Space Shuttle 188
80 CONCLUSIONS AND RECOMMENDATIONS 190
81 Conclusions 190
82 Recommendations 190
APPENDIX I - PREPROCESSOR COMPUTER PROGRAM 192
APPENDIX II - JOINT DAMPING PREDICTOR COMPUTER PROGRAM 246
APPENDIX III - POSTPROCESSOR COMPUTER PROGRAM 261
REFERENCES 312
iv
ILLUSTRATIONS
Figure Page
2-1 Schematic of Single Degree-of-Freedom Voigt 4 Joint Model
2-2 NASTRAN Rod Joint Damping Model 8
2-3 NASTRAN BAR Joint Damping Model 11
2-4 Plate Joint Damping Model Schematic 15
3-1 Space Shuttle Coordinate Systems 27
3-2 External Tank Gridpoint Numbering 29
3-3 External Tank Bar and Rod Numbering 30
3-4 External Tank Plate Numbering 31
3-5 Aft Orbiter Attachment Fitting 33
3-6 Solid Rocket Motor Math Model 35
3-7 Orbiter Math Model 41
3-8 Orbiter-- Forward Fuselage 42
3-9 Orbiter-- Fuselage Payioad Section 48
3-10 Orbiter-- Thrust Structure 61
3-11 Orbiter-- Wing 67
3-12 Orbiter-- Vertical Tail 70
3-13 Payload Math Model 73
3-14 Boeing 747 Structural Damping Data 77
3-15 External Tank Intertank Joints 81
3-16 SRM Case Joint Locations 86
3-17 Orbiter Fuselage Panel Joint Locations 89
3-18 Orbiter Wing Panel Joint Locations 90
3-19 Orbiter Wing and Vertical Tail Root Joint Locations 92
3-20 SRM Propellant Complex Shear Modulus 95
3-21 Maxwell Model for SRM Propellant 96
3-22 Complex Shear Modulus Maxwell Model 98
3-23 Finite Element Model SRM Propellant 100
V
ILLUSTRATIONS (Continued)
Figure Page
6-1 Comparison of Conventional and Realistic Models 165 Displacement Response
6-2 Comparison of Conventional and Realistic Models 171 Velocity Response
6-3 Comparison of Conventional and Realistic Models 183 Acceleration Response
1-1 NASTRAN Joint Damping Model Schematics 196
111-1 Postprocessor Program Flow 262
vi
TABLES
Table Page
3-1 Space Shuttle Coordinate Systems 28 3-2 External Tank Mass Data 34
3-3 SRM Mass Properties CLiftoff) 38
3-4 SRM Mass Properties CMax Q) 39
3-5 SRM Mass Properties CSRB Cut-Off) 40
3-6 Orbiter Mass Data 71
3-7 Payload and OMS Mass Data 74
3-8 Structural Joint Damping Parameters 83
3-9 Comparison of Desired and Actual Orbiter Modal Damping 93
3-10 SRM Propellant Modal Data 101
3-11 SRM Free-Free Modal Parameters and Damping Data 103
3-12 Space Shuttle Data Data Liftoff 105
3-13 Space Shuttle Modal Data Max q 106
3-14 Space Shuttle Modal Data SRM Cutoff 107
4-1 Space Shuttle Response and Excitation Locations 110
4-2 Rate Coefficients for Conventional Model iI
4-3 Position Coefficients for Conventional Model 138
1-1 DMAP ALTER Statements for the Preprocessor Computer Program 194
vii
10 INTRODUCTION
The presence of distributed damping in aerospace structures may significantly
affect predicted dynamic responses particularly of high-order modes The development and implementation of a general methodology framework for evaluating
the effect of distributed structural damping on spacecraft structures was begun
under Contract NAS8-30655 the results of which are reported in Reference 1
The purpose of the present study is to assess the influence of discrete damping elements on a structural model of the Space Shuttle using admittance techniques
The following three phases of the study are summarized herein
Phase I - Develop a realistic NASTRAN structural model using a preprocessor
for describing joint transmissibilities and a postprocessor for selecting signifshy
icant resonances
Phase II - Develop a conventional normal-mode structural model compare realistic
and conventional models and establish criteria for the excitability of highshy
order modes
Phase III - Update the mass stiffness and damping effects in the Space Shuttle structural model calculate admittances at liftoff max Q and SRB cut-off and
simplify the Space Shuttle structural models for use in attitude control POGO
stability dynamic loads and vibration analyses
These objectives were accomplished primarily through the calculation of admittances for a realistic NASTRANstructural model of the Space Shuttle The admittances
were computed with a postprocessor computer program using modal characteristics
including a coupled modal damping matrix from a NASTRAN restart tape The
damping characteristics were included in the structural model with the aid of a
preprocessor computer program Damping parameters for the joints in the Orbiter
were calculated using a joint damping predictor computer program
The results of this study are presented in two volumes Volume I contains the
technical approach used in describing distributed joint damping in a finite
element model of the Space Shuttle the method used to calculate individual joint
damping parameters to provide realistic modal damping and the techniques for
calculating structural admittances using a coupled modal damping matrix The
computer programs developed to perform these tasks are described in Section 20
with program descriptions and listings included inAppendices I II and III
The finite element model of the Space Shuttle vehicle is described in Section 30
Sections 40 and 50 present critical resonances for the conventional and
realistic models for the liftoff condition respectively Section 60 contains
a comparison of the realistic and conventional approaches Section 70 presents -computer time estimates and conclusions of all three phases of the study are
presented in Section 80
Volume IISection 20 contains the structural dynamic characteristics of the
Space Shuttle vehicle at liftoff max q and SRB cutoff including mode shapes
at selected freedoms modal frequencies generalized masses and coupled genshy
eralized modal viscous damping coefficients Admittances-for the three mass
conditions are shown in Section 30 of Volume II
2
20 TECHNICAL APPROACH
Methodology for developing the realistic NASTRAN Shuttle sttctural model is
contained in a preprocessor computer program to generate joint damping and
transmissibility data a joint damping predictor computer program to calculate
joint damping constants which will result in specified modal damping and a
postprocessor computer program to select significant resonances by the admittance
approach The methodology developed for each of these three computer programs
is described in Sections 21 22 and 23 respectively
2J1 STRUCTURAL JOINT MODELING
Structural damping is comprised of both material (hysteretic) damping and energy
dissipation in structural joints Material damping may be represented in linear
dynamic response analyses by uncoupled modal viscous damping ratios (6= CCc)
Energy dissipation in structural joints which is a nonlinear function of many
parameters must also be represented by linear models so that linear analysis
techniques may be used According to Mead (Reference 2) representing joint dampshy
ing by equivalent viscous damping isjustifiable for structures subjected to
sinusoidal excitation since sinusoidal response is not appreciably affected by
damping nonlinearities The linear model used successfully in Reference 1 to
represent structural joint transmissibility of beams is the Voigt model
The two-parameter Voigt unit shown schematically in Figure 2-1 consists of a
spring in parallel with a viscous damper It is the simplest complex-notation
model and possesses hysteretic properties characteristic of damping in materials
and structural joints For sinusoidal excitation the equivalent damping and
stiffness coefficients for the Voigt model in series with a spring CT and KT
are functions both of the structural parameters (KKC) and of the forcing
frequency (a)
CCT CT (K+K 2 + C 2 (1)
KK(K+K) + C-2K KT= J (2)2(K+Kj) 2 + Cj2
3
ZZZZampZKLZ
VOIGT Kj JOINT TOTAL
MEMBER (KT CT)
STRUCTURAL MEMBER
K
M
Figure 2-1 Schematic of Single Degree-of-Freedom Voigt Joint Model
4
For very low frequencies C _~K )123
CT(0O) = Cj(mT)- (3)
K(4
KT(C=O) = Kj K+Kj (4)
Equations (3)and (4)indicate that the total Voigt jointmember stiffness coshyefficient at very low frequencies is equal to the static stiffness of the series spring arrangement
For very high frequencies
CT(=) = 0 (5)
KT( =-) = K (6)
Equations (5)and (6)indicate that at very high frequencies the damper becomes
rigid These frequency-dependent characteristics of the Voigt model are conshy
sistent with the physical observations made by Ungar (Reference 3 page 149)
The preprocessor computer program was developed to implement this methodology by
adding structural damping representations to a NASTRAN finite-element structural
model The original preprocessor described in Reference 1 modifies the input
data for a conventional finite-element structural model and generates additional inputs necessary to incorporate the Voigt joint damping model at the ends of
specified BAR and ROD elements
The original preprocessor has been updated by several modifications The major modification is the additional capability for modeling riveted or bolted joints in quadrilateral plate elements The minor modifications include improving the ROD joint model the generation of double-field PBAR and PVISC cards which
eliminates certain format limitations and providing the capability of accepting
gridpoints defined in arbitrary cylindrical coordinate systems By the latter
5
modification all gridpoint coordinates defined in cylindrical and rectangular
coordinate systems are simply converted into the basic NASTRAN rectangular coshy
ordinate system
The procedure used for modeling riveted or bolted joints in plate elements is
consistent with the damping mechanism described by Mead (Reference 2) Accordshy
ing to this theory energy loss between two adjacent plates compressed by rivet
forming or bolt tightness occurs in three distinct stages determined by amplitude
of the motion
(1) elastic hysteresis or material damping due to small motions in the
elastic range
(2) local plastic defomation in the area of the attachment due to motions
in the plastic range
(3) dynamic friction losses due to local relative slipping
A detailed description of the input and output features of the preprocessor
computer program is presented in Appendix I
The extreme complexity of the stress distributions and friction characteristics
in the contact areas may preclude the theoretical prediction of local joint
energy losses The problem of assigning data values to parameters of the NASTRAN
joint model corresponding to this theoretical damping mechanism will therefore be
addressed by reference to major substructure modal damping data rather than to
joint damping data
211 Rod Joints
This section describes the procedures used by the preprocessor computer program
to add structural joint models to NASTRAN ROD elements The preprocessor modifies
the input data for a conventional finite-element structural model andgenerates
additional inputs necessary to incorporate a Voigt joint damping model at one end
of each specified ROD element The damping characteristics of ROD joints are
modeled by modifying the ROD properties and by including material damping
6
A schematic of a NASTRAN ROD element with a structural joint at one end is shown
in Figure 2-2 When the user requests a joint to be incorporated at gridpoint A
the preprocessor establishes the model as follows
a Properties of the original ROD are modified to incorporate the
effect of the joint stiffness characteristics
b Material damping in the ROD is incorporated based on the damping
constant supplied by the user
c A VISC element is added between gridpoints a and b if torsional
damping is required
The original preprocessor described in Reference 1 constructed a ROD joint by
inserting a new gridpoint at c modifying the properties of the ROD from a to
c and inserting a VISC element from a to c
Modifications were made to the preprocessor to eliminate the need for the additional
gridpoint (c) The user still specifies the length of the joint as a fraction of
the original ROD length the properties of the joint as fractions of the original ROD properties and the damping constant of the viscous damper between gridpoints
a and c The preprocessor now modifies the properties of the original ROD to
incorporate the joint stiffness and damping effects and incorporates a VISC
damping element between gridpoints a and b only if a torsional damping value isspeci
The equivalent ROD area (A) and torsional constant (J) are calculated based on
springs in series
A =A[-( ~(7)KA
KG(I-KJ) + KJ (8)
where KG = joint length factor
KA = joint area factor
KJ = joint torsional constant factor
A = original ROD area
J = original ROD torsional constant
7
a k c b
0=--c j ltp-m
ROD elements
- VISC element
a) Schematic of Desired ROD Joint
a it b
ml
modified ROD element
--------- modified VISC element
b) Modified ROD Joint Schematic
FIGURE 2-2 NASTRAN ROD JOINT DAMPING MODEL
8
If axial damping is requested (Cl 0) a new material card (MAT1) is generated
for the rod which includes material damping (GE)
GE = CI (9) A-E
= C KG + ]where Cl
= original ROD length
E = Youhgs modulus
C1 = original axial damping constant
If torsional damping is requested (C2 0 0) a VISC element is inserted between
gridpoints a and b The damping constants for this VISC element are
Cl = 0
C2 C2KG(I-KJ) + KJ C2 = C2F KGK+K] (10)
where C2 is the original torsionaldamping constant
This allows different damping constants to be specified for axial and torsional
motions
Default values are automatically specified by the preprocessor for the NASTRAN
data describing ROD joints The default value specifying joint length results
in ROD parameters equivalent to a joint whose length is ten percent of the origshy
inal element length Default values specifying joint member area and torsional
constant are unity ie the area- and torsional constant of the equivalent ROD
(with joint effects included) are the same as the original element However
joint flexibility effects can be included using different joint factors
The VISC elements and parameters chosen to define the joint damping characteristics
must result in a physical damping matrix which satisfies kinematic compatibility
The compatibility relations for the damping matrix are represented by
FBGG] R = 0 (11)
where [BGG] is the NASTRAN viscous damping matrix in physical coordinates and
9
fR is an arbitrary-vector of rigid-body translations and rotations
Equation (11) ensures that no damping forces are generated by rigid-body
motions With regard to kinematic compatibility the NASTRAN VISC damping
element is limited to two applications
a With translational damping the compatibility relations are
satisfied only when the axis of the VISC element is aligned
with an axis of the displacement coordinate system
b Without translational damping the compatibility relations
involving only rotational damping are satisfied for any
orientation of the VISC element
For the general case of an arbitrarily oriented element having both translashy
tional and rotational damping components the present NASTRAN VISC element
does not provide the translationrotation damping coupling terms required by
Equation (11) Therefore since VISC elements are used only for rotational
damping in the ROD joint kinematic compatibility is assured
212 Bar Joints
This section describes the procedures used by the preprocessor computer proshy
gram to add structural joint models to NASTRAN BAR elements The preprocessor
modifies the input data for a conventional finite-element structural model and
generates additional inputs necessary to incorporate a Voigt joint damping
model at one end of each specified BAR element The damping characteristics of the joints are modeled with the material damping in ROD elements
A schematic of a NASTRAN BAR element with joint damping model included at
one end is shown in Figure 2-3 The original element lies between gridpoints
a and b When the user requests a joint damping model to be included at
gridpoint a the preprocessor establishes the model as follows
a Gridpoint c is introduced on the BAR axis at a specified
distance from gridpoint a
10
a k g b
yI BAR ELEMENTS
ROD ELEMENTS WITHVISCOUS DAMPING
S- - MPCS
FIGURE2-3 NASTRAN BAR JOINT DAMPING MODEL
II1
b Properties of the BARbetween gridpoints a and c are altered as specified either by direct input or by default values to provide desired joint stiffness characteristics
c For the BAR element gridpoints e and f are established such that gridpoints a b e and f form an orthogonal axis system at gridshypoint a Gridpoint e is in plane 1 of the BAR element and gridpoint f is inplane 2 The distances from gridpoint a to gridpoints c e and f are identical
d ROD elements (m n and p) with desired material damping properties are inserted between gridpoints a and c a and e and a and f
e Gridpoints e and f are multipoint constrained to gridpoint c
Material damping in a ROD element provides damping along its axis and in torsion about its axis Therefore for a BAR element three ROD elements are required at each gridpoint to provide damping forall six degrees of freeshydom The locations of gridpoints e and f in Figure 2-3 are calculated in the rectangular coordinate system by vector analysis Vb and VR are defined as position vectors from gridpoint a to gridpoint b and from gridpoint a to
the BAR orientation gridpoint respectively The components of Vb for example are
Vbl xb xa
Vb2
Vb3
= Yb
zb
Yaj (2 (12)
The vector from gridpoint a in the direction of gridpoint f is calculated as
the vector cross product
Vf = b x VR (13) 0
This results in a vector which is perpendicular to plane 1 of the original BAR element The vector from gridpoint a to gridpoint F (Vf)is normalized
such that its magnitude is the same as the magnitude of the vector from a to
12
C
Vf 0(IVfIIV 0o) (14)
The location of gridpoint f is then calculated by
Yf j Ya + f2 (15) zf za tVf3
The vector from gridpoint a in the direction of gridpoint e is calculated using the cross product of Vf and Vbshy
e Vfx Vb (16) e0
The vector from gridpoint a to gridpoint e (Ve) is also normalized such that
its magnitude is the same as the magnitude of the vector from a to c
Ve= edeg (IVii i) (17)
The location of gridpoint e is then calculated by
Ye = Ya + Ve2 (18) ze a Ve3]
Default values are automatically specified by the preprocessor for the NASTRAN
data describing BAR joints The default value specifying joint length results
in a joint member whose length is ten percent of the original element length
The default values specifying joint member area moments of inertia and
torsional constant are unity ie the joint member has the same area and
moments of inertia as the parent member However factors different from
unity can be used to increase flexibility in the joint
Damping in the joint is obtained from material damping in the ROD elements
(m n and p) Material damping in NASTRAN is proportional to the element
stiffness in each degree of freedom The proportionality constant GE is
input on the material property card Using one value of the material damping
factor (GE) for all of the RODS in the joint representation the effective
13
damping for each degree of freedom can be made different by changing their
stiffnesses ie cross-sectional areas and area moments The material
damping factor (GE) is based on the specified joint damping constants and
is made arbitrarily large so that the stiffnesses of individual joint RODS
are small and do not affect the joint stiffness
(19)GE - k E KA A
where Ct = Clm + Cln + Clp + C2m + C2n +C2p
Then the individual ROD properties are
Am Clm( m = C2m( G
An = Cln(E ikGE) Jn= C2n (6 poundkGE) (20)
ClP( E nk k (20)) =
213 Plate Joints
This section describes the procedures used by the preprocessor computer program
to add structural joint models along one edge of some types of NASTRAN plate
elements A schematic of a NASTRAN quadrilateral plate element with a joint
damping model included along one edge is shown in Figure 2-4 The plate
elements may be referenced by any of the following NASTRAN connection cards
CQUADI CQUAD2 CQDMEM or CSHEAR For QUADI or QUAD2 plate elements having
both inplane and bending stiffness when the user requests a joint damping
model to be included along the edge between gridpoints a and b the preproshy
cessor establishes the model as follows
a Gridpoints c and d are introduced along the plate edges at a specified
distance from gridpoints a and b
b ROD or BAR elements if any located along these edges are attached to
the introduced gridpoints (c and d) for continuity
c ROD or BAR elements if any located along the joint between gridpoints
a and b are each divided into two members located between gridpoints a
and b and between c and d each of these elements has half of the original
element stiffness
14
QUADRI LATERAL PLATE ELEMENT
Cd
ai b
ROD ELEMENTS WITH VISCOUS DAMPING
Figure 2-4 Plate Joint Damping Model Schematic
15
d Axial ROD elements having axial stiffness and damping are introduced
between gridpoints a and c and between b and d to provide desired stiffshy
ness and damping characteristics
e Diagonal ROD elements having axial stiffness and damping are introduced
between gridpoints a and d and between b and c to provide desired stiffshy
ness and damping characteristics
f The out-of-plane (transverse) shear stiffness is considered a negligible
quantity and is therefore not explicitly treated in this model
g Depending on the structural characteristics of the joint being represhy
sented the local moment can be transferred across the joint if desired
by multipoint constraint equations using gridpoints a and b as indeshy
pendent freedoms and gridpoints c and d as dependent freedoms
The preprocessor model for QDMEM and SHEAR plate elements having only
inplane stiffness is identical to that just described except that the rotashy
tional freedoms must be multipoint constrained across the joint except when
BAR elements are used as edge members In addition when adjacent plate elements
lie in a plane the out-of-plane translational freedom must also be multishy
point constrained except when BAR edge members are used This is to eliminate
singularities resulting from the absence of bending and shear stiffnesses in
these plate elements
The preprocessor model for SHEAR plate elements also includes ROD elements
across the joint between gridpoints a and c and between b and d to provide
axial viscous damping
The multipoint constraint (MPC) equation for the out-of-plane translational
freedom across a joint is automatically generated even when the plane elements
are inclined to the basic rectangular coordinate system The MPC equation is
determined by transforming the standard rigid-body constraint matrix by the
direction cosines defining the vector normal to the plate elements The
direction cosines are determined from the scalar components of the vector
cross-product of the position vectors on the plate corner gridpoints adjacent
to the specified joint gridpoint The dependent freedom is chosen from the
grid across the joint from the specified joint gridpoint as that freedom
having the largest direction cosine The MPC feature for the out-of-plane
16
translational freedom is of course not required when the plates along the
joint meet at an angle and thereby transfer shear forces by permissible shell
membrane action
Default values are automatically specified by the preprocessor for the NASTRAN
data describing the structural joints For the riveted or bolted joints in
quadrilateral plate elements numerical default values are specified for joint
width area for axial ROD elements and area for diagonal ROD elements The
joint width is specified as five percent of the distance between gridpoints
a and b The nominal areas for both the axial and diagonal ROD elements are
defined so as to duplicate the inplane axial and shear stiffnesses of the
original plate The default values for these ROD areas are unity However
other joint factors based on estimated effectivity associated with the stress
distribution in the contact area near the individual rivets or bolts can be
specified if required
214 Data Preparation for Joint Damping Predictor
Specialized NASTRAN input is automatically generated by the preprocessor for
generating uncoupled partitions of the element damping matrix required for
the joint damping predictor computer program This input is described in the
following section
17
22 JOINT DAMPING PREDICTION
This section describes the procedures used by the joint damping predictor
(JDP) computer program to determine data values for the local NASTRAN damping elements The specific purpose of the JDP is to evaluate coefficients for
NASTRAN VISC and ROD elements such that specified damping ratios are obtained
for selected total vehicle or major substructure modes This approach accounts
for the fact that a given local damping element may contribute significantly to
the damping of several different vehicle modes The JDP program used with the
preprocessor program and such vehicle low-frequency modal damping equations as
those presented in References 4 and 5 permits the rational prediciton of strucshy
tural damping for the higher-frequency modes
The JDP program operates on damping data not readily available from NASTRAN
Required BULK DATA for this specialized use of NASTRAN is prepared automatishy
cally by the preprocessor specialized NASTRAN DMAP ALTER statements are also
required The output of this unique preprocessorNASTRAN run is used as input
by the JDP program The JDP program reads the following data from the NASTRAN
checkpointrestart tape
[D1 the matrix of overall vehicle mode shapes
[BGG) the overall vehicle element damping matrix
[DMIG] the partition vector used for separating matrices
into selected subsets
The JDP computer program requires sets of local damping elements to be separated
from each other so that an influence coefficient approach may be employed Thus
when two or more damping elements from different damping sets attach to the same
gridpoint duplicate gridpoints (having the same coordinates) must be defined
Modified element connections are then defined to attach damping elements to the
duplicate gridpoints as required To assure that the basic stiffness and mass
characteristics of the structure are not affected by these operations multipoint
constraint equations are required to constrain the duplicate gridpoints to move
with the original gridpoint
The preprocessor computer program automatically generates NASTRAN data for the
duplicate gridpoints modified element connections and multipoint constraint
equations required to generate uncoupled partitions of the element damping matrix
18
without modifying the dynamic characteristics of the structure The element damping matrix [BGG] is then partitioned into distinct damping sets [BGGj]
The set corresponding to j=O contains damping elements with parameters known The other sets (j=ln) contain damping elements with arbitrarily assumed
parameter values
Overall vehicle damping values may be determined from equations of energy loss per cycle vs modal kinetic energy such as described in References 4 and 5 These equations which are based on aerospace modal test data enable realistic damping values to be predicted for selected fundamental vehicle modes From these total modal damping ratios for m selected low-frequency modes and from the partitioned damping sets scale factors can be calculated for the damping
sets with the assumed values The joint damping predictor automatically pershyforms the following operations
a Calculate the contribution to the diagonal of the overall vehicle modal
damping matrix D due to the damping elements in sets j=ln
D = 2( - m)wM - BHHO (21)
whers i is the desired total modal damping ratio for the ith selected
mode
tmi is the modal damping ratio representing the material damping E is the frequency of the ith mode Mi isthe generalized mass of the i mode BHHO is the diagonal of the generalized damping matrix calculated
using the element damping matrix with known parameters [BGGO] and the partition of the matrix of mode shapes corresponding to these freedoms and the selected modes
b Calculate a matrix of damping influence coefficients [C] such that
D = [C]A (22) where A is a vector of scale factors
Ij ji EBGGjIsj i is the unit generalized damping contribution
of the jth damping set and the ith selected mode
c Solve for the scale-factor vector CAI using the standard least-squares
approach
A = ([c]T[c) [C]TD (23)
19
d Multiply the element damping sets by A (j=ln) and calculate-the
updated generalized damping matrix for verification of the analysis
The basic output of the joint damping predictor computer program is the scaleshy
factor vector AI by which the damping parameter values assumed for the initial
preprocessorNASTRAN run are multiplied The vector A is calculated such that
rationally specified modal damping values for selected fundamental vehicle modes
are obtained in the NASTRAN model Subsequent system dynamic characteristics of
this modelcombined with other models similarly calibratedcomprise realistic
and consistent damping ratios for the higher-order modes
20
23 ADMITTANCE MATRIX CALCULATION
The original post-processor computer program was developed to select critical modes for low-frequency control-system studies and higher frequency vibration analyses of the Large Space Telescope (Reference 1) using structural dynamic characteristics obtained from a NASTRAN restart tape The basic calculations were performed for ease of computation using uncoupled normal modes A study indicated that the effects of modal velocity c6upling could be significant to responses in certain frequency ranges (Reference 6) The original postprocessor has therefore been updated to use admittance techniques for selecting critical resonances for subsequent dynamic response and loads studies The NASTRAN calculation of the required coupled modal damping matrix is accomplished with DMAP ALTER statements in the NASTRAN EXECUTIVE CONTROL deck
The postprocessor reads the following structural dynamic characteristics from the
NASTRAN checkpointrestart tape
[M] the matrix of mode shapes for selected modes and freedoms MI the matrix of generalized masses for selected modes [D] the matrix of generalized coupled modal damping terms for
selected modes
10 the matrix of modal frequencies for selected modes
The coupled modal damping matrix is calculated by applying the modal transformation
to the viscous damping matrix BGG generated by NASTRAN in physical coordinates
[D] = []TEBGG] [ ] (24)
The postprocessor computer program accepts this data and with options 4-6 selects critical resonances within a specified frequency range using an admittance approach Discussions of the methodology for options 1-3 may be found in Reference 1 and in Appendix III as part of the users manual The computations for the admittance approach are performed primarily in generalized modal coordinates for maximum numerical efficiency The admittance matrices are then transformed back to physical coordinates for the selection process Each term in the complex
admittance matrix in physical coordinates for a specified frequency ($)is
21
defined as the response at one degree-of-freedom due to a unit sinusoidal input
of frequency S applied at another degree-of-freedom The responses of interest
are assumed to be either displacement or velocity and the unit input could be
either force or moment The displacement admittance matrix for frequency S in
Physical coordinates is defined by
X(js) = [AD(P)(j)]F(s)1 (25)
where
X(jM) column of complex physical displacements at the response
freedoms at frequency $
[AD(P)(jB)] complex displacement admittance matrix in physical
coordinates
F(S)1 = column of unit sinusoidal inputs at frequency applied
at the input freedoms
The admittance matrix in physical coordinates is related to the corresponding
matrix in modal coordinates as follows
[AD(p)(ji)] = [R][AD(M)(i$)]1[i]T C261
where
DRI = matrix of mode shapes by column for the response freedoms
41i T = matrix of mode shapes by row for the input freedoms
The modal displacement admittance matrix is expressed in terms of the dynamic
characteristics output on the NASTRAN restart tape as follows
[AD(M)(joS)] = N 2 _21 + jO[Do] C271
where
Wi = modal frequency of the ith mode
Mii = generalized mass of the ith mode
Dik = generalized damping term coupling the ith and kth modes
22
If desired for computational purposes an optional screening may be performed
to identify modes with potentially significant coupl-ing for inclusion in the
subsequent calculation The screening process is based upon the presumption
that potential coupling exists if the magnitude of an off-diagonal term in
the coupled damping matrix is sufficiently large in comparison with the
diagonal term and if the frequency of the mode associated with that off-diagshy
onal damping term is sufficiently close to the excitation frequency Potential
coupling exists if Dij (28)I
gt-rlDii
and if 1 Y C lt lt 1 + Y C (29)
where Yl and -2 are constants used to specify the degree of coupling for the
screening process and 0 DCshy
2wj M
is an equivalent modal viscous damping coefficient
Reference 7 presents a similar modal coupling assessment criterionfor lightly
damped modes Coupling can be ignored if
2Cj[ 2 11 12 ltlt 1 (30)
for pwj gt 1 and provided that DtDt 1 or smaller
Inverting Equation (27) by partitions results in the following expression for
the modal displacement admittance matrix
A(M) )] [CD(M)] jDD(M)31)
where [DD(M)] = [[BD] + [AD]BD -] [AD] = [ 2 2)M
[CD(M)] - [DD(M)][AD][B 0 -1 [BD] = a[D]
23
Transforming back to physical coordinates using Equation (26) results in a
computational expression for the displacement admittance matrix in physical
coordinates
[AD(P) (j)] = [ RJECD(M)][J]T + j[tR[DJ()][ I]T
= [Co(P)] + J[DD(P) (32)
The derivation for the velocity admittances is of course directly analogous
The modal velocity admittance matrix is
[AV(M) (j)] = [Cv(M)] + J[Dv(M)] (33)
where - 1
[cv(m [[BVJ + [AVJ[BV] 1[AV] [BV] = [D]
[Dv(M)]-= [Bv-Il[Av][Cv(M)] [AV] = - ( 2 2)M- ]
and the velocity admittance matrix in physical coordinates is
[Av(P) 00s)] = [R]CV(M)][I]T + j[OR][Dv(M)][ I]T
= [Cv(P) ] + J[Dv(P) ] (34)
For both displacement and velocity admittances the desired amplitudes and lead
phase angles are determined from either Equation (32) or Equation (34) as follows
IAijs(P)(0 = [Cij(P) ()2 + D ij(P)(5)2]
eij(0) = tan-liDi(P)( )ICij(P)()1
where i and j are indices referring to selectedresponse and input freedoms
For each pair of response and input freedoms the admittance amplitudes and lead
phase angles (defined from 00 to +1800) are tabulated versus increasing frequency
() as the primary output of the postprocessor The rank corresponding to each
admittance amplitude is also included in this data tabulation
24
Acceleration admittances are calculated from the corresponding displacement
admittances The displacement amplitudes are multiplied by a2 and the disshy
placement phase angles are shifted +1800 for the acceleration admittances
For each pair of response and input freedoms the admittance amplitudes and
lead phase angles (defined from 00 to +1800) are tabulated versus increasing
frequency (C)as the primary output of the postprocessor The rank correspondshy
ing to each admittance amplitude is also included in this data tabulation
25
30 REALISTIC STRUCTURAL MODEL
A realistic NASTRAN structural model of the Space Shuttle was developed using
the preprocessor to incorporate structural joint stiffness and damping charshy
acteristics The objective of the modeling task was to develop a sufficiently
detailed structural model to accurately represent the dynamics of the structure
below approximately 25 Hz while keeping the mass degrees-of-freedom to a
reasonable number for computational efficiency The number of mass degrees-ofshy
freedom established as a goal for each of the three Space Shuttle half-model
components were External Tank (ET) 100 Solid Rocket Motor (SRM) 50 and
Orbiter 150
Detailed descriptions of each of the Space Shuttle component models including
structural joints are presented in the following sections along with a descripshy
tion of the model developed to represent SRM propellant dynamics
31 SPACE SHUTTLE STRUCTURAL MODELS
External Tank and Solid Rocket Motor models were developed using structural
drawings supplied by MSFC and the NASTRAN model of the Orbiter was obtained
from JSCSMD Reference 5 and modified for use in this study Solid Rocket
Motor propellant data and Space Shuttle mass data were supplied by MSFC
Each of the three vehicles inthe Space Shuttle half-model has its own coordshy
inate system The relation of each coordinate system to the overall coordinate
system is shown in Figure 3-1 and Table 3-1
311 External Tank
The External Tank (ET) half-model consists of 86 gridpoints 484 stiffness
degrees-of-freedom and 96 retained freedoms The tank shell and intertank
structure were modeled using QUADI QUAD2 TRIAl and TRIA2 NASTRAN plate
elements Ring stiffeners were modeled using BAR elements BAR and ROD
elements were used to represent the Orbiter support structure The gridpoint
BAR and ROD and plate identification numberings are shown in Figures 3-2
through 3-4 respectively
The forward and aft elliptical LH2 tank domes are modeled using constant
thickness plate elements (QUAD2 and TRIA2) Nonhomogeneous plate elements
(QUAD1 and TRIAl) are used to model the cylindrical LH2 tank skin to account
26
zT y
YT
SM
y OI~
ORBITER
xo
x
FIGURE 3-1 SPACE SHUTTLE COORDINATE SYSTEMS
27
TABLE 3-1 SPACE SHUTTLE COORDINATE SYSTEMS
VEHICLE
EXTERNAL TANK
SOLID ROCKET MOTOR
ORBITER
X n(in)
0(0)
1389 (547)
1908 (751)
COORDINATE ORIGIN
Y -In(in) Zm (in)
0(0) 1016 (400)
636 (2505) 1016 (400)
0(0) 851 (335)
The range of gridpoint numbers for each vehicle is as follows
External Tank (ET)
Solid Rocket Motor (SRM)
Orbiter
forward fuselage
fuselage payload section
wing
thrust structure
vertical tail
payload
0 - 499
500 - 999
11000 - 11999
12000 - 12999
13000 - 13999
1400d - 14999
5000 - 5999
6000 - 6999
NOTE The preprocessor inserts gridpoints with numbers in the range 7000 shy
9000 for the structural joints
28
11
N Is en
2123 12 _ - _ut
1113 103t_ q3 741 LO 17- - 1A It~
-S
15~410
10s 450b SI3
tj j A
V~
53
o
2 83
A1Z
_W
62-2
7
i
7
78 11 3
171
460
8-B
63 jamp90qo
(S
131
3 8
13 6J 25
-)
133
13
14C
173
124
A N
tr LH n ~
7 ZS _ N_It ~u t 5 A t T
_ __ __ __ _ __ _ ~IA Aq 49I -
A-A c 7046
8-B --
FIUR 3- ETRA AKBA N O UBRN
(4
-
35s
6f
5
v7
O-z
57
46
-
47
- 4
41
T-
JL
isshy - 9
A
A-A
a
IVY
U
B-
41r
-Nlo
41
-got34 34-c
9
D-4
- o6
71
FICURE 3-4 EXTERNAL TARR PIATF W]IIHRPRHr
for the longitudinal stiffeners machined into the skin panels The ring
stiffeners at stations xT = 11299 13776 16243 18710 and 20580 and the longeron at the aft Orbiter attachment fitting are represented by BAR elements
The LO2 tank skin is modeled using homogeneous plate elements (QUAD2 and TRIA2) Ring stiffeners at stations xT = 74485 and 8510 are modeled using
BAR elements and include the effect of the slosh baffles attached to them
The ET intertank structure consists of skin panels stiffened longitudinally
by external hat section stiffeners and in the area of the SRM attachment
beam by stiffeners machined into the panels The effect of 4 of the 5
internal ring stiffeners are included in the properties of the QUAD and
TRIAl elements used to represent the stiffened intertank skin panels The
ring stiffener at station xT = 9857 and the SRM attachment beam running
through the intertank are modeled with BAR elements
ROD elements are used to represent the Orbiter forward attachment struts at
station xT = 11299
Details of the aft Orbiter attachment fittings are shown in Figure 3-5 Truss members are modeled using BAR and ROD elements Ball joint and pin joint
characteristics in the Orbiter attachment truss are modeled by appropriate
joint and member parameters
External Tank and liquid propellant weights are lumped at 37 gridpoints
Lumped masses for liftoff max q and SRB cut-off conditions are shown in
Table 3-2 The propellant is assumed to be frozen to the ET structure
312 Solid Rocket Motor
Each Solid Rocket Motor (SRM) consists of 9 cylindrical propellant case segshyments with a nose cone and forward compartment attached at the forward end and a tail cone and rocket nozzle attached at the aft end The steel SRM case
is represented by a single beam along its centerline using BAR elements as
shown in Figure 3-6 The SRM attachment points are constrained to the centershy
line model using multipoint constraint (MPC) equations
32
AT
CROSS BEAM
DIAGONAL14046
121 (220) VERTICAL
(219) STRUT
+ YT
VIEW LOOKING FORWARD
AFT 140461 ORBITER
(215) --J A T T A C H
VERTICAL (217) TH STRUT q- 2----(-16 ) STRUT
LH2 TANK LONGERON
SIDE VIEW
FIGURE 3-5 AFT ORBITER ATTACHMENT FITTING
33
Table 3-2 External Tank Mass Data
Half-Vehicle Mass kg (lb-sec2in)
GRID NUMBER LIFTOFF MAX Q
10 152 16 10200 17 20400 18 20400 19 20400 20 10200 31 20766 32 41531 33 41531 34 41531 35 20766 46 7370 47 14740 48 14740 49 14740 50 7370 82 2255 83 4511 84 4511 85 4511 86 2255
101 3490 102 6979 103 6979 104 6979 105 3490 121 1645 122 3289 123 3289 124 3289 125 3289 126 1645 131 301 132 603 133 603 134 603 135 301
thesame as liftoff
(09) (582) (1164) (1164) (1164) (582)
(1185) (2370) (2370) (2370) (1185) (421) (841) (841) (841) (421) (129)(257) (257) (257) (129) (199) (398) (398) (398) (199) (94) (188) (188) (188) (188) (94) (17) (34) (34) (34) (17)
145 5981 11963 11963 11963 5981
all
946 1892 1892 1892 946
( 08) (341) (683) (683) (683) (341)
other masses are
(86)(173) (173) (173) (86)
SRB CUT-OFF
145 (08) 1111 (63) 2221 (127) 2221 (127) 2221 (127) 1111 (63)
660 (38)1319 (75) 1319 (75) 1319 (75) 660 (38)
34
SI I iI I xB 200 395 5315 6915 8515 10115 11715 13315 14915 15775 16975 182385 198955
4427 15110 FWD ATTACH AFT ATTACH
=xT = 9857 xT 2058
MASS POINT p ROD ELEMENT
0 r--- PROPELLANT MASS VISC ELEMENT
a 5_3 553
~fot) ~o6) c07) Io S)1e rj
701 702 7o3
FIGURE 3-6 SOLID ROCKET MOTOR MATH MODEL
_______
(1661 63 16 r66___60
FORWARD ATTACHMENT FITTING
23 7Zol
702 SRM
AFT ATTACHMENT FITTING
SOLID ROCKET MOTOR MATH MODEL ( CONTINUEDFIGURE 3-6
-36
Also shown in Figure 3-6 are the Maxwell-type viscoelastic models used to
represent the complex modulus of the solid rocket propellant in the axial and torshy
sional directions Propellant masses and sprinq constants are derived in Section
333
The SRM model consists of 24 gridpoints 86 stiffness degrees-of-freedom and
60 retained freedoms SRM case and propellant weights lumped at 10 gridpoints
along the centerline are shown in Tables 3-3 through 3-5 for liftoff max q
and SRB cut-off respectively SRM nozzle weight is not included in the
model
313 Orbiter
A NASTRAN finite element model of an early version of the Space Shuttle Orbiter was obtained from NASAJSC (Reference 8) and was modified for this
study The model consists primarily of shear plates (SHEAR) and membrane
elements (TRMEM and QDMEM) with BAR elements along their edges Gridpoint
and element numbers for the Orbiter model are shown in Figures 3-7 through
3-12 The vertical tail and wing are attached to the fuselage with BAR
elements
The Orbiter model consists of 462 gridpoints 2460 stiffness degrees-ofshy
freedom and 136 retained freedoms Orbiter weights are lumped at 48 gridshy
points as shown in Table 3-6 Space Shuttle Main Engine (SSME) weights are
not included in the model
37
Table 3-3 SRM Mass Properties (Liftoff)
GRID MASS 2 I2 xx 2 I= 2yy=zz
NUMBER kg(lb-sec in) kg-m (in-lb-sec kg-m in-lb-sec
501 503
5982 56249
(341) (3004)
250E3 166E5
(221E4) (147E6)
117E4 514E5
(104E5) (454E6)
504(L) 610(A) 611(A) 505
46833 46833
468 91562
(2672) (2672)
(27) (5225)
0 404
40 296E5
(3571) (36) (262E6)
0 0 0 916E5 (810E6)
506(L) 620 (A)
46833 46833
(2672) (2672)
0 404 (3571)
0 0
621(A) 507
468 91332
(27) (5212)
40 301E5
(36) (266E6)
0 909E5 (804E6)
508(L)630(A)
46833 46833
(2672)(2672)
0 404 (3571)
0 0
631(A) 468 (27) 40 (36) 0
509 512( L )
93117 46833
(5314) (2672)
310E5 0
(274E6) 920E5 0
(813E6)
640(A) 46833 (2672) 404 (3571) 0 641(A) 513
468 53002
(27) (3025)
40 182E5
(36) (161E6)
0 501ES (443E6)
(L) = lateral mass (A) = axial mass
38
2
Table 3-4
GRID MASS 2 NUMBER kg(1b-sec in)
501 5982 (341) 503 36422 (2079) 504(L) 6100 (348) 610(A) 6100 (348) 611(A) 59 (03) 505 63174 (3605) 506(L) 6100 (348) 620(A) 6100 (348) 621(A) 59 (03) 507 64478 (3680) 508(L) 6100 (348) 630(A) 6100 (348) 631(A) 59 (03) 509 67038 (3825) 512(L) 6100 (348) 640(A) 6100 (348) 641(A) 59 (03) 513 41609 (2374)
(L) = lateral mass (A)= axial mass
SRM Mass Properties (Max Q)
g IIx yy=Iz
kg-m)n-lb-sec kg-m (in-lb-sec
250E3 (221E4) 177E4 (104E5) 117E5 (103E6) 276E5 (244E6) 0 0 0 0 0 0
201E5 (178E6) 482E5 (426E6) 0 0 0 0 0 0
205E5 (181E6) 491E5 (434E6) 0 0 0 0 0 0
214E5 (189E6) 510E5 (451E6) 0 0 0 0 0 0
134E5 (119E6) 314E5 (277E6)
39
Table 3-5 SRM Mass Properties (SRB Cut-Off)
Iyy=1zzGRID MASS Ixx
NUMBER kg(lb-sec 2in) kg-m2(in-lb-sec2 kg-m2 (in-lb-sec )
501 5982 (341) 250E3 (221E4) 117E4 (104E5) 503 10258 (585) 352E4 (312E5) 741E4 (656E5)504 (L) 0 0 0 610 (A) 0 0 0 611 (A) 0 0 0 505 10836 (618) 373E4 (330E5) 783E4 (6092E5) 506 (L) 0 0 0 620 (A) 0 0 0 621 (A) 0 0 0 507 12140 (693) 418E4 (369E5) 877E4 (776E5) 508 (L) 0 0 0 630 (A) 0 0 0 631 (A) 0 0 0 509 14700 (839) 505E4 (447E5) 106E5 (939E5) 512 (L) 0 0 0 640 (A) 0 0 0shy641 (A) 0- 0 0 513 - 15436 (881) 531E4 (469E5) 112E5 (986E5)
(L)= lateral mass (A) = axial mass
40
FIGURE 3-7 ORBITER MATH MODEL
41
ORITER - FORWARD FUSELAGE ftGURE 3-81
42
O 10 shy
ict rzo91 en llO ot) ift7 1(013 1VIOL11oZ4
STA Zt Z82Ji
--- Rot l4o
fiet (1103) 0 iozz
10I O~11024t
SMA X= 3844
FIGURE 3-8 ORBITER - FORWARD FUSELAGE (Continued)
43
1 11033 1I10 1(34
7 1104Ce c
104 i
ST7A X -416 4
FIGURE 3-8 ORBITER - FORWARD FUSELAGE (Continued)
44
tti 1142
(a11(03I8 I 03Z
ll~f I10LZ 0
1196
73(io amp gt 1bS1o 1 osO (IO Rq
11057o1o05 f05
STA X 5595
FIGURE 3-8 ORBITER - FORWARD FUSELAGE (Continued)
45
55es 8 5]q 4 22448V ___ I tXe
-~--- nof116) -11033 U(lOQ) flooriot
___Nt4I1 tIO07t
Ciaa) 2t~
1162Z r~l 3 mz floo3ucoCtg foo6
j 4r -2
IfIlo 10
not-
(1637
N2~i rto
I0 5tt22
(1429
enms)
9
o8
4
If0
FIGURE 3-8 ORBITER - FORWARD FUSELAGE (Continued)
46
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ II _ _ _ _ _ _ _ i__ _ _ _ _ _ _
Xc -4I--- IaSS ff0r4A Cuiz) (626 (123)
110
FoXARD FUSampIAC-AS 8OrMM PANECLS
FIGURE 3-8 ORBITER - FORWARD FUSELAGE (Continued)
47
~826 So
WINFO TAC3TLI I
PAYLOAD SECTION ORBITER -FUSELAGEFIGURE 3-9
Ce J2003
tz~o4
~~zoo
1
2 It Cr2ampZ
12NO Ztcl tzaos Z6o7 q
FIGURE 3-9 ORBITER - FUSELAGE PAYLOAD SECTION (Conttnuedl
49
IgoZ IZD 74 XgDZ73
FIGURE 3-9 ORBITER FUSELAGE PAYLOAD SECTION (Continued)
50
)203 ) 14(Z07 207
t 0 Zo3 ZO3
524 Xo 82amp
FIGURE 3-9 ORBITER - FUSELAGE PAYLOAD SECTION (Continued)
51
12o4(O f~zo~1)flog
-(J20f7 (12056
1201
oss4l I za5 Zo
2
1)205S
12ooSshy
(Zo78)
=57-A e6 373
FMULRE 3-9 ORBITER - FUSELAGE PAYLOAD SECTION (Continued)
53
2-t0 lo
IZ417 4l
2075 13gt7Y IZo73 1e
i z~~e a
57A = o47
FIGURE 3-9 ORBITER - FUSELAGE PAYLOAD SECTION (Continued)
54
Z
7-9 1z9 2os7eo
zoss124)5 128l) 208 20IO5
LIZo11
5TA X = 1133
FIGURE 3-9 ORBITER - FUSELAGE PAYLOAD SECTION (Continued)
55
12099
20ol z12097
12Ii 12o 9 12
_STA Xo=1191
FIGURE 3-9 ORBITER FUSELAGE PAYLOAD SECTION (Continued)
56
-ii
~7~
C
so
m
t0
0 -~
-
w
N
-N
H
--~
m
1213
B)
czi~
sshy
______________________
-
N
0
1
~
-~
(nsq
) ni
t1
~
A
fr~
C
E
n (3
1
-1
Cshy o
N
N
m
C-
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z C
-)0
K
rt
C
CD
0~
N
Ii
IT I I I I I I If I I I t-t----- 15ot I zza) Q 1LampO9 0 Z053 lZo Zool 71zo9Q 2ott(I229 (12 0 C zl WI0 72) C2Z0) CIZ73) ((247) l26a) 6ZSz) (156
1211 t2lm - 00 2447 1205 104 kZOz8I20 1201o5 IWOE
I nI24 247 273 1246 z4t6 i2455 447 2413 L4 (242 I
(iI
IZowI 1s-2l03 (~~l 266 zo~fz IVo ZOI( QVo3 1OS
4Dzz) Z22o53) 021110 (1210i) (izJrZ) ( 11 S) az6o) e121461) (249) 1zis-r-l
cn I
-tq Vzlo7- avsj) te -FIT76-7-- J(2-747-
l 1247q 12473 (24 1z41 126fY 1 4 -6zL 17V__7 1243
ZO0 ZZlZ) 1225 CjZf) Il I 1(277)- 6A70) (cent 03028J) Z-
12101q ZO6 t03 17070 12057 IZo44 JZaS Itoa iZoo5
FU 3-9o4R 3AGE P
FIGURE 3-9 ORBITER - FUSELAGE PAYLOAD SECTION (Cont~inued)
t 1 V7 601 75)367 1219 1133 e373 826 653- S5
12109_ _ _ I I I I I I 14oLMI9 17057 4 IZO31 Ig203 11053170 42 oj
I (t12gt)3 (126) Zg) 771) (1218S) (12177) (12170 ) (257 I___ (Z75o)
2484 IZ112490 12271247 Z4s48z - Zqg~ 124412o 4 ~tB 4314009 ZL 40124319 I45-6 1= t~~~ll12 Z Z~ 120 0 1054Ijbq g7 203 19 fInj
14ooa9 (IZ1 (2206) (Iz99) (zig2f (1 ) (IOI) (IZ5 (1z7) I(Z28 (121-5
20o7) 1(IZ2o (12)e-5) )Iq- 021 (jZlq33 CIVl4 1 (12174) 1 (1777 (zl C 51) 12111 IZof3 05 IZO72 9059 1264 )i 3 IZO20 2O07 f1sS
FIURO E USDE (PAACLE i
FIGURE 3-9 ORBITER - FUSELAGE PAYLOAD SECTION (Continued)
0 -
-77 4e 1)9
I I I 106 (me2w ) 1r114
1 (1214z) (12239)WZW)
1251-6 J25IIo 1207
33 10417 573 941 22A
I 1 I I I 120AI261 120 I06Z 1203amp Zo23
(IZ23) eiz) (Z227) (12221) CIZZfl)
2555 12o 15o6 124a
751
I (W2218)
lz2
655 6595
I 1 100 Ilofa
(IZ5) I
IZ9
(24 12113 160 12102 20Z61 1QM) 2031 Zozz o 15
1____
) FIzGURE (23-7)
12511
ORBTER -U
12556 jQz5o
L (AYLO$)
zo
CIs
12418
(12- -T
1249f
dzjq)
12491 1 119
1404 2z(x zz41) (2230)
121 29 2755)~
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(12221)
20e40
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IloO7 CIZZZS3)
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121 121 120ff
wzl(21)2207)
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12098 lzaOSS g207Z 12050
FUSCL416E BorroM
io6
PlANELS
gampL 625)
23 ZO2o 15)
M00o7
FIGURE 3-5 ORBITER - FUSELAGE PAYLOAD SECTION (Continued)
FIGURE 3-10 ORBITER - THRUST STRUCTURE
61
141 I tq~bj Ioo
go 14005
4117) 04116)
-141) (140
-I
1411419Z10 014W24 (14123) 4122101
Er ArTAcit
BULkHEAD VA X0 = 130
FIGURE 3-10 ORBITER - THRUST STRUCTURE (Continued)
62
1402 ( 1 4 2
No )oo 2
14003oCO
1t 4
1403 (1412 11t4 4 o43 P o E
N 4 14o0
La(1 -4 17
144 o3 I
4 (26
403 1 401 4 0
14iozl
(1o133 il4i4
A4( ( 31) 1N~ o 4419
51AE WAqLL
1414- 3 (14132)
FIGURE 3-10 ORBITER -THRUST STRUCTURE (Cont~nued)
63shy
1403zA4038
1039
4oss -
4o34zo
UPP=k TWC U-7
Q doo3
-W4A
FIGURE 3-10 ORBITER -THRUST STRUCTURE (Continued)
64
A
S
143 S
433 Ioz
B 403
Z1o3 A
403Z L110351
r4 N I4oos 4037
4192i~o4ol
4IS- I4~
1407
N
SECT 5-
___________________
A
14 30)
400f
-
FIGURE 3-10
SECr A -A
LoWiR rgYvSrsrz
ORBITER - THRUST STRUCTURE Ceontinued)
65
141amp9)
T49lSTPOIT5 0
4036
Iz4OO3S
1iov J4o itVz401Z -t
nRVST PLANIE
- THRUST STRUCTURE (Continued)-fIGURE 3-10 ORBITER
66
FIGUJE 3-11 ORBITER - WING
67
200
5 qfi f- a
11go
__
fof
11119
ISO1
Z38o __ 111
yxI 3
12m
_
1
A14 IP974 ____ it1 1
twK7 975
1lshy
amp 11 Ac
o
di35__ zrhoboR
9
iz
38
3
F7IGUREZ91
3111
OOF
41 4s
-RIE- WIN
9
UPPERWING URFAC
120 i I __f I___ ____ I
St 159
WlIt6 IVi
Le 0710
120
06
h5
0
12 16
03
7
) 457-
J5-
40 13b-2
~o77 - i
437 0
7PYo6 Z
--
Za
t goy P9
LOWER WING SURFACE
472o 2 1127 V6
FIGURE 3-11 ORBITER - WING (Continued)
- 3
9039iI f 923
Sba
S02 IAla
S5-0z
FIUR 3-2CoITR-VRTCLTI
5o1~ V 70
Orbiter Mass Data
GRID NUMBER
13037 13064 13066 13096 13098 13100 13134 13156 14001 14005 14013 14016 14029 14032 14034 14039 14042 14045 5001 5005 5007 5011 5015 5019 5021
MASS 2 kg(lb-sec in)
6884 (393) 5590 (319) 6051 (346) 5001 (285) 6188 (353) 8993 (513) 3570 (204) 3550 (204) 2873 (164) 22084 (1261) 7482 (427) 14200 (811)
941 (054) 3991 (228) 27596 (1576) 7198 (411) 4462 (255) 5462 (312) 5531 (316) 1059 (061) 1000 (057) 4246 (242) 882 (050)
1961 (112) 1402 (080)
Table 3-6
GRID MASS 2 NUMBER kg(lb-sec in)
11017 12905 11021 - 3903 11023 12121 11026 6423 11049 2275 11053 17917 11055 8375 11058 6708 12018 26958 12020 6619 12023 3844 12044 26517 12046 5649 12049 2314 12070 22898 12072 6639 12075 2040 12096 17201 12098 6678 12101 1824 13001 1118 13016 4246 13035 2334
(737) (223) (692) (367) (130)
(1023) (478) (383)
(1540) (378) (220) (1514) (323) (132)
(1308) (379) (116) (982) (381) (104) (064) (243) (133)
Includes OMS Kit Mass
71
314 Payload
The payload is modeled as a rigid body as shown in Figure 3-13 Its mass
properties represent the Large Space Telescope (LST) The attachment structure
is modeled using BAR elements with pin flags to represent the statically detershy
minant payload supports The weight of the Orbital Maneuvering Subsystem (OMS)
kit in the aft portion of the payload bay is included in the weights on the aft
bulkhead (forward bulkhead of the thrust structure) Payload and OMS kit mass
properties are shown in Table 3-7
32 STRUCTURAL JOINTS AND DAMPING
Structural joints were included in each of the three half-model vehicles The
joints were inserted in the structure by the preprocessor computer program
Free-free mode shapes of each vehicle were obtained with arbitrary damping in-the
joints to provide a starting point for the determination of proper joint damping
coefficients ET and SRM damping constants were calculated by hand while the
damping coefficients for the orbiter were calculated using the joint damping
predictor computer program All damping parameters were calculated at liftoff
A study was performed to determine the extent of Coulomb type damping in the
SRMET forward attachment ball joint and the orbiterET aft attachment ball joint
An equivalent viscous damping coefficient (Reference 9) was calculated for the
SRMET forward attachment as follows
C - 4F (35)7rAm
where
F = VFn = friction force
A = amplitude of motion
= frequency of vibration
= friction coefficient
Fn = normal force
For rotational motion the friction force in Equation C35 is replaced by the
friction moment and the amplitude of motion is in radians Using the moment due
72
152 120 7 O- -(6000) Fz F
6000 5001
(6003) (6004)
0deg F (6002)
Fz FyYoY
0XxoV 12076
FIGURE 3-13 PAYLOAD MATH MODEL
73
Table 3-7 Payload and OMS Mass Data
PAYLOAD (half-model)
W - 3715 kg (212 lb-sec2in)
2657 kg-m 2 (50040 lb-in-sec )Ix shy
y 28850 kg-m 2 (2552x]05 lb-in-sec )
28850 kg-m 2 (2552xlO5 lb-in-sec2)Iz -
OMS KIT (half-model)
W - 2723 kg (1554 lb-sec2in)shy
74
to the preload in the ball joint bolt (89 x 106 N x 178 m) a friction coshy-efficient of 046 an estimated amplitude of rotation of 243 x 10 radians
and a frequency of 188 radsec the equivalent viscous damping coefficient is 20 x 107 N-mradsec Applying this damping to the Space Shuttle modes given
in Reference 10 results in unrealistically high modal damping for some of the modes It is concluded that the high preloads in the ball joints preclude joint motion and therefore no coulomb damping is generated Further it is assumed that the spherical bearings designed into the SRMET aft attachment struts the OrbiterET forward struts and the OrbiterET aft support truss contribute
negligible damping to structural deformations Therefore all structural damping is assumed to be generated by internal structural deformations of the joints in
the Shuttle components and by material damping
Desired modal damping values were obtained from the empirical damping study
performed for the Space Shuttle in Reference 4 In that study expressions were derived which relate energy dissipation per cycle (D)to the kinetic energy (T) of the vehicle based on data obtained from existing space vehicles Two expresshy
sions were derived for bending One which includes Saturn I data and one which does not
For bending (without Saturn I data)
D = 153 T893 (36)
For bending (with Saturn I data included)
D = 286 T 746 (37)
For longitudinal modes
(38)D= 057 T11 04
For torsion modes
D = 101 T1 279 (39)
where D and T are in SI units
75
Equivalent viscous damping is related to energy dissipation per cycle and
kinetic energy
D- (40) 41rT
Therefore an expression for equivalent viscous damping can be obtained for
bending longitudinal motion and torsion from Equations (36) - (39)
For bending (with Saturn I data)
286 -254 (41)
For bending (without Saturn I data)
B2 - 153 T-1 10 (42)4 -f
For longitudinal motion 1 04 057 T (43)
For torsional motion
101 T 279 (44)T - T
Kinetic energy written in terms of modal parameters is
T = 1 M 2X2 (45)
where M is the generalized mass in kilogram w is the modal frequency in radians
per second and X is the modal displacement in meters
A similar study was performed for a Boeing 747 airplane and the results are
documented in Reference 5 Energy dissipation versus kinetic energy are shown in Figure 3-14 The best straight line fit through these data points was found
using linear least-squares regression and is shown in Figure 3-14 The equation
of this line is
D = 2196(T) 911 (46)
Also shown in the figure is the line derived by Chang (Referencell) whose equation
is
76
I
LJ
w
50shy
gtX
F YT
T bulli
+ IdIIl
- CHANG
U
S EQUATIONI
T1 -uKVEri I- I
O-ASYMMETRIC MODES-SYMMETRIC MODES
BEST FIT
D =2196 (T) 9 1 1 Ill
o
Iji
-4
-2 11 1 1 114
I
LL
0 i ll cw - _
1i0H50 ~ I50I I PEAK KINETIC ENERGY CTo) v
000k__
NEWTON-METERS
5000 10000
FIGURE 3-lh BOEING 747 STRUCTURAL DAMPING DATA
I
D = 313(T) 8 0 (471
Equation (46) was used to determine the equivalent modal damping for the Orbiter
2196 089
The calculation of realistic modal damping from these equations is therefore
dependent upon the determination of the kinetic energy T for that mode This
is according to Equation (45) equivalent to determining the maximum modal
deflection which can only be determined from the dynamic analysis for which the
model is being constructed Therefore a rational method must be used to detershy
mine the kinetic energy to be used in the damping equations
One method which could be used is based upon the determination of the modal
deflection which results in the maximum allowable strain in a critical element
For tension and compression of aluminum or steel structures the ultimate
allowable strain (Reference 12) is
Sa = 002
For torsion of a thin-walled circular tube the material is in a state of pure
shear where the stresses and strains are
y = re
Ss = Gy (49)
Here e is the angle of twist per unit length of the shaft and r is the radius
to the outer fiber From a uniaxial tensile test the yield stress is
ay = Esy (50)
According to the Mises yield condition the allowable shear stress (Ty) and the
allowable normal stress (ay) are related by
Ty = y 7 (51)
or
SS = Es V Gre (52)
78
Therefore since G = E2(lI+) the allowable angle of twist per unit length is
= (1I)(53)
For y =002 and p 3
(54)118r (radm)ea
Limit allowable strain and angle of twist can be obtained by dividing by the
ultimate factor of safety (FS) I -
EYFoS-y
(55)a eaF0S
Subtracting the strains caused by static forces gives the limit allowable strain
for dynamic loading The maximum allowable deflection of the predominant mode
can then be found by calculating the ratio of allowable dynamic strain to the
strain in the critical element due to a unit modal deflection Then the kinetic
energy of that mode can be calculated from Equation (45)
Structural joints and damping values for each vehicle are discussed in the
following sections
79
321 External Tank
The only mechanical joints on the ET are at each end of the intertank shell
where it is attached to the LH2 and LO2 tanks These joints consist of two
flanges bolted together as shown in Figure 3-15 Plate joints were inserted
at both interfaces using the preprocessor computer program Free-free mode
shapes and modal damping matrix were obtained using arbitrary damping values in
the structural joints Final damping parameters were calculated by ratioing
these arbitrary values based on estimated kinetic energy in appropriate modes
Damping parameters for the axial joint members were derived from the first
free-free ET bending mode (f = 37 Hz) and Equation (41)
The maximum strain for this mode occurs in the interstage forward of the ET
SRB attachment beam The limit allowable strain is
002 002 00133 (56)
The static strain in the forward interstage due to 17 g longitudinal accelerashy
tion at liftoff is
st 00115 (s7
Therefore the limit allowable strain for dynamic events is
= 00018 (58)
Assuming that the dynamic strain due to bending and axial motion are the same
we have
EC 90x10-5 (59)
b ax
The strain in the interstage due to a unit (l0 m) deflection of the first ET
bending mode is 00445 Therefore the modal deflection (q)which results in the
limit allowable bending strain is
59Oxlo =202xlO -3 m (60) q - 0445
The kinetic energy of this mode is then
80
x T 851O
1655 R IO2TN
1650 R
x= 11299
NERTANK
17TERTANK
LH 2 T N
165R
1650 R
FIGURE 3-15 EXTERNAL TANK INTERTANK JOINTS
81
bq2bb 2 1f Kq 2T = I M wq =
= 1 (315x197)(202x 10-3)2 = 643 N-m (61)
Then using Equation (41) the desired damping ratio for the first ET bending
mode is
0228 T - 0079 (62)
The damping parameter for the axial joint members in the ET intertank joints
is then calculated by multiplying the damping parameter used in the unit
damping case by the ratio of the desired damping ratio shown above to the
damping ratio obtained in the arbitrary damping case This calculation gives
CA = 4-68xi0 6 Nmsec
Using this damping value the modal viscous damping ratio for the first ET
free-free longitudinal mode C000 HzI is C=013
Calculations of the damping parameters for the diagonal joint members based on
allowable torsional motion of the ET resulted in unreasonably high modal damping
values Therefore a representative value of torsional kinetic energy was
selected from the test data used in Reference 4 to develop the torsional damping
equation Equation (39) The range of kinetic energy used in Reference 4
results in ET torsional mode damping from =008 to =024- For conservatism
the low value of kinetic energy was used as a representative value for the
external tank resulting in modal damping of
C=008 (63)
Based on the arbitrary damping case the damping constant for the diagonal-plate
joint members which would give this value of modal damping is
C 2084 x 105 Nmsec (64)
Joint damping parameters are summarized in Table 3-8 All damping parameters
are assumed to remain constant for all flight conditions
82
TABLE 3-8 STRUCTURAL JOINT DAMPING PARAMETERS
BAR JOINTS
ELEMENT JOINT LOCATION ID Clm Cln Clp C2m C2n C2p
0 134 x 10I0 134 x 10o SRM CASE JOINTS 502 - 508 amp 299 x 109 0 Q
510 - 512 (171 x 107) (119 x 1011) (119 x 1011)
0 0 0 3428 x 106 3428 x 106 3428 x 106 ORBITER WING ROOT 3108 3109
3111 3112 (3034 x 107) (3034 x 107) (3034 x 107) 3113 3115 3116 3118 3119 3120 3121
0 0 0 2302 x 105 2302 x 105 2302 x 105 VERTICAL TAIL ROOT 15024 shy
15027 (2037 x 106) (2037 x 10 ) (2037 x 106
15030 shy15037
UNITS Cl = Nmsec (Ibinsec) C2 = N-m-sec (Ib-in-sec)
TABLE 3-8 STRUCTURAL JOINT DAMPING PARAMETERS (Continued)
PLATE JOINTS
JOINT LOCATION ELEMENT ID CA CD
ET INTERTANK JOINTS 26 through 33 468 x 106 Nmsec 208 x 105 Nmsec
(26700 Ibinsec) (1190 ibinsec)
ORBITER FUSELAGE JOINTS 12432 12433 1159 x 108 Nmsec12438 124395 7442 Nmsec 12444 12445 (425 Ibinsec) (662 x 105 ibinsec)
12450 12451 12456 12457 12462 12463 12468 12469 12474 12475 12480 12481 12486 -12515 12610 12612
ORBITER WING JOINTS 13019 - 13021 35860 Nmsec 35860 Nmsec 13036 - 13040 (2048 1binsec) (2048 Ibinsec) 13065 - 13067 13082 - 13084
322 Solid Rocket Motor The nine cylindrical SRM case segments are connected together using pinclevis
joints as shown in Figure 3-16 Ten joints were inserted in the centerline
representation of the SRM using the preprocessor computer program Damping
constants were supplied to provide damping in the axial and the two beam bendshy
ing directions Free-free SRM modes and modal damping coefficients were calshycuaated using arbitrary damping in the structural joints to provide the basis
for kinetic energy and damping parameter calculations
Damping constants for bending were calculated using the first free-free bendshy
ing mode and Equation (41) The limit allowable strain is 002
- 0a 00133 (65)
The static strain in the SRM case is caused by thrust loads and internal presshy
sure loads
C1st = 00119 (66)
Then the limit allowable strain for axial and bending dynamics is
= 00014 (68
Assuming that the dynamic strain due to bending and axial motion are equal
C = 6 x = 00007 C69)
The maximum strain in the SRM case due to a unit CI0 m) deflection of the first
bending mode is 00187 Therefore the modal deflection q)which results in th
limit allowable bending strain is
70x105 = 374xi0-3 m P69 q 0187
Using Equation (45) to calculate the kinetic energy for this mode
1 2(70)7 2T = =z C738xlO)(374x10_3) 516 N-m
Then from Equation C41) the desired damping ratio for the first SRN bending
mode is
= 0228T-254 = 0047 710
85
I I I I II 5315 69i5 8515 10135 11715 13315 14915 15775 16975 82385 1xBi 200 395
151104427 AFT ATTACHFWD ATTACH JOINTS x= 2058XT = 9857
1460 DIA146O DIA -PIN
JOINT DETAIL
FIGURE 3-16 SRM CASE JOINT LOCATIONS
The modal damping produced by the arbitrary joint damping values is = 00287
Therefore the damping constant necessary to give the desired modal damping in
bending is
C2n = C2p = 0047 C 134xi0 10 N-mradsec (72)00287 arb
For axial motion the damping constants were calculated using the first longshy
itudinal SRM mode and Equation (43) The maximum strain in the SRM case due
to a unit (10 m) deflection of the longitudinal mode is 0106 Therefore
the modal deflecflection (q) which results in the limit allowable axial strain i
-4 7Oxi0-5 = 660x10 m (73) 106
From Equation (45) the kinetic energy for the longitudinal mode is
T = L (506xl0 9)C660xl0-4)2 = 1102 N-m (74)
Then the desired modal damping ratio for the first longitudinal mode from
Equation (43) is
= 00454 TI04 = 0094 (75)
The modal damping produced by the arbitrary joint damping values is 406x1O
Thereforethe damping constant necessary to give the desired modal damping is
CIm - 0094 C 299xlO 9Nmsec (76 4060x1 6 unitN
Joint damping parameters are summarized in Table 3-8 All joint damping
parameters are assumed to be constant for all flight conditions
87
323 Orbiter
Structural joints were inserted in the Orbiter structure at ten stations
along the fuselage at two spanwise stations in the wing and at the wing and
vertical tail roots The fuselage joints are located in the payload section
side panels and fuselage bottom panels at stations times0 = 5595 655 751
826 901 973 1047 1133 1191 and 1249 as shown in Figure 3-17
Wing panel joints are located in the upper and lower surface panels at stashy
tions y = 1950 and 2802 as shown in Figure 3-18 Wing and vertical
tail root joints were inserted in the BARS which attach the wing and vertical
tail to the fuselage as shownin Figure 3-19
Symmetric and antisymmetric orbiter modes were calculated with structural
joints included The damping elements in each joint were assigned to one of
five damping sets and arbitrary damping parameter values were used These data
were used by the joint damping predictor computer program to calculate proper
damping parameter values necessary to obtain proper modal damping in specified
modes Details of the methodology used in the joint damping predictor computer
program are found in Section 22
The number of modes for which-desired modal damping is specified must be equal
to or greater than the number of damping sets Therefore for this case
desired damping for at least fiye modes is required The five selected modes
the desired modal damping and the modal damping resulting from the damping
parameters calculated by the joint damping prediction computer program are
shown in Table 3-9 Damping parameter values calcul-ated for Orbiter joints
are shown in Table 3-8
324 Payload
Damping at the payload attachment fittings was not modeled because its resshy
onant frequency is higher than 50 Hz and would not contribute significantly
to the damping at frequencies corresponding to the first 50 Space Shuttle
modes
88
ca
i~oX
jot
9739 o
PANEL JOINTS
FIGURE 3-17 ORBITER FUSELAGE PANEL JOINT LOCATIONS
1528 tVeo 44g 38g
SI___
I~o
I t2amp
I V)76
I 1o07
I 973
I X M-11 1 (So0 3 lIZ I Io log
15t4o O~aLaa kkari 64 - -
4-- li 1- 4 UPPER WING SURFACE
3
35 3 PANEL JOINTS
FIGURE 3-18 ORBITER WING PANEL JOINT LOCATIONS
--
I5zj to I19 l3Be 1307 121 n1e 479Z6 1o41 93I I I I I I I I 6 34 1f- ho I19 I 17 64
6989 f07 105 00
I Q so
32 ot Z
301a 0(7 9 yeniota- - It 3______z
LOWER WING SURFACE
is- 117 0634 za 9
-PANEL JOINTS
32Uo 1sf(
4tT 03 27I 121
FIGURE 3-18- ORBITER WING PANEL JOINT LOCATIONS (continued)
t i I I SI I I I
JOINT
I
WING WING WING WING WING WING
FUS FUS FUS FUS FUS Pus
x = 973 1047 1191 1249 1307 1380
N VERTICAL TAIL
ORBITER THRUST STRUCTURE
I
FIGURE 3-19 ORBITER WING AND VERTICAL TAIL ROOT JOINT LOCATIONS
Table 3-9 Comparison of Desired and Actual Orbiter Modal Damping
Modal Damping ( ) Mode Description Desired Actual
4 Sym wing bending 0110 0110
5 first sym fuselage bending 0088 0088
34 vertical tail bending 0105 0105 36 first antisym fuselage bending 0101 0101
37 first fuselage torsion 0065 0065
93
33 SOLID ROCKET MOTOR PROPELLANT DYNAMICS
The dynamics of the solid rocket motor propellant could have a significant
effect on total vehicle dynamics The propellant is a viscoelastic material
whose properties are characterized by complex elastic moduli Finiteshy
element modelingof the solid propellant using a Maxwell-type viscoelastic
model is described in Section 333 Parametric values used in this Maxwell
model were determined from two studies Section 331 demonstrates that a
Maxwell-type viscoelastic model can accurately represent the observed
frequency-dependent stiffness characteristics of the solid propellant
Relationships between the Maxwell parameters and the propellant shear
modulus are presented Section 332 presents a modal analysis of a solid
propellant segment using solid finite elementsshy
331 MODELING OF COMPLEX MODULUS
The complex shear modulus of a viscoelastic material is wriLten
G = G + j G (77)
Test data for the TP-HI123 propellant used in the SRM were provided by
NASAMSFC and are shown in Figure 3-20 The fact that stiffness increases
as the frequency increases suggested the applicability of a Maxwell-type
structural model (Reference -)to represent these characteristics
(Figure 3-21)
For the Maxwell model the complex shear stiffness is
K(j$) = K + jKsII (78)
and is proportional to the complex shear modulus
K(j8) = A (79)
94
1600 TP-HI123 PROPELLANT
Tested at 70degF and Ambient Pressure G Mix 8350271
1400 _
G
EXTRAPOLATED VALUES G
120C
80C
60 G== +J Gi l
4o - -
200
0
FIGURE 3-20
10 20
FREQUENCY (Hz)
SRM PROPELLANT COMPLEX SHEAR MODULUS
40 60 80 100
PROPELLANT MASS
FIGURE 3-21 HAAXWELL MODEL FOR SRM PROPELLANT
96
The real and imaginary components of the Maxwell model stiffness are given
in Reference 13 as follows
K = K + K2n(1 + n2 (80)s220+f2) 1 (8
K = K2 2(0 + S2)(81) 2 2 (2-1
where n2 the loss factor is
2 p (82)
Substituting Equation (82) into Equations (80) and (81)
KK K fl (jL (83)K1 K
Sc [C2] (84)
As shown in Equation (79) for a block of propellant having unit area and
unit length the stiffness components given by Equations (83) and (84) are
numerically identical to the shear modulus components of Equation (33) Therefore Equations (83) and (84) with known data values of G and G
substituted for Ks and Ks may be used to find the Maxwell parameters
K1 K2 and C2 which closely match the complex shear modulus characteristics The Maxwell model accurately represents either the real or imaginary composhy
nent of the shear modulus as shown in Figure 3-22 The parameters of Case A
were chosen to be used for the SRM propellant because the imaginary component
matches the test data very closely and the real component is only 63 percent
below the test data at the frequency of the first longitudinal propellant
mode (116 Hz)
97
l
i
S i I I I1 i I Ii
4 1 m tt itl ii I i t i ll i
3 Ii L TEST DATA
MAXWELL MODEL K1 K2
2 CASE A -------- 500 1380 246 C +
CASE B 500 1380 4io0
l iiI) 0it+ 111
-shy
o ~ ~~~~ iET V 61 l- shy
i4
3
li ltIIt ii II
111 I 1 V HEgtI H J
IU 111 II iI I 11111 i 1 1 H L I I II I I I IIII 1 1 llI I II
1001 Il ) 1lT I I 1 -1TI I 1 111 1 1 1 I IM11111 1111i1i
T 3 4 5 67910 2 3 6
FREQUENCY Hz
FIGURE 3-22 COMPLEX SHEAR MODULUS MAXWELL MODEL
98
332 Propellant Modes
The dynamic characteristics of the solid propellant were determined from
a solid finite-element model of a propellant segment 4064 cm (160 in) in
length The propellant cantilevered from a rigid tank wall was modeled
using the NASTRAN WEDGE element as shown in Figure 3-23 The propellant 2density is 1772 gcm 3 (1657E-4 sec )b The shear modulus at zero
in42frequency 3447 Ncm (500 psi) was used for propellant mode calculations
The Youngs modulus of 10342 Ncm 2 (1500 psi) was used with a Poissons
ratio of 045
Symmetric and antisymmetric modes and frequencies were calculated and are
tabulated in Table 3-1Q The first longitudinal mode frequency is 116 Hz
and the first torsional mode frequency is 167 Hz
333 Propellant Structural Model
The SRM consists of four indiyidual propellant sections Three of these
segments are 8128 cm (320 inj long and the fourth is 3433 cm (332 in)
long The analysis of Section 331 shows that theMaxwell-type model
accurately represents the complex modulus of the yiscoelastic propellant
Therefore Maxwell structural models were used to model each of the four
propellant segments as shown in Figure 3-6 The propellant masses are conshy
nected to the centerline structural model using NASTRAN ROD and VISC elements
The mass freedoms were specified to allow propellant motion in the X and RX
directions only
The propellant masses and primary spring constants (K) were established to
represent the first longitudinal and torsional propellant modes as determined
in the propellant mode study (Section 332) Propellant masses were detershy
mined by multiplying the generalized mass of the first mode by the ratio of
total propellant segment mass to propellant mass used in the modal analysis
The remaining propellant mass was added to the SRM centerline mass points
Total segment masses were obtained from the SRM weight breakdown supplied by
NASAMSFC (Reference 14) The values of K1 (axial and torsional propellant
stiffness at zero frequency) were obtained from the generalized stiffness (kg)
of the first longitudinal and torsional propellant modes and were assumed to
be constant for each of the four propellant segments
99
13
Iz
FINITE ELEMENT MODEL SRM
PROPELLANT
FIGURE 3-23
100
TABLE 3-10 SRM PROPELLANT MODALDATA
MODE FREQUENCY GENERALIZED MASS TYPE NUMBER Hz kg (1b-sec 2in)
1 116
2 133
3 163
4 167
5 SYMMETRIC 182
6 190
7 201
8 215
9 221
10 230
11 133
12 163
13 167
14 174
15 ANTI- 192
16 SYMMETRIC 201
17 218
18 229
19 235
20 236
A - axial mode
L - lateral mode
T - torsion mode
10300
5400
7250
4330
4730
3960
9250
5960
4340
5380
5710
4450
15600
5900
3920
8410
3140
4820
8220
3940
(588) A
(308) A
(414) A
(247) AL
(270) AL
(226) AL
(528) A
(340) A
(248) AL
(307) AL
(326) A
(254 AL
(892) T
(337) A
(224) AL
(480) A
(179) AL
(275) AL
(469) A
(225) AL
I01
(KI)X 4 (kg)lX = 2492 x 107 Nm (14235 x 10l6 bin)
(KI)RX = 4 (kg)R X = 4417 x 15 N-mrad(391 x 106 in-lbrad)
The Maxwell parameters K2 and C2 were determined from the results of the
complex modulus study (Section 331) From Equations (83) and (84) the
components of the complex-stiffness are defined when KI n and K2K1 are
known Using the results of the complex modulus study
K2K 1 = 276
and
n = 17826 x 10-3
Therefore using the values of K1 calculated above
CK2) X = 6880 x 107 Nm C39289 x 106 lbin)
CK2RX = 1219 x 106 N-mrad Cl079 x 107 in-lbradl
And assuming a constant loss factor ()
CC2)X = 122630 N-secm (70036 lb-secin
(C2)RX = 2173 N-mradsec C19234 in-lbradsecY
SRM free-free modes were calculated with the four propellant models included
The resulting modal parameters for the first twenty flexible modes are summarizE
in Table 3-11 Mode numbers five through eight are the longitudinal modes
associated with each of the four propellant segments and modes 9 through 13 are
propellant torsion modes
OZ
TABLE 3-11 SRM FREE-FREE MODAL PARAMETERS
MODE FREQUENCY GENERALIZED MASS TYPE NUMBER Hz kg (lb-sec2in)
1 443 957E4 ( 5460) 1st bend pitch
2 443 957E4 ( 5460) 1st bend yaw
3 1016 968E4 ( 5525) 2nd bend pitch
4 1016 968E4 (5525) 2nd bend yaw
5 1092 107E5 (6126) axial propel
6 1143 176E5 (10062) axial propel
7 1151 109E5 ( 6196) axial propel
8 1402 214E5 (12198) axial propel
9 1558 151E7 (86016) tors propel
10 1666 131E5 (7486) tors propel
11 1666 117E5 6664) tors propel
12 1666 IOOE5 5713) tors propel
13 1666 121E5 6902) tors propel
14 1681 123E5 7031) 3rd bend pitch
15 1681 123E5 7031) 3rd bend yaw
16 2335 177E5 (10108) 4th bend pitch
17 2335 177E5 (10108) 4th bend yaw
18 2574 193E5 (11025) Ist long case
19 2804 297E5 (16930) 5th bend pitch
20 2804 297E5 (16930) 5th bend yaw
103
34 SPACE SHUTTLE MODES AND MODAL DAMPING
Sixty free-free modes were calculated for the Space Shuttle half-model at each
of the three trajectory times using NASTRAN 30 symmetric modes and 30 antishy
symmetric modes Antisymmetric modes were calculated first and DMAP ALTER
statements were used to write the modal information on a user tape DMAP ALTER
statements were also added to-the symmetric modes run which combined the antishy
symmetric modal data from the user tape with the symmetric modal data and wrote
the combined set of modes and the merged modal damping matrix (BHH) on the-
NASTRAN checkpointrestart tape The symmetric modes were written first
then the antisymmetric modes
The first 25 symmetric flexible modes and 25 antisymmetric flexible modes were
selected to be used by the postprocessor computer program to determine critical
resonances The frequencies and generalized masses for these 50 modes for each
mass condition are listed in Tables 3-12 through 3-14 A complete set of strucshy
tural dynamic characteristics for each mass condition including frequencies
generalized mass modal damping and mode shapes at selected points on the Space
Shuttle structure are listed in Section 20 of Volume II
The equivalent modal viscous damping ratios for the liftoff condition shown in
Table 3-12 are calculated from the diagonal terms in the coupled modal damping
matrix (BH-) The structural joints incorporated in the model result in modal
damping ratios in the range of 002 to 020 for the primary structural modes
while some of the higher frequency modes have damping ratios greater than 10
The modes are local modes characterized by large amplitude motion in the joints
which contribute large amounts of damping
The joint damping parameters were assumed to be constant for all trajectory time
points Equivalent modal viscous damping ratios for the max q and SRB cutoff conshy
ditions are tabulated in Tables 3-13 and 3-14 respectively The damping in the
primary modes at max q are somewhat higher than at liftoff and are even higher
for SRB cutoff This suggests that joint damping parameters do not remain constan
throughout flight and that they should be recalculated for each mass condition
104
Table 3-12 SPACE SHUTTLE MODAL DATA LIFTOFF
EQUIVALENT
MODE NUMBER FREQUENCY GENERALIZED MASS DAMPI G RATIO 4 013764230E 02 031418E 06 003
5 017524689E 02 053878E 06 005
6 018133037E 02 020166E 06 048
7 019370438E 02 023247E 06 003
8 022939240E 02 019507E 05 289
9 025795609E 02 071901E 05 170 10 028701675E 02 034791E 05 306
11 12
02894(4275E 02 030096359E 02
038672E 05 029977E 05
007
098
13 031603180E 02 032339E 05 012
14 032383667E 02 0356722 05 967
15 0327293852 02 017819E 06 056
16 034836258E 02 033781E 06 014 17 036577789E 02 0138102 04 387
18 038610626E 02 010745- 05 292
19 03S3185882 02 048755E 04 124
20 041914459E 02 010181E 05 349 21 048224747E 02 012909E 06 267
22 049329636E 02 076124E 04 4316
23 051161975E 02 013862E 06 388
24 052124176E 02 048587E 05 001
25 052243576E 02 054716E 05 005
26 052839355E 02 089283E 05 004
27 052912048E 02 093129E 04 4154
28 34-
055803299E 02 011956779E 02
039785E 05 095077E 05
3082 017
35 012445990a 02 056738E 06 002
36 016301208E 02 048963E 05 160
37 017309418E 02 048436E 06 007
38 020951965E 02 062331E 05 671 39 023871979E 02 068545E 04 935
40 027019867E 02 015617E 06 525
41 029155258E 02 071354E 04 164
42 030047516E 02 036676E 06 035
43 030799728E 02 051000E 04 300
44 031635300E 02 048226E 04 1563 45 032753357E 02 012161E 05 381 46 033122925E 02 019105E 05 721
47 I 036919678E 02 010426E 05 275 48 037888133c 02 040696E 04 3051
49 gt 038871368E 02 064075E 04 742 50 043467697E 02 075786E 05 234
51 045840668E 02 098341E 04 1291 52 051102036E 02 032159E 05 2064
53 052131180c 02 047597E 05 001 54 052227005E 02 010977E 06 007
55 059475139E 02 019469E 06 005
56 060747559E 02 078698E 04 6525 57 065134735E 02 023504E 05 829
53 067310837E 02 012182E 06 358
radsec kilograms
105
Table 3-13 SPACE SHUTTLE MODAL DATA MAX Q
EQUIVALENTIODE NUMBER FREQUENCY GENERALIZED MASSDAMPING RATIO
4 015798579E 02 5 019863358E 02 6 022897659E 02 7 024014236E 02 8 025154358E 02 9 028750290E 02
10 029368500E 02 11 029516068E 02 12 030276810E 02 13 032514328E 02 14 032923279E 02 15 033142456E 02 16 u 034732986E 02 17 037009567E 02 18 039742020E 02 19 042457657E 02 20 044433228E 02 21 047920227E 02 22 048343109E 02 23 048527176E 02 24 049307709E 02 25 052916168E 02 26 055562759E 02 27 056489227E 02 28 058523239E 02 34 013293739E 02 35 015512980E 02 36 018812180E 02 37 020997528E02 38 023715759E 02 39 025793839E 02 40 028850606E 02 41 029790405E 02 42 030732376E 02 43 031451477E 02 44 032414566E 02 45 033011047E 02 46 035498917E 02 47 S 038564667E 02 48 038901428E 02 49 044856186E 02 50 C 046534348E 02 51 047931808E 02 52 048243439E 02 53 051123520E 02 54 056279968E 02 55 058737076E 02 56 062650467E 02 57 067074478E 02 58 071453018E 02
radsec
016388E 06 014 026006E 06 063 010801E 06 020 018544E 05 371 010913E 06 055 027003E 05 186 019652E 06 232 024377E 06 025 034978E05 052 018386E 06 048 033558E 05 241 025770E 05 698 036005E 06 002 013292E 04 377 027215E 04 424 041007E 05 369 066609E 05 116 059381E 05 001 066023E 05 00 010363E 06 001 073052E 04 4480 084754E 04 4540 053302E 05 1870 010038E 06 1410 020368E 06 108 062323E 05 029 039855E 06 011 027646E 05 414 011191E 06 051 028859E 05 1420 055375E 04 1240 037731E 05 052 035870E 06 038 018739E 05 203 036952E 04 085 071497E 04 2730 071085E 05 300 055165E 04 567 038636E 04 1250 046699E 04 2430 011183E 06 329 014940E 05 1140 057895E 05 002 013857E 06 024 045802E 05 1230 027750E 05 2110 018500E 06 004 080243E 04 8840 018895E 05 7170 028199E 05 3390 kilograms
106
Table 3-14 SPACE SHUTTLE MODAL DATA SRB CUTOFF
MODE NUMBER FREQUENCY 4 020559067E 02 5 026607239E 02 6 027987335E 02 7 028858627E 02 8 030375336E 02 9 031237579E 02
10 032712769E 02 11 033140091E 02 12 055107529E 02 13 035248657E 02 14 037567795E 02 15 040230258E 02 16 044707397E 02 17 046505005E 02 18 049328049E 02 19 052415176E 02 20 054798798E 02 21 056951309E 02 22 057882385E 02 23 064516739E 02 24 065359177E 02 25 071718246E 02 26 073347260E 02 27 076281036E 02 28 076884216E 02 34 015647510E 02 35 022611206E 02 36 025484436E 02 37 026599609E 02 38 029311096E 02 39 030888367E 02 40 031821198 02 41 033145477E 02 42 033365005E 02 43 033950378E 02 44 038024887E 02 45 040358887E 02 46 043295227E 02 47 w 049701279E 02 48 050916428E 02 49 055457657E 02
50 062247055E 02 51 C 065659256E 02 52 066961060E 02 53 0716760252 02 54 075262177E 02 55 081694839E 02 56 083266098E 02 57 085406967E 02 58 086414337E 02
radsec
EQUIVALENT GENERALIZED MASS DAMPING RATIO
025567E 05 190 039178E 05 258 027441E 05 154 027970E 05 242 050671E 05 117 013397E 06 003 0634352 05 955 019225E 07 022 050324E 04 153 032385E 06 001 017005E 04 263 032143E 04 385 032038E 05 463 044722E 05 102 074425E 04 4440 012404E 05 3480 020719E 05 2300 011173E 06 823 070118E 05 1305 014556E 06 481 034289E 05 2070 075959E 04 1430 045761E 04 1710 020253E 05 622 046221E 05 090 023900E 05 115 024693E 05 1309 099066E 04 310 011383E 05 1070 024523E 05 058 031855E 05 031 033824E 04 099 010697-E 05 1100 039287E 05 503 0613922 04 695 046689E 04 3860 035964E 04 988 013758E 06 390 015029E 05 1527 048697E 05 1698 010987E 06 367 082898E 04 6500 022044E 05 8120 014647E 06 759 025396E 05 9420 028321E 04 4390 044440E 04 1605 014946E 05 1826 012034E 05 6950 092264E 04 4030
kilograms
107
40 CRITICAL RESONANCES FROM CONVENTIONAL MODEL CLIFTOFF)
Critical resonances for the Space Shuttle at liftoff were obtained using
uniform modal damping and conventional modal selection techniques The
conventional model was obtained by removing the distributed structural joint
damping from the realistic model A uniform modal viscous damping ratio C=00
was used to represent structural damping in all the modes Modal resonances
were ranked according to rate or position coefficients calculated using postshy
processor Option 1 The coefficients represent the steady-state dynamic
amplification at resonance which occurs at a point on the structure due to a
sinusoidal force input at another point Rate or position coefficients for the
jth requested mode are calculated for the selected freedoms as in the following
examples
R(140323 7014) = fi40323j 7014j (85)i (2 j) j Mj
P(140322 110264) = 140322j 0110264j
(86)(2cj) tj2 Mj
where R and P denote rate and position coefficients respectively Gridpoint freedoms for the input point and response point are specified in parentheses
The last digit of each ID is the input or output freedom specified at the
gridpoint indicated by the preceding digits For example P(140322 110264)j
is the position coefficient calculated for the jth mode at gridpoint 11026 in
the freedom 4 (ex) direction due to a unit sinusoidal force at gridpoint 14032
in the freedom 2 (y)direction
At the resonance condition the modal displacement response always lags the
input generalized force by 90 degrees and the modal velocity response is always
in phase with the input generalized force If the mode shapes at the response
point and the input force point have the same sign then the physical displaceshy
ment response lags the input force and the physical velocity response is in
phase with the input force The positive or negative sign on the coefficients
shows whether the physical response is in phase or out of phase with the modal
response respectively The positive sign on the coefficients indicates of
course that the mode shapes at the response point and the input force point
have the same sign
108
The excitation and response degrees of freedom chosen for this study are
shown in Table 4-1 One outboard SSME gimbal and one SRB gimbal were chosen
as the excitation points (three degrees-of-freedom each) The response points
were chosen to demonstrate the application of critical resonance selection
using admittance techniques for three technical disciplines guidance and
controlPOGO and dynamic loads Position gyro rate gyro and accelerometer
responses are calculated for use in attitude control studies LOX tank aft
dome acceleration admittances-for POGO investigations are calculated and payload
attachment acceleration admittances are calculated to demonstrate the use of
the method for dynamic loads calculations
The ranking of rate and position coefficients for the selected excitation
response points are shown in Tables 4-2 and 4-3 respectively The zero coeffishy
cients shown in some of the rankings indicate that the mode shape of either
the excitation freedom or response freedom is zero for that mode For example
if the excitation point is on the plane of symmetry (eg gridpoint 14032)
the symmetric modes (modes 4 through 28) will not be excited for a force in the
y-direction because the centerline gridpoints are constrained in the y-direction
for symmetric modes Therefore only antisymmetric modes (modes 34-58) will
be excited by this force Likewise coefficients for response points on the
plane of symmetry (eg gridpoint 9005) are zero for either symmetric or antishy
symmetric modes
Acceleration coefficients are determined by multiplying the position coefshy2
ficients by -
109
TABLE 4-1 SPACE SHUTTLE RESPONSE AND EXCITATION LOCATIONS
LOCATION x y z GRIDPOINT DIRECTIONS
Excitation Points
SRM Gimbal(+y)
SSME (+y) gimbal
18238
1450
0
530
0
3340
513
14039
xyz
xyz
Response Point (displacement)
IMU 4140 0 4190 9005 R RyRz
Response Points (velocity)
SRM forward rate gyro
SRM aft rate gyro
Orbiter rate gyro
48325
115110
13125
-305
0
58
528
730
4073
901
902
9004
RxRyR
RxRyRz Rx RyR z
CD Response Points(acceleration)
Crew comp inst unit LOX tank aft dome
Payload keel support
3806
9621
1047
100
217
0
4065
0
3070
9001
52
12076
x~yz
x
y
SRM coordinate system (in)
Orbiter coordinate system (in)
ET coordinate system (in)
Table 4-2 RATE COEFFICIENTS FOR CONVENTIONAL MODEL
RATE COEFFICIENTS RESPONSE FROM - 9014 INPUT FROM - 5131 RATE COEFFICIENTS RESPONSE FROM 9015 INPUT FROM - 5131
FREQUENCY MODE NO COEFFICIENT 013764E 02 4 -024174E-07
RANK a
FREQUENCY MODE NO COEFFICIENT 01376E 02 4 051351E-09
RANK 29
017525E 02 5 -0157962-07 14 017525E 02 5 0821262-10 38
018133E 02 6 0726672-07 1 018133E 02 6 -017162E-08 23
0193702 02 7 -0191692-08 26 019370E 02 7 0330062-10 44
022939C 02 8 -065894E-07 3 022939E 02 8 -019824E-07 I
025796E 02 9 021146E-07 10 025796E 02 9 015329E-07 4
028702C 02 10 014266C-08 29 0287022 02 10 -0452452-10 41
028944E 02 11 052910E-08 22 0239442 02 11 025162E-08 19
030096E 02 12 -010401E-08 35 0300962 02 12 -036193E-09 33
031603E 02 13 027622E-09 40 031603E 02 13 0920992-10 37 032334E 02 14 0222112-07 9 0323842 02 14 067389E-08 9
0327292 02 15 013851E-08 30 032729E 02 15 072649E-09 28
0348362 02 16 -012600E-08 31 034836E 02 16 -026155E-09 35
036578E 02 17 -057213E-08 21 036578E 02 17 -018290E-08 21
C38611E 02 18 -031470E-07 7 038611E 02 18 -074482E-08 8 038019E 02 19 010417E-07 18 0388192 02 19 0114032-07 7
041914C 02 20 012213E-07 15 0419142 02 20 -048860E-08 13 048225E 02 21 -012111E-08 32 048225E 02 21 -041437E-C9 31
049330E 02 22 -034072E-10 051462E 02 23 011490E-08
45 34
049330E 02 22 -017341E-10 051462E 02 23 0q0217E-09
46 32
052124E 02 24 -045962E-12 50 052124E 02 -24 -074653E-12 50 052244E 02 25 -0966462-10 44 052Z42E 02 25 -057974E-10 40
0528392 02 26 -060853E-11 0529122 02 27 -0463472-09
47 38
052839E 02 26 -031594E-11 052912E 02 27 -0203692-09
48 36
055803E 02 28 -097199E-10 43 0558032 02 28 -0346772-10 42 011957E 02 34 -096094E-09 36 011957E 02 34 0343642-08 15 0124462 02 35 022841E-08 24 012446E 02 35 -0125552-08 14 06801F a 36 -0483072-07 5 016801E 02 36 059743E-08 10 017309E 02 37 066416E-07 2 017309E 02 37 -013144C-07 5
020952E 02 38 0188812-07 11 0209522 02 38 0168582-07 3 023872E 02 39 -06395E-07 4 023872E 02 39 -017914E-07 2 02702o0 02 40 000002-07 6 027020C 02 40 011656E-07 6
029155E 02 41 -011101E-07 16 029155E 02 41 -030352E 08 17 030048E 02 42 -0658352-09 37 030048E 02 42 -020863E-10 45
03080OE 02 43 071583i-08 19 030800E 02 43 017423E-08 22 0316352 02 44 059649-C 20 031635E 02 44 0151912-6S 27
032753E 02 45 023014E-09 41 032753C 02 45 066971E-10 39 033123E 02 46 -0109758-07 17 033123E 02 46 -033288E-08 16 036920E 02 47 -017046E-07 12 036920E 02 47 -0557642-08 11 03788SE 02 48 016720E-07 13 0378852 02 48 050562S-08 12 038871E 02 49 -031508-OS 23 0388712 02 49 -050095E-09 30
0434682 02 50 011887E-00 33 0434682 02 50 -0296372-09 34 045841E 02 51 022192E-08 25 0458412 02 51 0163532-08 25
051102E 02 52 015369E-08 27 051102E 02 52 015776E-08 26 0521312 02 53 032374E-11 48 052131E 02 53 0299362-11 49
052227E 02 54 -074939E-12 059475E 02 55 019550E-10
49 46
052227E 02 54 064946E-11 059475E 02 55 033190E-10
47 43
060748E 02 56 -0401342-09 39 0607482 02 56 -016897E-08 24
06515E 02 57 -099571E-10 42 065135E Z 57 -0209112-08 20
067311E 02 58 -014542E-C8 28 067311E 02 58 027156E-08 18
RATE COEFFICIENTS RESPONSE FROM r 9016 INPUT FROM = 5131 RATE COEFFICIENTS RESPONSE FROM 9014 INPUT FROM = 5132 FREQUENCY NODE NO COEFPICIENT RANK FREQUENCY MDE NO COEFFICIENT RANK013764t 02 4 -0205896-09 33 013764E O 4 012475E-08 37017525E 02 5 -0368862-07 4 017525E 02 5 024800C-0701813ZE 02 6 -00149E-08 15 13
018133E o 6 039027E-06 20193702 02 7 -079132E-09 24 019370E 02 7 -047924E-06 1O22131E 02 8 0134539-09 3C 022939E 02 a 016076E-07OZ5796E 02 9 -059578E-09 26 1 0Z87026 02 025796E 02 9 -015910E-07 1110 -010q58E-09 38 026702E 02 10 026076E-08 33028944E 02 11 -05955IE-09 27 028910E 02 11 010907E-07 21030096E O2 2z -0321522-09 - 30 0300966 02 12 078343-00 27031603C D2 13 099123E-09 21032384C 02 14 031603E 02 13 018193E-08 35-040392E-05 14 032334E 02 14 -013115E-07 20032729E 02 15 -030832E-09 31 032729E 02 15 -0104712-08 39034036E 02 16 -010076E-03 20 034836E 02 16 0144442-08 36036578E 02 17 -060S81E-09 25 036578E 02 17 024339E-07 14030611E 02 18 -040672E-07 3 030611E 02 18 022117E-07 16038819E 02 19 -0602836-08 9 036819E 02 19 -070626E-09 41OA290E 02 20 -O411746-08 13 041914E 02 20 -0123682-03 38048225E 02 21 -055752E-10 40 043225C 02 21 0704462-08049330E 02 22 044190E-12 49 28
049330E 02 22 -0145622-09051462E 02 23 012297C-08 10 44 051462E 02 23 0379402-07 17052124E 02 24 0847102-13 50 052124E 02 24 -0912702-11 4052244E 02 25 -025105E-09 32 052244E 02 25 012558E-09 45052339E 02 26 -0-40917E-11 47 052839E 02 26 -0306152-11 49052912E 02 27 0705952-10 39 052912E 02 27 -0791462-08 2505580SE 02 28 0436892-1] 46 055803E 02 28 -019739C-08 34011757E 02 34 -0149322E-0 35
0124462 011957E 02 34 -085381E-09 4002 35 079 25E-06 8 0124146 02 35 0959542-08 22016501E 02 36 093666-09 22 016801E 02 36 -086143E-07 6017309E 02 37 -058609E-07 2 017309E 02 37 040272E-08 31020952E 02 38 -056027E-08 10 020952E 02 38 -08391E-08 24023872E02 39 -025541E-07 5 023872E 02 39 -0127572-06 4027020E 02 40 -059628E-07 1 0270200 02 40 012319E-06 30291552 02 41 -051649E-08 11 0291552 02 41 -055933E-07 7030043E 02 42 -019935E-10 44 030048E 02 42 -079110E-08 260303BOO 02 43 041632E-IU 43 030300E 02 43 -013163E-07 19031635E 02 44 -0372482-09 29 032753 031635E 02 44 -055310[-07 802 45 047859E-10 41 032753E 02 45 066957E-09 42033123E 02 46 018738E-08 16 033123E 02 46 C100402-060369200 02 47 0116712-07 7 5
0369202 02 47 040476E-07 9037838E 02 48 049154E-08 32 037388E 02 48 -040070E-07038371E 02 49 -092069E-09 23 19 038871E 02 49 -056032E-08 300434686 02 50 015324E-09 34 043466E 02 so 023865E-07 150458412 02 51 011942E-08 19 0453410 02 51 026497E-07 12051102E O 52 044376E-10 42 051102E 02 52 029070E-06 32052131E 02 53 -004167E-11 45 0521tl 02 53 -011063E-10 47052227E 02 54 -045671E-12 48 052227E 02 54 016323E-11 so059475E 02 55 -0130272-07 37 059475E 02 55 -011935E-09 460607482 02 56 017475E-O8 17 060746 O 56 -065Z62-08 29065135E 02 57 051 10E-09 2 0o65135E 02 57 -052065E-09 43067312E 02 5a 020336E-07 6 067311E 02 58 -093532E-08 23
RATE COEFFICIENTS RESPONSE FRDOM 9015 INPUT FROM 5132 RATE COEFFICIENTS RESPONSE FROM 9016 INPUT FRDM = 5132
FREQUENCY MODE NO COEFFICIENT 013764E 02 4 -026S002-10
RANK 46
FREQUENCY MODE NO COEFFICIENT 013764E 02 4 0106252-10
RANK 46
0175252 02 5 -0I28942-09 42 017525E 02 5 0579132-07 4
018133E 02 6 -092171E-08
019370E 02 7 0825162-06 022939E 02 8 048364e-08
15 16 23
018133E 02 6 -021563E-07
019370E 02 7 -019783C-06 022939E 02 8 -032813E-10
11 1
4
C25796E 02 9 -02603ZE-07 4 025796C 02 9 010168E-08 30
0Z702E 02 10 -082705E-10 028944E 02 11 0516712-08 030096E 02 12 027260E-08
43 22 29
028702E 02 10 -019117E-09 02894 E O 11 -012276E-08 030096E 02 12 0242182-08
38 27 23
031603E 02 13 061136E-09 C323842 02 14 -039790E-08
35 24
0316032 02 13 065286E-05 032334E 02 14 02349E-03
16 24
(327292 02 15 -0549102-09
034836E 02 16 029982E-09
36 33
032729C 02 15 02334E12-09
0348362 02 16 011551E-08 37 29
0365782 02 17 07780eE-08 17 036578E 02 17 025771E-08 21
039611F 02 18 052345E-08 21 038611E 02 1 028582E-07 a
038E19E 02 19 -077314C-09 33 038819E 02 19 040871E-09 33
019142E 02 20 049479E-09 37 041914E 02 20 041695E-09 32
048225E 02 21 024102E-08 30 048225C 02 21 032428E-09 35
049330E 02 22 -0741132-10 45 049330E 02 22 018886E-i1 48
051462E 02 23 062794-08 19 051462S 02 23 0192002-07 12
052124E 02 24 -014824E-10 47 0521242 02 24 0163212-11 49
05224A4 02 25 075334E-10 44 0522442 02 25 032622E-09 34
052amp39E 02 26 -015895E-11 so 0528392 02 26 -020585E-11 47
0529122 02 27 -034704E-08 25 0529122 02 Z7 0120552-08 28
055803E 02 28 -0704231-09 54 055803C 02 28 087242-10 41
011957E 02 34 030532E-08 27 011957E 02 34 -0132672-09 40
012446E 02 35 -017877E-07 7 012 6E 0 35 033281E-07 6
0168012 02 36 010655E-07 14 0168012 02 36 016699E-08 25
0173092 02 37 -0197012-09 020522 02 30 -074922E-08
32 18
017309E 02 37 -035538E-03 0209522 O 38 0249012-08
17 Z2
023272E 02 39 -035732E-07 2 023872E 02 39 -050946E-07 5
027020E 02 40 037355E-07 I 027020E 02 40 -019109E-06 2
0291552 02 41 -015292E-07 10 029155E 02 41 -026022E-07 10
030(482 02 42 -025(692-09 39 03004E 02 42 -023955E-09 36
(30O0E 02 43 -032039E-08 26 030300E 02 43 -076556E-10 43
0316352 02 44 -014085E-07 11 031635E 02 44 0345392-08 18
032753E 02 45 019485E-09 41 032753E 02 45 013924E-09 39
033123E 02 46 0304512-07 3 0331232 02 46 -017142E-07 13
036920E 02 47 015859E-07 9 036920F 02 47 -033192E-07 7
0378SE 02 68 -012117E-07 12 0378282 02 48 -011828E-07 15
038871E 02 09 -089166E-09 31 033371E 02 49 -01638E-08 26
04346ampE 02 50 -059502E-08 20 0434682 02 50 030765E-08 19
045841E 02 51 019532E-07 6 04581 02 51 014260E-07 14
051102E 02 52 0298IE-08 28 051102E 02 52 083938E-10 42
062131E 02 53 -010235E-10 49 052131E 02 53 028877E-10 45
052227E 02 54 -0145802-10 48 052227E 02 54 010252E-11 50
(59475E 02 55 -0202622-09 060748E 02 56 -025904E-07
40 5
059475E 02 55 079527E-09 0607A8E 02 56 0267902E-07
31 9
0651351 02 57 -010934E-07 13 065135E 02 57 026882E-03 20
067311E 02 58 017467E-07 8 067311E 0 58 013080E-06 3
RATE COEFFICIEIITS RESPONSE FROM u 9014 INPUT FROM = 5133 RATE COEFFICIENTS RESPONSE FROM = 9015 INPUT FROM = 5133
FREQUENCY MODE No COEFFICIENT RANK FREQUENCY MODE NO COEFFICIENT RANK 011764E 02 4 -081937E-06 1 013764E 02 4 017405E-07 13 017525E 02 5 016782E-07 16 01752SE 02 5 -087254E-10 40 018133E O 6 022q222-06 6 010133C 02 6 -052955E-08 13 019370E 02 7 -0966112-09 39 019370E 02 7 0166355-10 47 022939E 02 a 0429002-06 3 022939E O 8 0112906E-06 4 025796E 02 9 024995E-06 4 025796E 02 9 013119E-06 3 023702 02 10 -016335E-03 33 028702E 02 10 05196ampE-10 43 0289148 02 11 020595E-03 29 028944[ OZ 11 0979438-09 29 030096E 02 2 -0121512-10 48 0300962 02 12 -0422812-11 50 031603E 02 13 0756838-10 44 031603E 02 13 025456E-10 46 032384E 02 14 -019975E-03 31 0323848 O 14 =0606058-09 33 0327292 02 15 06767LE-09 40 032729C 02 15 0354872-09 36 034836E 02 16 -026986E-09 42 034836E 02 16 -0560168-10 42 0365788 02 17 -017374E-07 15 036578E 02 17 -0555402-08 17 038611E 02 18 -075513E-08 20 OS3611E 02 18 -017872E-08 2S 038819E 02 19 0741372-08 21 038819E 02 19 081158E-08 16 0419142 02 20 -044123E-07 11 041914E 02 20 0176518-07 1z 048225E 02 21 -010459E-06 9 048225E 02 21 -0357825-07 8 0493302 02 22 -0146938-03 35 049330E 02 22 -0748062-09 31 051462E 02 23 -0489702-09 41 051462E 02 3 -017140E-09 39 052124E 02 24 -026757E-10 47 052124E 02 24 -0434608-10 45 052244E 02 25 -074604E-10 45 052244E 02 25 -044752E-10 44 0523398 02 26 -011263E-10 49 0528391 02 26 -058501E-11 43 052912E 02 27 -0459822-08 25 052912E 02 27 -020209E-08 22 0558032 02 28 -051964E-08 24 055803E 02 28 -018539E-08 24 011957E 02 34 053790E-07 10 011957E 02 34 -0192352-06 2 012446E 02 35 01172(E-08 01600E 02 36 -043667E-06
37 2
012446E 02 35 -021841E-08 016301E 02 36 054010E-07
20 5
017309C 02 37 -013727E-07 17 0173D92 02 37 0271688-08 19 020952E 02 38 02296GE-06 5 020952E 02 38 02050SE-06 1 023872E 02 39 013687E-06 7 023872E 02 39 0385339E-07 7 027020E 02 40 -02e41OE-Os 029155E 02 41 -078659E-03
28 19
027020E 02 40 -082790E-09 029155E 02 41 -021506E-08
30 21
03004E O 42 -085894E-08 18 O300qBE OZ 42 -0272198-09 38 030O8 02 43 -0118612-8 36 0308000 02 43 -028702-09 37 031635E 02 44 0412282-07 13 031635E 02 44 010499E-07 14 032751E 02 45 -0157511-08 34 032753C 02 45 -045837E-09 35 033123E 02 46 0540562-08 22 033123E 02 46 016396E-08 26 036920E 02 47 -035464E-08 26 036920E 02 47 -011602[-08 2a 0378BOE oz 48 -032497E-07 14 0378E OZ 43 -098274E-08 15 038871E 0Z 49 -03134ampE-08 27 0388712 02 49 -049842E-09 34 04346C2 02 50 -011459E-06 8 043468E 02 50 028571E-07 l 045841E 02 51 -020026E-03 30 045841C 02 51 -014762E-08 27 051102E 02 52 -042338E-07 12 051102E 02 52 -03460E-07 6 052131E 02 53 -05440E-11 50 052131E 02 53 -050309E-11 49 052227E 02 54 081537E-10 43 0522278 02 54 -0706642-09 32 059475E 02 55 -044034E-10 46 059475E 02 55 -074763E-10 41 060718E 02 56 -052757E-08 23 060748 02 56 -022212E-07 11 0651352 02 57 -016961E-03 32 0651352 02 57 -035619E-07 9 0673112 02 58 010093[-08 38 067311E 02 58 -013349E-08 23
RATE COEFFICIENTS RESPONSE FRDM = 9016 INPUT FROM = 5133 RATE COEFFICIENTS RESPONSE FRDM = 9024 INPUT FROM 5131
FREQUENCY N0DE NO COEFFICIENT RANK FREQUENCY MODE NO COEFFICIENT RANK 013764C 02 4 -069787E-08 16 0137649 02 4 -019498E-07 11 017525E 02 5 039189E-07 3 017525E 02 5 -015805E-07 13 018133E 02 6 -012389E-07 8 018133E 02 6 067241E-57 2 019370E 02 7 -039882E-09 32 019370E 02 7 -017486E-08 30 022939E oZ 8 -0875632-09 29 O2939E O a -069650E-07 1 025796E 02 9 -070776E-08 15 025796E 02 9 021509E-07 9 028702E 02 10 012012E-09 43 028702E 02 10 015220E-08 31 02894E 02 11 -023180E-09 39 02894E 02 11 040525E-08 22 030096E 02 12 -037563E-11 50 030096E O 12 -083027E-09 34 0316032 02 13 027161E-09 36 031603E 02 13 07787EE-10 41 032384E 02 14 036326E-09 33 032384E 02 14 016114E-07 12 032729E 02 15 -015082E-09 42 032729E 02 15 084829E-09 33 034836E 02 16 -021580E-09 40 034636E 02 16 -087395E-09 32 036578 02 17 -0103972-08 24 036578E 02 17 -035331R-OS 24 038611E 02 18 -097592E-08 10 038611E 02 18 -020359E-07 10 038819E 02 19 -042903E-0 i8 038819E 02 19 -037591E-08 23 041914C 02 20 014875E-07 5 041914E 02 20 024278E-07 8 040225E 02 21 -046143E-03 17 048225C 02 21 -023057E-08 28 (493302 02 22 019063E-10 45 09330E 02 22 -073391E-10 42 051462E 02 23 -052409E-09 31 051462E 02 23 -043299E-09 39 052124E 02 24 049315E-11 49 052124E 02 24 -016786E-11 50 052244E 02 25 -019379E-09 41 052244E 02 25 -062750E-10 43 052839C 02 26 -075743E-11 47 052839E 02 26 -019725E-11 49 052912F 02 27 070039E-09 30 052912E 02 27 -029912-10 44 055803E 02 28 023357E-09 38 055303E 02 28 024I356-10 45 01157E 02 34 083581E-08 14 011957E 02 34 -015363E-08 20 012416C 02 35 040663E-08 20 012416E 02 35 066063E-08 18 01600IE 02 36 084652E-08 13 016801E 02 36 -042478E-07 5 017309E 02 37 012114E-07 9 017309E 02 37 051256E-07 4 020952E 02 38 -O68I5IE-U7 I 020952E OZ 38 030119E-07 7 023872E 02 39 054663E-07 2 023872E 02 39 -066956E-07 3 027020E 02 40 042351E-08 19 O7020E 02 40 037714E-07 6 029155E 02 41 -036596E-08 21 029155E 02 41 -096293E-08 16 030048E 02 42 -026009E-09 37 030fl48E 02 i2 -059829E-09 36 C30800E 02 43 -06984E-11 48 030800C 02 43 05858E-08 19 031635E C2 44 -025745E-08 22 031635E 02 44 043499E-08 21 032753E 02 45 bull-032756E-09 34 032753E 02 A5 017130E-09 40 033123E 02 46 -092296E-09 27 033123E 02 46 -078467E-08 17 036920C 02 47 O24283E-08 23 036920E 02 47 -011161E-07 15 03738E 02 48 -095926E-08 11 03788SE 02 48 0112732-07 14 038871E 02 49 -091603E-09 28 038371E 02 49 -0262032-08 25 043468E 02 50 -014772C-07 6 O3468E 02 50 025584E-08 26 045841E 02 51 -010777E-08 26 Oq5841E 02 50 -018227E-08 29 051102E 02 52 -012225E-08 25 051102E 02 52 024190E-08 27 052131E 02 53 014195E-10 46 052131E 02 53 025636E-11 48 052227E 02 54 049692E-10 44 052227E 02 54 0677E-0 46 059475E 02 55 029345E-09 35 059175E 02 55 026816E-11 47 06074E 02 56 022971E-07 4 060748E 02 56 -047164E-09 37 065135E (2 57 0875715-08 12 065135E 02 57 061975E-09 35 067311E 02 58 -0141 5E-07 7 067313E 02 58 044685E-09 38
tow PAGE is PO
RATE CEFFICIENTS RESPONSE FROM - 9025 IPUT FRDM - 5131 RATE COEFFICIENTS RESPHE FRCMM 926 ZINUT FRD 0 5131
FP0EHGY MODE NO COEFFiCIENT RANg -FREQUENCY f10E NO CDEFFICIE1T RANK
013T E -02g4 - R5 013764E OR q 091700-IC 36 017525E 02 3 O7860l-ta Is V1E525E 02 5 0207710-07 6 0- 81331 02 A 026800 34 C 281338 02 6 061990-oa 8
019137 OR 7 -042491amp-10 38 01917E O 7 O-03400E-9 I 02293E 02 a 04406$e-07 3 02z9352 OR 8 -020VE0a3 4 0235760 OR 9 - 122531e-07 g5 023571E 94 21 0ze701 02 10 -Ot3D2ZE-09 2 0287029 02 10 0322700-09 RE 0289441 030OV51
02 0
13 12
-0211530-06 0137591-G0
)9 a6
02a94 0 030076E 0l2
LI 02
028405E-08 -036613E-09
is 30
031603C 02 13 -013335E-09 37 03163 02 13 00990-00 1amp
0123l8e O 14 -O 697E- 3 14 032384E 02 14 02043-Q0 16
03272 0R2 s -033497E-09 30 03 2E 0 15 -0is3238-U I$ 01 636 02 16 -0457791-11 46 034836E 02 1d -0656000-09 24 3678E 02 17 025207E-09 32 04570 02 17 0178E4--0 2
0384 1E O 1is Ofl672E08-0116M IT 0003018611E7 6i 0386319 O 19 -670789 -oa A1 08613E 02 i5 -0172198E-0 19
04139146 RD 092132E-08 7 0419140E O 20 -0114A0E-08 20 0482256 02 1 25- 257SS6 0e2oz 21 0 VE-1 39 0493339 02 2 -024516E0 )9 043ao30 02 2 0975 7E-l 47 QS1I2E 052124E
02 02
23 24
015515E-09 -0634SE-12
as so
0514626 052224
02 R
23 24
04942a0-o0 0330216-l
11 q7
932244E 0 25 - 403E5-6 40 C52S244 0 2 -093109- 37 0303 9E 02 26 -082926E-2 49 052838 02 26 O1352-f11 Q 062720E 02 27 -023504k-10 42 0 2E OR 27 031124-O7 32 0538E6 02 28 0-7465SE-13 47 055800E ampa 2a D571 E-0 9 44
0119$7E 02 34 072126E-46 10 011957C 02 1 02635C-09 26 912 444 O 25 8 12446E 02 55 0VI21~106 1 02660 ampZ u6 -6110M07 amp 0166a33 03 16 -031008-09 31 017301 0 37 020253C-07 I GMU1 E 0 3l -034106E-07 3 02900E 02 35 -026969E-07 2 0209S26 oz is 08973E0-9 22
023972e o 39 0$5710E-07 4 023872E 0Z 35 0143 8E7-- 7
0274260 0oz 4 -O4Z032f-9B 1 027020E 0 40 033ZI10007 4 029159 O2R 4 061496E09 21 0291556 02 41 D32305008 12 03049E 02 4 -0-16951E810 43 033446k 6 42 0323E8-10 4z 9 306008 02 43 -063744E-09 26 C 308000 oz 4 -D 751635-1fl 38 031635E U2 44 0110746-0S 13 03L635E 02 4-O610-9 23 0327530 02 45 -0136996-I0 41 03 7538 02 45 0164786l0 45 D331250 02 46 O132s72-08 16 D331230 C2 46 -0210276-80 17
0369200 02 47 0264679-09 30 D3MO28 cz 47 -049912amp-07 2 037a8e 02 46 0Z34938-U1 33 0318330 amp2 48 V3590 9 038B710 0 49 Z935400 0 38871V 02 49 05631t09 27 0434686 02 so 079592E0S 24 041r639 0a so 054889e-Io S 0456419 02 57 -980 l370-09 23 0453416 O 51 015359E09 3$
051162E 02 52 099640-09 19 051102E f 32 0O23727E-10 43 0521301 02 53 lZ375c-11 43 052131E 02 33 091211 4 0322270 02 34 047956E-13 45 U62 27E 0 54 -0352068013 so
050475E 02 55 096270-1I 44 05475E 0 33 0 44874510n 41 0407460 02 56 -05997469-09 27 060746E 02 56 0420288-09 29 C651359 102 57 054574C-09 I$ 0651355 02 57 016Z649-09 34l
067311E 0 58 0192444E09 20 067311 0 50 056758-0 104
RATE COEFFICIENTS RESPONSE FRDM 9024 INPUT FROM = 5132 RATE COEFFICIENTS RESPONSE FROM 9025 INPUT FROM 5132
FREQUENCY MODE NO COEFFICIENT RANK FREQUENCY NODE NO COEFFICIENT RANK 013764E 02 4 010062E-0 36 01376E 02 4 Oq6736E-09 37 017525E 02 5 0248145-07 14 0175252 02 5 -043741E-08 16 018133E 02 6 036113E-06 2 018133E 02 6 -012182E-08 26 019370E 02 7 -043715E-06 1 019370C 02 7 -010623E-07 9 022q39E 02 8 016993E-07 16 022939E 02 a -058705E-03 1 025796E 02 9 -036526E-07 10 025796E 02 9 020777E-07 3 028702E 02 10 027821E-08 34 028702E 02 10 0150902-08 24 028914z 02 11 083542E-08 23 028944E 02 11 -043617E-08 16 030096E 02 12 062539C-03 27 030096E 02 12 -010394E-08 29 031603E 02 13 051291E-0 40 031603E 02 13 -087801E-09 31 032384E 02 14 -095144E-03 22 0323346 02 14 013992E-08 25 032729E 02 15 -0641162-09 39 032729E 02 15 0253182-09 39 034836E 02 16 010018E-08 37 034836E 02 16 052478E-11 48 036578E 02 17 015030E-07 17 03657E 02 17 -010723E-08 28 038611E 02 18 014308E-07 18 038611E 02 18 082028-~09 32 033819E 02 19 0254862-09 44 038319E 02 19 0479945-59 36 041914E 02 20 -024586E-08 35 0419146 02 20 -0932932-09 30 0482252 02 21 013411E-07 19 08225E 02 2l 043665E-c8 17 049330C 02 22 -031366E-09 43 0A93302 02 22 -010478-09 41 0514622 02 23 -067607E-08 26 051462E 02 23 -0242252-08 21 052124E 02 24 -033333E-10 47 052121E 02 4 -0127775-10 47 05224E 02 25 0815392-10 45 052244E 0 25 0317125-10 45 052839E 02 26 -099237E-12 50 052839E 02 26 -041720E-12 50 052912E 02 27 -073416E-09 38 052912E 02 27 -0402012-09 38 055603E 02 28 049013E-09 4z 055803E 02 28 055758E-10 44 0119575 02 34 -040304E-03 30 011957E 02 34 064083E-08 13 012446E 02 35 027752E-07 12 0124462 02 35 -038676C-07 1 01601E 02 26 -075719E-07 5 016801E 02 36 -019740E-07 4 0173095 02 37 031080E-08 32 0173092 02 37 0171312-08 23 020952E 02 38 -013386E-07 20 020952E 02 38 011986E-07 8 023amp72E 02 39 -013355E-06 3 023872E 02 39 031335E-07 2 027020E 02 0 0120836-04 4 027020E 02 40 -0137261-07 6 029155C 02 41 -048516E-07 8 029155E 02 41 0420685-08 19 030048E 02 42 -071893E-03 25 03004ampE 02 42 -020369E-09 40 03080OE 02 q3 -010772E-07 21 030300E 02 43 011715E-08 27 0316355 02 44 -040335S-07 9 031635 02 4 010268E-07 10 032753E 02 45 0498392-09 41 032753E 02 45 -068950E-10 42 033123E 02 46 071781E-07 6 033123E 02 46 -012127E-07 7 0369209 02 47 031742E-07 11 03692E 02 47 -075837E-09 33 037858 02 48 -027017E-07 13 03788E 02 48 -056302E-09 35 038871E 02 0436SE 02
49 so
-046640E-0 051364-07
28 7
033871E 02 043463E 02
49 50
-063798E-09 015979E-07
34 5
045841E 02 51 -021763E-07 15 045341E 02 51 -096402E-08 11 051102E 02 52 0457552-08 29 051102E 02 52 018757E-08 22 052331E 02 53 -08764E-11 49 052131E 02 53 -0423085-11 49 0522272 02 54 -037596E-10 46 052227E 02 54 -015255E-10 46 0594755 02 55 -0163705-10 48 059475E 02 55 -059996E-10 43 06078E 02 56 -072304E-08 24 06074CE D2 56 -0919412-03 12 0651352 02 57 032407E-08 31 065135E 02 57 -02853E-08 20 067311C 02 55 028742E-03 33 067311E 02 58 0594602-03 14
RATE COEFFICIENTS RESPONSE FROM = 9026 INPUT FROM 5132 RATE COEFPICIENTS RtSPONSE FROM 9024 INPUT FRDM 5133
-o
FREQUENCY 0137642 02 0175252 02 0181332 02 0193702 02 0229392 02 0257962 02 026702E 02 0289442 02 030096E 02 0316032 02 032384E 02 0327292 02 03136E 02 0365782 02 033611E 02 0388192 02 041914E 02 D482252 02 0193302 D2 0514622 02 0521242 02 052214E 02
MODE NO 4 5 6 7 8 9
10 11 12 13 14
15 16 17 18 19 20 21 22 23 24 25
COEFFICIENT -0491122-11 -0341822-07 0332932-07 0753552-06 0705102-09 0191792-08 095561E-09 05396a2-08 0275702-08 013233E-07 015611E-U8 015512E-09 0752002-09 0259002-03 013184-07 0116752-09 0115852-09 0320192-09
0844382-11 07790IE-07 065572E-11 012113E-09
RANK 48 7 a 1
30 2z 27 17 19 13 24 38 29 20 14 41 42 36 46 5
47 40
FREQUENCY 0137645 02 017525E 02 0181332 02 019370E 02 0229392 02 025796E 02 023702E 02 0239442 02 03D096E 02 031603E 02 032334 02 032729E 02 0348362 02 0365780 02 0386112 02 033819E 02 041914E 02 0482252 02 0493301 02 051462E 62 052124E 02 052244E 02
MODE No 4 5 6 7 8 9
10 11 12 13 14 15 14 17 16 19 20 21 22 23 24 25
COEFFICIENT -0660902-06 0167912-07 0207482-06
-088126E-09 0453 62-06 025424E-06
-017401E-08 015775E-03
-096999E-11 0213392-10
-0144922-08 041436E-09
-018717C-09 -0107292-07 -048552-08 -0267532-08 -0877102-07 -019910E-06 -031659c-08 0184542-09
-0977222-10 -04343EE-10
RANK 1
15 8 33 2 5
31 33 47 46 34 40 q2 16 22 27 11 9
25 43 44 45
052839E 02 0529122 02 055803E 02 0119572 02 012A461 02 016801E 02 017309E 02 0209522 02 023372C 02 027020E 02 02915EE 02 0300482 02 008002 02 0316352 02 0327532 02 0331232 02 0369202 02 0378832 02 038B71E 02 043468E 02 0458412 02 0511022 02 052131E 02 052227E 02 0594752 02 0607422 02 0651352 02 067311E 02
26 27 28 34 55 36 37 30 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57
58
0660822-12 053150E-08 0361302-09 0504742-09 0468482-06
-05622E-09 -020680E-03 -039334E-09 0290962-07 0106432-06 0162762-07 038896E-09 0138222-09 0640832-08
-0479432-10 0210652-07 0113512-06 014276E-07 010133E-08 011020E-OB 018339E-0B
-04B8E-1o 0167902-10
07903E-13 0273952-09 064429E-0B 0S146E--09 0365042-07
49 18 35 32 2
31 21 33
9 4
11 34 39 16 43 10 3
12 26 25 23 44 45
50 37 15 23
6
0528392 02 0529122 02 055803C 02 011957E 02 012146E 02 016301E 02 0173092 02 020952E 02 023872E 02 0270202 02 0291552 02 0300480 02 030amp00E 02 031635[ 02 032753E 02 033123E 02 0369202 02 0378H82 02 0388712 02 043463E 02 0458412 02 051102C 02 052131E 02 052227E 02 0594752 02 0607402 02 0651352 02 0673112 02
26 27 28 34 35 36 37 38
39 40 41 42 43 44 A5 46 47 48 49 50 51 5z 53
54 55 56 57
58
-0365242 -11 -042653E-09 O12903E-08 0253922-06 033907208
-0381982-06 -01059E-07 036636E-06
0143302-06 -0267872-08 -08229E-08 -0780532-08 -0970672-09 0300662-07 -0117252-08 0336SO-08
-023222E-08 -0219IIE-07 -026071E-08 -024664E-06 01644E-08
-0666372-07 -043082C-11
-016222E-B -0604052-11 -061998E-08 0105572-07
-0310162-09
50 39 35 6
24 3
17 4
10 26 zo 19 37 13 36 23 29 14 28 7 32 12 49 30 48 z1 18
41
RATE COEFFICIENTS
FREQUENCY MODE 0137642 02 0175252 02 013133E 02 0193702 02 0229390 02 025796L 02
RESPONSE FROMl
NO COEFFICIENT 4 -0306972-06 5 -029599E-08 6 -06978E-09 7 -021415f-1O a -0156662-06 9 -014462E-06
0287022 02 10 -0948152-09 0289442 02 11 -0323582-99 030096E 02 12 0161222-11 0316032 02 13 -0365282-10 032384C 02 14 021112E-09 03Z7290 02 15 -016362E-09 0436E 02 16 -098C45E-12 03657CE 02 17 076545E-09 038611E 02 13 -02000ampE-09 038819E 02 19 -O50330E-O 0419142 02 20 -033234-07 03 252 02 21 -064026E-07 049330E 02 22 -010576E-08 0514G2E 02 23 066124E-10 052124E 02 24 -03745E-10 052244E 02 25 -01839c-10
t0 0528392 02 26 -0153552-11 0529012E 02 27 -023356E-09 0558 03 02 26 014678E-09 011957E 02 34 -040371C-06 012 6E 02 35 -0472542-00 01601E 02 36 -00007 -06 0173092 02 37 -058395E-08 020952E 02 38 -0032804E-06 0230722 02 39 -0336222-07 0270202 02 40 0304222-09 02915S2 02 41 0591611-09 030043E 02 42 -0221162-09 0308002 02 43 0105562-09 031635C 02 44 -0765402-08
032753E 02 45 016220V-09 0331232 02 46 -065297E-09 0369208 02 47 0554302-10 037882 02 48 -04-5662C-09 038871E 02 49 -035661E-09 0434682 02 50 -0767292-07 045341E 02 51 072U60E-09 0511022 02 52 -0273182-07 052131E 02 53 -020797E-1 052227Q 02 54 -0739332-09 0594752 02 55 -0221382-30 060782 02 56 -078837E-08 065135E 02 57 -092968E-c8 067311E 02 5B -064165-09
9025 INPUT FROM - 5133
RANK 3
18 25 45 4 5
20 21 48 43 35 36 50 22 32 16 10 8
19 40 42 46 49 33 38
I 17 6
is 2 9
31 28 34
39 14
37 26 41 29 30 7
54 11 47 23 44 13
12 27
RATE COEFFICIENTS RESPONSE FROM =
FREQUENCY MODE NO COEFFICIENT 013764E O 4 032258E-08 017525F 02 5 -0231312-07 018133E 0 6 019124E-07 019370E 02 7 015292E-08 022939E 02 8 018821E-07 025796E 02 9 -0133500-07 02a7026 02 10 -06004E-09 028944E O 11 0111342-08 030096E 02 12 -0427752-11 031603C 02 13 05507S2-09 0323842 02 14 02377a2-09 032729E 02 15 -010025E-09 034836E 02 16 -014050E-09 0365782 02 17 -01868GE-08 033611E 02 18 -0450I 0-08 038819E 02 19 -012255E-08 04190 0E2 20 O41330E-08 0482252 02 21 -0475362-DO 049330E 02 22 085227E-10 05146220 2 23 -021236E-08 052144 02 24 0192E-10 0522442 02 25 -0719590-10 0528290 02 26 024321E-11 052912E 02 27 0308792-08 05$803E 02 28 0951122-09 0119572 02 34 -6319250-07 012446E 02 35 0572392-07 016601E 02 36 -028753E-03 017309E 02 37 07049 0-08 0209520 02 38 0109160-07 023872E 02 39 -0312192-07 0270202 02 40 -0235872-08 029155E 02 41 0228902-08 030048E 02 42 0422322-09 030800E 02 43 012454E-10 0316352 02 44 -047767E-08
032753E 02 45 0112782-09 033123E 02 46 0113120-08 0369200 02 47 -0830382-03 0378882 02 48 0115782-07 038871E 02 49 056643C-09 043462 02 50 -052914E-08 0458312 02 51 -013860E-09 051102E 02 52 065364E-09 052131E 02 53 082531E-11 052227E 02 54 0383080-11 0594752 02 35 010109C-09 060712 02 56 0552(62-03 065135E 02 57 0277372-04 067311E 02 58 -0393920-00
9024 INPUT FROMl 5133
RANK 19 4 5 27 6 7 33 30 40 35 37 42 38 26 16 28 17 is 43
5 45 44 s0 20 31 2 1 1
11 9 3
23 24 36
46 14 40 29 I 3 34 13 39 32 47 49 41 12 22 18
INPUT FROM = 5131 RATE COEFFICIENTS RESPONSE FRDM 90045 INPUT FROM = 5131RATE COEFFICIENTS RESPONSE FROM = 90044 FREQUENCY MODE NO COEFFICIENT RANK FREQUENCY MODE NO COEFFICIENT RANK
013764E 02 017525E 02 01181332 02 01937(E 02 0229392 02 0257962 02
4 5 6 7 8 9
00 00 00 00 00 00
50 49 48 47 46 45
0deg1376AE OZ 0175252 02 0181332 02 0193702 02 022939E 02 025196E 02
4 5 6 7 0 9
-054056E-08 -0164622-08 -016567E-07 051215E-09
-0692D2 -07 -015557E-07
9 i5 6 19 1 7
0287022 02 0289442 02 030096E 02
10 I 12
00 00 00
44 43 42
028702E 02 029044E 02 030096E 02
10 11 12
028132E-07 -034513E-08 -034299E-08
5 10 11
031603E 02 13 00 41 0316032 02 13 -02980E-08 13
032384E 02 U3Z7ZE 02 034336r 02
14 15 16
00 00 00
40 31 38
032366E 02 0327295 02 034836E 02
14 15 16
049854E-07 0284882-08
-0740612-09
4 14 16
0365782 D2 17 00 37 036578E 02 17 0312292-08 12
038611E 02 18 00 36 0386116 02 18 048754E-07 3
0333102 02 19 00 35 0388192 02 19 -038078E-07 4
041914E 02 0482252 02
20 21
00 00
34 33
041914C 048225C
02 02
20 21
-0825952-08 0125612-09
8 20
0493302 02 22 00 32 049330E (2 22 012134E-09 21
051462E 052124E
02 02
23 24
00 00
31 30
051462E 2 05212E (2
23 24
-054018E-09 063324E-13
18 25
052244E 02 052339 D2
25 26
00 00
29 28
0522442 0528392
C2 02
25 26
052076E-10 -042938E-11
23 24
f)(D
052912E 02 05580E 02 011957E 02
27 28 34
00 00
-0140792-07
27 26 6
052912E 02 0558035 02 011957E 02
27 28 34
-069719E-09 0963082-10 00
17 22 50
012446E 02 01601E 02
35 36
012932E-07 041334E-07
8 4
OZ446E (2 0168012 (2
35 36
00 00
49 48
017309C 02 37 -0637342-07 2 017309E 02 37 00 47
0209522 02 38 -0518992-07 3 0209522 02 38 00 46
023372E 02 39 0849472-07 I 023872E 02 39 00 45
027D202 02 029155E 02
40 41
-0831702-08 -015102E-07
12 5
027020E 02 029155E 02
40 41
0O 00
44 43
030048E 02 42 -023645E-09 1 030048E 02 42 00 qz
030300E 02 43 032968C-0 15 03080OE 02 43 00 41
031635E 02 44 059412E-03 13 0316352 02 44 00 40
032753E 02 0331232 02 036920E 02
45 46 47
-083392E-10 0353422-08 0010E-07
21 14 7
032753E 02 033123E 02 036920E 02
45 46 47
00 00 00
39 3 37
03738E 02 48 -011282E-07 9 0378881 02 48 00 36
038571E 02 49 -U25866E-08 17 038871E 02 49 00 35
043S682 02 045S412 02
so 51
-0121862-09 -0106992-10
20 23
043468E 02 045841E 02
50 51
00 00
34 33
051102E 02 52 -0276832-08 16 01102E 02 52 00 32 052131C 02 53 0227332-11 25 052131E 02 53 00 31
0522272 02 54 -062986E-11 24 052227E 02 54 00 30
0594752 02 0607482 02
55 56
0764192-10 -094277C-08
22 11
0594750 02 0607482 02
55 56
00 00
29 28
065135C 02 57 022672E-08 18 065135E 02 57 (0 27
067311E 02 58 010517E-07 10 067311E 0Z 58 00 26
RATE COEFFICIENTS RESPONSE FROM -
FREQUENCY MODE NO COEFFICIENT 013764F 02 4 00 017525E 02 5 00 018133E 02 6 00 0193702 02 7 00 022939E 02 8 00 0Z57963 02 9 00 028702E 02 10 00 028944 02 11 00 030096E 02 12 00 031603E 02 13 00 0323342 02 14 00 032729E 02 15 00 031836E 02 16 00 036578E 02 17 00 038611E 02 18 00 038319E 02 19 00 0419144 02 20 00 0482252 02 21 00 0493303 02 22 00 051462C 02 23 00 052124E 02 24 00 052244E 02 25 O0 0528392 02 26 00 0529122 02 27 00 055303E 02 28 00
90046 INPUT FROM = 5131 RATE COEFFICIENTS RESPONSE FRDM -
RANK FREQUENCY MODE NO COEFFICIENT
so 013764E 02 4 00 49 017525E 02 5 00 48 018133E 02 6 00 47 019370E 02 7 00 46 022939E 02 8 00 45 025796E 02 9 00 44 028702E 02 10 00 43 028944E 02 11 00 42 030096E 02 12 00 41 031603E 02 13 00 40 032384S 02 14 00
39 032729E 02 15 00 38 034836E 02 16 00
37 0365762 02 17 00 36 038611E 0Z 18 00 35 038819E 02 19 00 34 041914E 02 20 00 33 0482252 D2 21 00 32 049330E 02 22 00 31 051462E 02 23 00 30 052124E 02 24 00 29 0522q4E 02 25 00 26 052839E 02 26 00 27 052912E 02 27 00 26 055803E 02 28 00
011957E 02 34 040438E-08 16 011957E 02 34 -012509E-07
012446E 02 35 033674E-07 5 0124463 02 35 054324E-07 016301a 02 36 091195E-05 9 016801C 02 36 073710-07
017309E 02 37 095788E-07 I 017309E 02 37 -038646E-08
020952E 02 38 -027653-07 7 020952E 02 38 0230663-07
023872E 02 39 -093995E-07 2 023872E 02 39 016944E-06
0270202 02 10 030053E-07 6 027020E 02 40 -026653E-07 0291562 02 41 052135E-08 13 029155E 02 41 -076090E-07
03004E 02 42 -019543E-09 21 030048E 02 42 -034121E-08 030800E 02 43 026246E-09 20 030800E 02 43 -060624E-08 0316353 02 44 0844152-08 10 031635E 02 44 -055090E-07
032753E 02 45 -09E292E-10 22 032753E 02 45 -0257172-09
033123E 02 46 0296382-08 17 033123E 02 46 -032330E-07
036920E 02 47 0356e6E-07 3 0369202 02 47 -036999E-07 037888E 02 48 -0348722-07 4 037838E 02 48 0270383E-07
038871C 02 49 062712k-08 12 038871E 02 49 -046039E-08
0434682 02 50 -0129202-08 19 043468E 02 50 -024465E-00
045841E 02 051102E 02
51 52
-010508r-07 019933E-08
8 18
04581 02 051102E 02
51 52
-012775E-09 -052362c-08
052131C 02 53 -0969942-11 25 052131E 02 53 -077719E-11 052227E 02 54 010924E-10 24 052227E 02 54 014139E-10
059475E 02 060748E 02
55 56
-0690022-10 042721E-08
23 15
059475E 02 060748E 02
55 56
-0466522-09 -014453E-06
0651351 02 57 -045913E-08 14 065135E 02 57 0118552-07
0673118 02 58 070564E-03 11 067311C 02 58 067647E-07
90044 INPUT FROM 5132
RANK 50 49 43 47 46 45 44 43 42 41 40 39 33 37 36 35 3 33 32 31 30 29 28 27 26 13 7 4
18 12 1
I1 3
19 i 6
32 9 3 10 17 20 23 16 25 24 21 2
14 3
RATE COEFFICIENTS RESPONSE FROM -
FREQUENCY MODE NO COEFFICIENT 013764E 02 4 017525E 02 5 0181332 D2 6 019370E 02 7 022939E 02 a 025796E 02 9 028702E 02 10 028944E 02 11 030096E 02 12 031603E 02 13
032384E 02 14 032729E D2 15 034836E 02 16
03657ampE 02 17 032611E 02 1s 038C19E 02 19 041914E 02 20 048225E 02 21 049330E 02 22
051462E 02 23 052124E 02 24 052244E 02 25 052839E 02 26 052912R 02 27 055803E 02 28 011952E 02 34 012446E 02 35 016801E 02 36 0173092 02 37 0209520 02 3B 023872E 02 39 027020R 32 40 029155E 02 41 US00431 02 42 030300E 02 43 0316350 02 44 032753E 02 45 033123E 02 46 036920E 02 47 037533E D2 43 032871E 02 49 0434682 02 50 0458410 02 51 051102E 02 52 052131E 02 53 0522276 02 54 059475E 02 55 06074E 02 56 06513SE 02 57 067311E 02 50
027896E-09 25845E-U8
-0885975-07 012804E-06 016633E-07 02618E-07 051516E-07
-0711482-08 025835E-07 -019627E-07 -029e36E-07 -021532E-08 O84899E-09
-013285E-07 -034264E-07 025917E-08 083641E-09
-073061E-09 051860E-09
-084343E-08 0125750-11
-067669E-10 -021602E-11 -011906E-07 019558E-08 00 00 00 00 00 00 00 00 00 00 O 00 00 00 00 00 00 00 00 00 00 00 00 00 O0
90045 INPUT FROM 5132 RATE COEFFICIENTS RESPONSE FROM -
RANK FREQUENCY MODE NO COEFFICIENT 22 013764E 02 4 00 14 017525E 02 5 00 2 018133E 02 6 00 1 019370E 02 7 00 9 022939E 02 8 00 6 025796E 02 9 00 3 U2 702E 02 0 00
13 028944E 02 11 00 7 030096E 02 12 00
a 031663E 02 13 00
5 032384E 02 14 00 16 032729E 02 i5 00 18 034836E 02 16 00
10 036578E 02 17 00 4 038611E 02 18 U0
15 033819E 02 19 00 19 0419l4E 02 20 00 20 21
048225 02 21 00 049330E 02 22 00
12 051462E 02 23 00 25 0521242 02 24 00 23 052244E 02 25 00 24 052839E 02 26 00 l1 052912E 02 27 00 17 055803E 02 23 00 50 011957E 02 34 035929E-O 49 012446E 02 35 014146E-06 48 016801E 02 36 016262E-07 47 017309E 02 37 058082E-08 46 020952E 02 38 012293E-07 45 023U72E 02 39 -018749E-06 44 027020E 02 40 096309E-07 43 029155E 02 41 026267E-07 42 0300402E 02 42 -023483E-08 41 030800E 02 43 -048264E-09 40 031635E 02 44 -078274E-07
bull 39 032753E 02 45 -028597E-09 38 033123E 02 46 -027113E-07 37 036920E 02 47 -010037E-06 36 0378380 02 48 083573E-07 35 038871C 02 49 011162E-07 34 0434632 02 50 -025939E-07 33 0458412 02 51 -012547E-06 32 051102E 02 52 037703E-08 31 052131E 02 53 0331602-10 30 052227E 02 54 -024523E-10 29 059475E 02 55 042124E-09 28 0607480 02 56 065493E-07 27 065135E 02 57 -024008E-07 26 067311E 02 58 045387E-07
90046 INPUT FROM 5132
RANK 50 49 48 47 46 45 44 43 42 41 40 39 38
37 36 35 34 33 32
31 30 29 Z8 27 26 19 2 14 17 15 1 5 11 20 21 7
23 10 4 6 16 12 3
18 24 25 22 8 13 9
5133 RATE COEFFICIENTS RESPONSE FROM 90045 INPUT FROM RATE COEFFICIENTS RESPONSE FROM - 90044 INPUT FROM 5133
FREQUENCY MODE NO COEFFICIENT RANK FREQUENCY NCDE No COEFFICIENT RANK
so 013764E 02 4 -0183222-06 3 013764E 02 4 00
017525E 02 5 0174892-08 150175252 02 5 00 49
018133E 02 6 -0511192-07 4480181332 02 6 00 0193702 02 7 025312C-09 19470193702 02 7 00 022939E 02 8 0450532-06 146022939E 02 8 00 0257962 02 9 -0183882-06 245025796E 02 9 00 0237021 02 10 -032369C-07 5
0287022 02 10 00 44 0289442 02 11 -013434-OB 17
02a9q2 02 11 00 43 23030096E 02 12 -040071[-10030096E 02 12 00 42
031603E 02 13 -081657L-09 1841031603E 02 13 D0 032354C 02 14 -044335E-03 14
0323842 02 14 00 40 032729E 02 15 013915E-08 16
0327292 02 15 00 39 0348362 02 16 -015862E-09 21
0348362 02 16 00 38 036578 02 17 094833E-08 10
0365782 02 17 00 37 0386112 02 13 0116932-07 a
0336112 02 18 00 36 038819E 02 19 -0271002-07 735033819E 02 19 00 041914E 02 20 0293392-07 6
0419142 02 20 00 34 0q82252 02 21 010847E-07 9
0482252 02 21 00 33 049330E (2 22 0523452-08 12
049330E 02 22 00 32 051462C 02 23 023022E-09 20
051462E 02 23 00 31 0521242 02 24 036365E-11 25
0521242 02 24 00 30 052241 02 25 0401992-10 22
0522442 02 25 00 29 052839E 02 26 -0795052-11 24
052839E 0 Z6 00 28 0529122 02 27 -0691712-08 11
0529122 02 27 a0 27 055032 02 28 051488E-08 130558032 02 28 00 26
500119572 02 34 00
012446E 02 35 0663732-08 14 0119572 02 34 078806E-06 1
012446E 02 55 00 49
0168012 02 36 037365E-06 3 016801F 02 36 00 48
0173092 02 37 0131732-07 10 017309E 02 37 00 47
0209522 02 38 -063130E-06 z 0209522 02 38 00 46 45023872E 02 39 00
027020E 02 40 0590722-09 21 0238722 02 39 -0101802-06 4
027020E 02 40 00 44
02V155E 02 41 -0107012-07 12 0291552 02 41 00 43
03D04E 02 42 -037373E-03 1 0300482 02 42 00 42 41030300 02 43 00
0316350 02 44 04106E-07 7 031635E 02 44 00 40
0327532 02 45 060498E-09
0308002 02 43 -0541282-09 22
20 0327532 02 45 00 39
03313E 0 46 -0174082-08 18 033123E 02 46 00 38
036920C 02 47 0270672-08 16 0369202 02 47 00 37
037882 02 48 0219282-07 9 0378882 02 48 00 36
038871E 02 49 -0257352-03 17 038371E 02 49 00 35
0134682 02 50 0117472-07 11 0434682 02 50 00 34
045341E 02 51 0965532-11 24 0458412 02 51 00 33
051102E 02 52 0762602-07 6 051IOZE 02 52 00 32
0521312 02 53 -03amp2032-11 25 052151 02 53 00 31
052227E 02 54 04amp5312-09 19 0522272 02 54 00 30
059415E 02 55 -017214-09 23 0594752 02 55 00 29
0607482 02 56 -0123935-06 5 60748E 02 56 00 28
065135E 02 57 0386192-07 a 0651352 02 57 00 27
067311E 02 s3 -072999E-08 13 067311[ 02 58 00 26
RATE COEFFICIENTS RESPONSE FROII 90046 INPUT FROM 5133 RATE COEFFICIENTS RESPONSE FROM = 9014 INPUT FROM - 140391
N -P
FREQUENCY 013764E 02 017525E 02 018133E o 019370E 02 0ZZ939E O 025796F 0 028702E 02 0209E 0 030096E OZ 031603E 02 032341 O 0327Z92 02 034836E 02 036578E 02 038611E 02 038819E 02 041914C 0 043225E 02 049330E 02 051462E 02 052I4E O 052214E O 052839E 0 0529122 02 055803E 0 011957E 02 012446E O
ODE NO 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 34 35
COEFFICIENT 00 00 00 00 00 00 00 0
00 30 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00
-022635E-06 0172042-07
RANK 50 49 18 47 46 5 4 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 2
12
FREQUENCY 013764E 02 017525E 02 0181338 02 019370E 02 022939E 02 025796E 02 0287021 O OZ8944E 02 030096E 02 031603E 02 032384E 02 032729E 02 034836E 02 036578E 02 038611E 02 033819E 02 019142 02 08225E 02 049330E 02 051462C O 052124E 02 052244R 02 052839E 02 052912E 02 055803E 02 011957E 02 01246E 02
MODE NO 4 5 6 7 8 9
10 11 12 13 14 15 16 17 18 19 zo 21 22 23 24 25 26 27 28 34 35
COEFFICIENT 019423E-06 029316E-07
-0a7413E-06 -029917E-07 0982288-06
-023991E-06 -010283E-07 -061543E-03 -023355E-07 -051429E-09 -020576E-06 -011954E-07 -030533E-08 015300E-07 017759E-03 0307BIE-07 075344E-07
-07675P-07 -011670E-08 -043157E-10 -026487E-11 -010807E-09 -010704C-10 -024482E-08 -022969E-09 018382Q-98 -031422E-09
RANK 3 14 z 13
1 4 23 27 19 41 5 22 32 21 36 12 7 9 39 45 50 44 47 33 43 35 42
0
018018 0 017309E OZ 020952E OZ 0233722 02 027020E 02 029155E 02 030048E 02 030800 02 031635E OZ 032753E 02 033123E 02 036920E 02 037888E 02 038671E 02 043468C 02 2458412 02 051102E 02 052131E 02 0522272 02 059475E 02 060748E 02 065135E 02 067311E 02
36 37 38 39 40 41 42 43 4q 45 46 47 48 49 50 51 52 53 54 55 56 57 5
082437E-07 -019795E-07 -033643E-06 0201172-06
-021345E-08 036940E-08
-025497E-03 -043490E-10 050345E-07 (67274E-09
-014598E-08 071162E-08 067779E-07 062395E-08 012455E-06 094827E-08
-(54911E-07 0163002-10
-011886E-08 015543E-09 056158E-07
-078209E-07 -048978E-08
5 11 1 3
19 17 18 24 3
22 20 14 7
15
13 10 25 21 23 9 6
14
016801E 02 017309E 02 020952E 02 023872C 02 027020E 02 0291552 02 0300482 02 030800E 02 0316352 02 032753E 02 033123E 02 036920E 02 037888C 02 0388712 02 043468E 02 045841E 02 051102E 02 052131E 02 0522272 OZ 059475E 02 060748E 02 0651E35 02 067311E 02
36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58
0734062-07 -056546E-08 032792E-07 -012506E-06 -023956E-07 08585E-08
-035060Q-08 -023553E-07 -0268762-07 0319i1E-08 079403Z-08 053285E-08 0271122-07 020452-08 0164722-07 037069E-07 068040Q-08 030120C-11 063412-11 014246E-10 016541E-08
-011809E-08 0113412-08
a 28 11 6 17 24 30 18 16 31 25 29 15 34 20 10 26 49 48 46 37 38 40
I
R4TE COEFFICIENTS RESPONSE FRDM =
FREQUENCY MODE No COEFFICIENT D13764E 02 4 -0837442-03 0175252 02 5 -015242E-09 018133E 02 6 02064R-07 019370E 02 7 051512E-09 D22939E 02 8 029552E-06 0257962 02 9 -021006E-06 0287022 02 10 0326122-09 023944E 02 11 -0292685-08 D30096E 02 12 -0812632-08 0316035 02 13 -0172972-09 032342 02 14 -024272-67 0327292 02 15 -O62687E-08 0343361 02 16 -063378E-09 036578E 02 17 0491662-08 038611E 02 i8 042030E-09 03amp819E 02 19 033696E-07 D41914E 02 20 -030142c-07
048225E (2 049330E (2
21 22
-016311E-07 -0593952-09
050l62E OZ 23 -0151062-10 0521242 02 24 -0430202-11 052244amp 02 25 -064826C-10 052839E 02 052912E (2
26 27
-055574-11 -0107592-08
055803E 02 28 -0819462-10 011957E 02 34 -065735E-08 012446E 02 35 058541209 014801E 02 36 -0907912-08 017309E 02 37 0111911-08 020952E (2 38 029278C-07 023372E 02 39 -035029C-07 027020E 02 40 -069810E-08 029155E 02 A1 0234742-08 0300482 02 42 -0113642-09 030800E 2 43 -057326E-08 031635E 02 44 -0684442-08 032753E 02 45 0929502-09 033123E 02 0369202 02
46 47
0240842-08 017i 3 2 2-08
03788E 02 48 0819902-08 038871C O q9 03251SE-09 045468E 02 50 -0410702-08 04581E 02 51 02732E-07 051102E 02 52 0698442-08 052131E 02 53 027853E-11 052227E 02 54 -0549822-10 0594752 02 55 024185E-10 0607482 02 56 0696422-08 065135E 02 57 -0247992-07 067311E 02 58 -021178E-08
9015 INPUT FROM 140391 RATE COEFFICIENTS RESPONSE FROM -
RANK FREQUENCY MODE NO COEFFICIENT 13 013764E 02 4 0335772-08 41 017525E 02 5 0684592-07 10 018133E 02 6 048296E-07 36 019370E 02 7 -012350E-07 I 022939E 02 8 -020049E-08
a 0257962 02 9 002093E-08 33 028702E 02 10 0753822-09 25 02894E 02 11 069267E-09 15 0300962 02 12 -0721962-08 40 0316032 02 13 -018i 6E-08 3 032384E 02 14 0374172-07
21 032729E 02 15 026647E-08 33 034336E 02 16 -024417E-08 23 036578E 02 17 016285E-08 37 038611E 02 18 022951E-08 5 038819E 02 19 -0178132-07 6 041914E 02 20 -0254002-07
11 04822EE 02 21 -021946E-08 34 043302 02 22 015136E-10 47 051462C 02 23 -0461882-10 49 052124E 02 24 0488162-I 44 0522(4E 02 25 -028072E-09 48 052839E 02 26 -071972E-11 31 052912E 02 27 037290E-09 43 0558032 02 28 010324E-10 20 011957E 02 34 028563E-09 35 012446E 02 35 -010899E-08 12 O16OIE 02 36 -0142302-08 30 017309E 02 37 049399E-06 7 020952E 02 38 -097309E-08 4 023872C 02 39 -049943E-07
17 027020E 02 40 0357112-07 27 029155E 02 41 039945E-08 42 030048R 02 42 -0108592-09 22 03080DE 02 43 -013698E-09 19 031635E 02 44 0167832-08 32 0327532 02 45 066422E-09 26 0331232 02 46 -0135572-08 29 0369202 02 47 -036485E-08 14 037888E 02 48 080031E-08 39 038871E 02 49 059759E-09 24 0434 6BE 02 50 0212352-08 8 0458412 02 51 0199492-07
16 051102E 02 52 019646209 50 052131E 02 53 -078587E-11 45 052227E 02 54 038664E-11 46 059475E 02 55 -094928E10 18 0607482 02 56 -0720232-08 9 0651351 02 57 0609702-08
28 0673112 02 58 -0158602-07
9016 INPUT FROM 140391
RANK 20 I 3
10 24 1a 33 34 14 27 4 21 2a 29 23 8 6
24 43 4q 50 39 18 37 46 38 32 30 17 11 a 5 18 42 41 28 35 31 19 13 36 25 7
40 47 49 43 15 16 9
RATE COEFFICIENTS RESPONSE FROM
FREQUENCY MODE NO COEFFICIENT 013764E 02 4 -010583E-O 01752SE 02 5 -081293r-10 018133E 02 6 -010175E-08 019370E 02 7 018371C-09
022939E 02 a -041284E-08 025796E 02 9 064851E-09 028702E 02 10 -0216272-09 02894E 02 11 -012462E-10 030096E 02 12 -030349E-09 031603E 02 13 073633E-11 032384E 02 14 -027681E-08 032729E 02 15 -013828E-09 034836E 02 16 043712E-11 03657SE 02 17 021448E-08 038611E 02 10 04f278EL08 038019E 02 19 049434E-08 041914E 02 20 066472E-08 048225E 02 21 -028995E-08 049330E 02 22 -020917E-09 051462E 02 23 048360R-11 0521242 02 24 -08087aE-13 05224e4E 02 Z5 -051593E-11 052839E O Z6 050317E-I 0529122E 02 27 076591E-09 055803E 02 23 -019004E-10 011957E 02 34 -033298E-07 012446E 02 35 0304641-08 n16RO]r n2 36 0242361-06 017309E 02 37 039411E-07 020952E 02 38 -066230E-07 023872E 02 39 050190E-06 027020E 02 40 078443E-07 029155E 02 41 045076E-07 030048E 02 42 039380E-07 030300E O 43 044078C-06 031635E 02 44 023997E-06 032753E 02 45 -049590E-08 0331231 02 46 --032328E-07 036920E 02 47 -049482E-07 03788BE 02 46 -018455E-06 038871E 02 49 -00015E-07 043468E 02 50 -010930E-06 045841E 02 51 -029399E-06 051102E 02 52 -017053E-06 052131E 02 53 -0215732-10 052227E 02 54 057358E-10 059475E 02 55 0492770-11 060743E 02 - 56 02502SR-07 065135E 02 57 024236E-00 067311E 02 58 -012898E-07
9014 INPUT FRCM 140392
RANK 30 39 31 37 23 33 35 43 34 44 27 38 48 29 24 22 20 26 36 47 50 45 49 32 42 15 25 4
13 10 1 9
12 14
a 5
21 16 11 6
19 8 3 7
41 40 46 17 28 18
RATE COEFFICIENTS
FREQUENCY MODE 013764r 02 017525F 02 018133E 02 019370E 02 022939E 02 025796E 02
4 5 6 7 8 9
028702E 02 028944E 02 030096E 02 031603E 02 032384E 02 032729E 02 034336E 02 036573E 02 038611E 02 038819E 02 041914E 02 048225E 02 049330E 02 05162E 02 052124E 02 0522441 02 052839t 02 052912E 02 0S5803E 02 011957C 02 012446E 02 016801E 02 017309E 02 0209E2E 02 023872C 02 OV270 Oz 029155E 02 030048E 02 030800E 02 031635E 02 032753C 02 033123E 02 036920E 02 03788E 02 035871E 02 043468E 02 045841E 02 051102E 02 052131 02 052227E 02 059475E 02 060748E 02 065135E 02 067311C 02
10 11 12 13 04 15 16 17 18 19 20 21 22 23 24 25 26 27 28 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58
RESPONSE FROM
ND COEFFICIENT 022402-lO O42266E-12 024030E-10
-031632E-11 -01220E-08
047041E-09 068592E-11
-059265E-lI -010560E-09 024764E-11 -083985E-09 -072513E-10 0907341-12 068563E-09 097694E-09 05411SE-08
-026593E-08 -099202E-09 -010646E-09 016927E-11 -013136E-12 -030949E-11 026124E-12 033661E-09 -067000E-11 011907E06
-056755E-0U8 -029976E-07 -077997E-08 -O59173E-07
014058E-06 022839c-07 012324E-07 012479E-08 010728E-06 061112E-07
-014131C-08 -099571E-08 -016188E-07 -055810E-07 -O15924E-08 027253E-07
-021671E-06 -01750SE-06 -019948E-10 -049710E-09 083653E-11 010536E-06 050897E-07 024087E-07
9015 INPUT FROM 140392
RANK 37 43 36 43 25 31 40 42 34 45 28 35 47 29 27 20 21 26 33 46 50 44 49 32 41 4 19 11 18
8 3 14 16 24 5 7 23 17 15 9 22 12 1 2 38 30 39 6 10 13
INPUT FRDM 1 RATE COEFFICIENTS RESPONSE FROM - 9014 INPUT FROM - 140393RATE COEFFICIENTS RESPONSE FROM - 9016 140392
FREOUENCY MODE NO COEFFICIENT RANK REQUENCY NODE NO COEFFICIENT RANK
013764E 02 4 -09014E-11 42 213764E 02 4 -066442E-06 2
017525E 02 5 -018953E-09 28 017525E 02 5 -048002E-07 15
018133F 02 6 05A218F-lO 34 01B133E 02 6 -020170E-06 4
019370E 02 7 075837E-10 32 519370E 02 7 072227E-07 12
022939E 02 5 0826SE-11 q3 022939E 02 8 -079302E-06 1 025796E 02 9 -0187SE-10 39 025796E 02 9 070178E-07 13
028702E 02 10 01585SE-10 40 02 72E 02 10 -013118E-07 27
02394E 02 11 014026E-11 47 023944E 02 11 -011529E-08 39
030096C 02 12 -093817E-10 31 030096E 02 12 -0152138-07 25
031603E 02 13 026423E-10 38 031663E 02 13 037949E-09 41
032384E 02 14 050339E-09 26 032384E 02 I -O10669-06 6
03279E 02 15 030024E-10 37 032729E 02 1 -049577E-08 34
034836E 02 16 034956E-ll 45 034836E 02 16 064116E-09 40
036578E 02 17 0227102-09 27 036578E 02 17 093656E-07 7
038611E 02 18 053547E-08 16 03861E 02 18 087123E-07 9
0388191 02 19 -028607E-08 21 038819E 02 19 093229E-07 8
041914E 02 20 -022409E-08 23 04194E 02 20 073376E-07 11 048225E 02 21 -013347E-09 29 043225E 02 21 026777E-07 23
049330E 02 22 027128E-11 46 049330E 02 22 085789E-10 44
051462E 02 23 051756E-11 44 051462E 02 23 012727E-07 28
052124E 02 24 014906E-13 50 052122E 02 24 084840E-11 48
052244E 02 25 -013402E-10 41 B522442 02 25 021926E-09 42
052539E 02 26 033833E-12 49 052839E 02 26 022813E-10 45
052912E 02 27 -011666E-09 30 054912E 02 27 062854E-08 33
055803E 02 20 085419E-12 48 055803E 02 28 032571C-07 21
011957E 02 34 -051740E-08 17 011957E 02 34 074527E-08 32
012446E 02 35 010566E-07 14 012446E 02 35 014131E-09 43
n16RnIE 0 36 -046984E-08 19 0161301 02 36 -024903E-06 3
017309E 02 37 -034778E-07 7 017309E 02 37 -034619E-08 37
020952E 02 38 019668E-07 10 020952E 02 38 -040940E-07 17
023872E 02 39 020044E-06 1 023872E 02 39 -012674E-06 5
027020E 02 40 -011694E-06 4 027020E 02 40 -017369E-07 24
029155E 02 41 020971E-07 9 029155E 02 41 035033E-07 18
030048E 02 42 011925E-08 24 030048E 02 42 07990ZE-08 29
030800E 02 43 025635E-08 22 030800E 02 43 0868702-07 10
0363SE 02 032753E 02
44 45
-D1498SE-07 -010313E-08
11 25
031635E 02 032753E 02
44 45
068784E-07 -014314E-07
14 26
033123E 02 036920E 02
46 47
056050E-0U8 033881E-07
15 a
033123E 02 036920E 02
46 47
-020179E-07 -033363E-08
22 38
037888E 02 48 -054477E-07 6 037868E 02 48 -044223E-07 16
038871E 02 49 -029266E-08 20 038671E 02 49 -04 53E-08 36
043468C 02 50 -011091E-07 12 043468E 02 50 -033106E-07 20
045841E 02 51 -015821E-06 3 045841E 02 51 -034384E-07 19 051102E 02 52 -049238E-28 18 0511OE 02 52 077994E-08 30
052131E 02 53 0562851-10 33 052130E 02 53 -013675E-11 5o
052227E 02 54 034956C-10 35 052227E 02 54 -011178E-10 47 059475E 02 55 -032836L-10 36 059475E 02 55 004531E-11 49 06074B6E 02 56 -010897E-06 5 060748E 02 56 0766OOE-00 31 065135E 02 57 -0125135-07 13 065135E 02 57 -0153292-10 46 067311E 02 58 018038E-06 2 067311E 02 58 -047031E-08 35
RATE COEFFICIENTS RESPONSE FROM
FREQUENCY NODE NO COEFFICIENT 013764E 02 4 014114E-07 017525E 02 5 024957E-09 018133E 02 6 047635E-08 019370E 02 7 -012436E-08 022939E 02 8 -023558E-06 0257162 02 9 050873E-07 0287022 02 10 041606E-09 02894142 02 11 -054828-09 030096E 02 lZ -052953E-08 0316032 02 13 0127636-09 0323846 02 14 -032370E-07 032729E 02 1s -0259982-08 034B36E 02 16 0133090-09 0365782 02 17 0299402-07 03amp621E 02 18 020620E-07 038192 02 19 010206E-06 04f914E 02 20 -029354E-07 048225E 02 21 091612E-08 049330E 02 22 043663E-10 0514622 02 23 0449475-08 052124E 02 24 013786E-10 05224 2 02 25 013152E-09
m 052839E 02 26 0118442-10 00 0529122 02 27 027624C-03
055803E 02 28 011620E-07 0119575 02 34 -026650E-07 012446E 02 35 -026326E-09 016801E 02 36 0308010-07 017309E 02 37 068513E-09 020952E 02 38 -036553E-07 023872E 02 39 -035500E-07 027020E 02 40 -050615E-08 029155E 02 41 010399E-07 030048E 02 42 025320E-09 030800E 02 43 021144E-07 0316352 02 44 017517E-07 032753E 02 45 -041655E-08 0331235 02 46 -085472E-08 036920E 02 47 -010914E-08 037808E 02 43 -013375E-07 038871E 02 49 -070788E-09 043468E 02 50 0825432-08 0458412 02 51 -0253462-07 051102E 02 52 080062E-08 0521319 02 53 -012645E-11 0522272 02 54 096871E-10 0594752 02 55 0143510-10 060768E 02 56 0322845-07 0651352 02 57 -032192E-09 067311E 02 58 087829E-08
9015 INPUT FROM - 140393
RANK 16 41 27 32 I 3
37 36 25 44 6
31 42 9
14 2
10 20 46 28 48 43 49 30 18 11 39
8 35 4 5
26 19 40 13 15 29 22 33 17 34 23 12 24 50 45 47 7
38 21
RATE COEFFICIENTS RESPONSE FRDH =
FREQUENCY NODE NO COEFFICIENT 013764E 02 4 -056590E-08 017525E 02 5 -011209E-06 018133E 02 6 011144E-07 019370E 02 7 029816E-07 022939E 02 a 016186E-08 025796E 02 9 -019872E-08 028702E 02 10 096170E-09 028944E 02 11 012976E-09 030096E 02 12 -047045E-08 0316035 02 13 01361PE-08 0323842 02 14 019402E-07 032729E 02 15 011051E-08 034836E 02 16 051272E-09 0365782 02 17 0991696-08 0386112 02 18 011260E-06 038819C 02 19 -053952C-07 041914E 02 20 -024736E-07 0482252 02 21 012326-08 0493302 02 22 -011127E-11 0514622 02 23 0136215-07 052124E 02 24 -015636E-11 0522442 02 29 056954E-09 052839E 02 26 015339E-10 052912E 02 27 -095738E-09 055803E 02 28 -014640E-08 0119572 02 34 0115802-08 0124462 02 35 0490132-09 016801E O 36 08276E-08 017309E 02 37 030549E-08 0209522 02 38 012149E-07 023872E 02 39 -050615E-07 027020E 02 40 025892E-07 029155E 02 41 017695E-07 030048E 02 42 024195E-09 030800E 02 43 050522E-09 0316352 02 44 -0429531-08 0327532 02 45 -029767E-08 0331232 02 46 048113E-08 036920E 02 47 0228440-08 037388E 02 48 -013055E-07 038871E 02 49 -013010-08 043468E 02 50 -0426792-08 045841E 02 51 -018504E-07 051102L 02 52 022520E-09 052131E 02 53 0356792-11 052227E 02 54 -068120E-11 0594752 02 55 -056327E-10 0607482 02 56 -033388E-07 065135E 02 57 079145r-10 067311E 02 58 065772E-07
9016 INPUT FROM 140393
RANK 18 2 16 7 28 27 35 43 21 30 10 34 38 17 I 4 9 32 50 13 49 37 46 36 29 33 40 19 24 15 5 8
12 41 39 22 25 20 26 14 31 23 11 42 48 47 45 6
44 3
1140391INPUT FROM - 140391 RATE COEFFICIENTS RESPONSE FROM - 9025 INPUT FRDM RATE COEFFICIENTS RESPONSE FRDM = 9024
FREQUENCY MODE NO COEFFICIENT RANK FREQUENCY NODE NO COEFFICIENT RANK
013764E 02 4 014769E-06 3 013764E 02 4 031798E-06 3
O17525E 02 5 -051706E-08- 16017525E 02 5 029333E-07 13
018133E 02 6 027285E-08 21018133E 02 6 -080866E-OS 2
0193702 02 7 -066316E-09 32019370E 02 7 -027290E-07 14
022939E 02 8 -035870E-06 1O939E 02 8 010383E-05 1
025796E 02 9 016774E-06 2 025796E 02 9 -0294892-06 4
028702E 02 10 -059503E-08 15023702E 02 10 -010971E-07 21
29 028944E 02 11 0246103-08 24028944E 02 11 -047138E-08 030096E 02 12 030986E-08 19
030096E 02 12 -018643E-07 18 031603E 02 13 0248211-09 36
031603E 02 13 -01450E-09 42 032384 02 14 021952E-07 8
0323842 02 14 -0149297-06 6 032729E 02 15 0289042-08 20
0327Z9E 02 15 -0731962-08 27 034836E 02 16 -011093E-10 44
0348362 02 16 -021177E-OE 35 036573E 02 17 -067760E-09 31
036578E 02 17 094974E-03 23 038611E 02 18 065864-10 41
038611E 02 18 0114892-05 38 038819E 02 19 -0209182-07 9
038819E 02 19 -011108E-07 20 041914E 02 20 056836E-07 4
041914E 02 20 014977E-06 5 043225E 02 21 -0295503-07 7
O48225E 02 21 -090759E-07 8 049330E 02 22 -083971E-09 29
049330E 02 22 -0251372-08 33 051462E 02 23 050276-11 47
051462E 02 23 016264E-10 46 052124E 02 24 -037079E-11 48
052124E 02 24 -096732E-11 47 052244E 02 25 -027289E-10 43
052244E 02 25 -070166E-10 44 48 052839E 02 26 -014506E-11 49
052839E 02 26 -034696E-11
Lo 052912E 02 27 -022709E-09 41 052912E 02 27 -0124362-09 38 055803E 02 28 064881C-11 46
055803E 02 28 057032E-10 45 011957E 02 34 -013797E-07 11
011957E 02 34 0867741-08 24 012446E 02 35 0126652-08 27
012446E 02 35 -0908BOE-09 39 016801E 02 36 016822E-07 10
916801E 02 36 064549E-07 9 0173092 02 37 -02054E-08 25
017309E 02 37 -043639E-08 30 020952E 02 38 -0468402-07 5020952E 02 38 052311E-07 10 023872E 02 39 030719[-07 6
023872E 02 39 -013092E-06 7 027020E 02 40 25652E-08 22
O27020E 02 40 -022587E-07 15 25 0291552 02 41 -064575E-09 33
0291552 02 41 074473C-08 32 030048E 02 42 -092334E-10 390300482 02 42 -032589E-08 17 030800E 02 43 020960E-08 26030800E 02 43 -019274E-07
0316352 02 44 049896E-08 17031635E 02 44 -019600C-07 16 032753C 02 45 023775E-08 34 0327532 02 45 -03289E-09 35
0331232 02 46 -095915E-09 28033123E 02 46 056772E-08 28 036920E 02 47 034891E-08 31 036920E 02 47 -033360E-10 40
19 037883 02 48 0380952-09 34037888E 02 48 0182802-07
038871E 02 49 023264E-09 37038871E 02 49 017008E-08 37
0434682 02 50 011030E-07 13043468E 02 s0 035453C-07 11 045841E 02 51 -030146E-07 12 045841E 02 51 -0134862-07 12
0511O2E 02 52 043902E-08 18051102E 02 52 010709E-07 22 49 O52131E 02 53 011514E-11 50
052131E 02 53 023851E-11 43 052227E 02 54 -0575302-10 42052227E 02 54 -014178E-09
0594752 02 55 071615E-11 45059475E 02 55 019541E-11 50
060748 02 56 024718E-08 2306074E 02 56 019439E-08 36 065135E O 57 0735002-08 26 065135E 02 57 -064727E-08 14
067311202 58 -072095E-09 30067311E 02 53 -0348492-09 40
RATE COEFFICIENTS RESPONSE FROM = 9026 INPUT FROM 140391 RATE COEFFICIENTS RESPONSE FROM m 9024 INPUT FROM 140392
FREQUENCY NODE NO COEFFICIENT RANK FREQUENCY MODE NO COEFFICIENT RANK 013764E 02 4 -0155202-08 32 0137642 02 4 -085365E-09 32 01752SE 02 5 -040406E-07 4 017525E 02 5 -081339E-10 39 018133E 02 amp -074569E-07 1 018133E 02 6 -094152E-09 31 0193702 02 7 0473542-07 2 019370E 02 7 016753E-09 37 02939E 02 a 0430952-07 3 022939E 02 8 -043633E-08 23 0257962 02 9 0154842-07 8 025796E 02 9 066004E-09 33 028742E 02 10 -037682E-08 16 0287022 02 10 -0230742-09 36 0289442 02 it -033272C-08 18 028944E 02 11 -0954502-11 42 0300962 02 12 -082213E-08 12 030096E 02 12 -0242272-09 35 031603E 02 13 -037423E-08 17 031603C 02 13 020759E-11 46 032384E 02 14 024492E-07 6 032334E 02 14 -020082E-08 27 0327292 02 15 017709E-08 25 O32729E 0Z 15 -084671E-10 38 0348362 02 16 -0158962-08 30 0348362 02 16 030318E-11 45 0365782 02 17 0163662-08 29 036578E 02 17 013244E-08 29 0386112 02 18 010586E-08 34 0386112 02 18 0267042-08 26 038819E 02 19 -050882E-08 14 038819C 02 19 -01783E-08 28 0419145 02 20 -070575[-00 13 041914E 02 20 013211E-07 19 048225E 02 21 -0216692-08 23 0482252 02 21 -0551992-08 22 09330E 02 22 0676702-10 44 049330E 02 22 -045054E-09 34 0514622 02 23 -0187162-09 40 0514622 02 23 -018224E-11 47 0521242 02 24 0190292-11 49 052124E 02 24 -029537E-12 49 052244E 02 25 -0104242-09 43 0522442 02 25 -033498E-11 44 052839E 02 26 D231042-1 48 0523392 02 26 016310E-12 50 052912E 02 27 016440E-08 28 052912C 02 27 0710462-10 40 055803E 02 28 042042E-10 45 0558032 02 28 047187E-lI 43 011957E 02 34 -010918-08 33 011957E 02 34 -015718E-06 8 0124462 02 35 -3153422-07 9 012446E 02 35 0881082-08 20 016801C 02 36 0483352-09 36 0168012 02 36 021312E-06 6 017309C 02 37 029037E-08 20 0173092 02 37 030(415-07 15 020952E 02 33 015586E-08 31 020952E 02 38 -0105732-06 10 023872L 02 39 028524E-07 5 0238722 02 39 0525452-06 1 O7020E 02 40 -019889E-07 7 027020E 2 40 0739612-07 11 029155E 02 41 -024984E-08 22 029155E 02 41 0390998-07 12 03080E 02 42 0116312-09 41 030048E 02 42 035788E-07 13 0308002 02 43 024731E-09 38 030800E 02 43 036011E-06 2 031635 02 44 031139E-08 19 03163S2 02 44 0175002-06 7
0327532 02 45 -022871E-09 39 032753E 02 45 -0369122-08 25 0331232 02 46 0166608-08 27 033123E 02 46 -023471E-07 17 0369202 02 47 012477E-07 10 036920E 02 47 -032400E-07 14
0378888 02 48 -0965962-08 11 037088C 02 48 -U12443L-06 9 038371F 02 49 -036952E-09 37 0388712 02 49 -083292E-08 21 0434632 02 50 0760632-09 35 043468E 02 50 -023526E-06 5 0458412 02 51 0256558-08 21 045841E 02 51 021611E-06 4 051102E 02 52 -0105058-09 42 051102C 02 52 -0268402-06 3 052131E 02 53 -I45692E-11 47 052131E 02 53 -017033E-10 41
052227E 02 54 029306E-12 50 052227E 02 54 -01281E-08 30 0594752 02 55 -D32701E-10 46 059475E 02 55 0675912-I 8
0607482 02 56 -017322E-08 26 060748E 02 56 029409E-07 16 065135E 02 57 019312E-08 24 065135E 02 57 -015085E-07 18 067311E 02 58 -i44260-08 Is 067311E 02 58 0396352-08 24
RATE COEFFICIENTS RESPONSE FROM - 9025 INPUT FROM 140312 RATE COEFFICIENTS RESPONSE FROM - 9026 INPUT FRDM - 140392 FREQUENCY
013764E 02 017525S 02 018133S 02 019370E 02 022939E D2 0257962 02 028702E 02 023944E OZ 0300962 02 031603E 02 032384E 02 0327292 02 034tamp38 E 02 0365782 02 038611E 02 0388192 02 01914E 02 04B22SE 02 0493301 02 0514622 02 052124E 02 0522442 02 052839E (2 052912E 02 055003 02 0119572 02 0124462 02 016801E 02 0173091 02
NODE NO 4 5 6 7 8 9
10 11 12 13 14 1s 16 17 18 19 20 21 22 23 24 25 26 27 28 34 35 36 37
COEFFICIENT -039650E-09 014333E-10 031760E-11 040722E-11 015076E-08 -03754SE-09 -0125150-09 049834E-11 040266E-10
-035536E-11 029533E-09 033135E-10 015281E-13 -0944932-10 015309E-09 -033593E-08 050144R-08
-017972E-08 -0150512-09 -065300E-12 -011322E-12 -013028E-11 O68569E-13 0389036-10 053681E-12 024992E-C6
-012279E-07 055539E-07 016765-07
RANK 28 38 43 41 az 29 33 40 35 42 30 37 50 34 31 19 16 21 32 46 48 45 49 36 47 I
13 7
11
FREQUENCY MODE No 013764E 02 4 D175251 02 5 018133E 02 6 0193702 02 7 022939E 02 a 025796F 02 9 028702 02 10 32894E 02 11 030096E 02 12 031603E 02 13 032384E 02 14 0t32729E 02 is 034836E 02 16 036578E 02 17 0386112 02 18 038819E 02 19 0419142 02 20 048225E 02 21 049330C 02 22 051462E 02 23 052124C 02 24 052244E 02 25 052839F 02 26 052912E 02 27 055803E 02 28 0119571 02 34 012446E 02 35 016801E 02 360173092 02 37
COEFFICIENT 041666E-11 011205E-09
-0867996-10 -029078E-09 -018112E-09 -034658E-10 -0792552-10 -067373[-11 -010603E-09 053579E-10 032950E-09 020485E-10 0227572-11 022823E-09 0246052-08
-08171s-O9 -062265E-09 -013177E-09 012129E-10 020972E-10 058106E-13
-049764E-11 -010861E-12 -051434C-09 034784E-11 0197632-07 014874E-06 015959E-08-202386-7
RANK 45 32 34 28 30 37 35 43 33 36 27 40 48 29 19 23 24 31 41 39 50 44 49 25 46 11 1
2210 020952E 02 0238721 02 027020E 02 029155E 02 03004E 02 030800E OZ 031635E 02 032753E 02 0331230 02 0369200 02 0378880 02 03887E 02 043468E 02 0458f1E 02 051102E 02 052131E 02 052227E 02 059475E 02 060748 O 065135C 02 067311E 02
38 39 40 41 42 43 44 45 46 47 43 49 so 51 52 53 54 55 56 57
58
0946740-07 -012329E-06 -083996E-08 -033902R-08 010140E-08
-039227E-07 -044551amp-07 051066E-09 039654E-08 077410E-09 -0259300-08 -011393(-03 -073189C-U7 010696-06
-011003L-06 -082163E-11 -052013L-09 024771C-lI 037397L-07 01328E-07 08199SE-08
5 2
14 1 24 9 8
27 17 25 20 23 6 4 3
39 26 44 10 12 15
0209522 02 0238722 02 027020E 02 029155E 02 (30082 02 030800E 02 031635E 02 032753E OZ 033123E 02 0369202 02 0378A82 02 039371C O 043468E 02 04a334E 02 05I2E 02 052131E 02 052227E 02 059475E 02 060748E 02 065135E 02 0673112 02
38 39 40 41 42
43 44 45 46 47 48 49 50 51 52 53 54 55 56 57
58
-031503E-08 -011411E-06 065127E-07
-0131172-07 -0193622-08 -0462322-08 -027803E-07 0355072-09
-06880c-08 -O115 6E-06 065753C-07 016097E-08
-050473E-08 -0203471-07 026327E-08 032725[-10 026942E-Il
-0113112-10 -026206E-07 -03963 E-08 050339E-07
17 3 5
12 20 15 7
26 13 2 4
21 14
9 18 38 47 42 8 16
6
r
C
RATE COEFFICIENTS RESPONSE FROM = 9024 INPUT FRON 140393 RATE COEFFICIENTS RESPONSE FROM = 9025 INPUT FRDN - 140393 FREQUENCY MODE NO COEFFICIENT RANK 013764E 02 FREQUENCY MODE NO COEFFICIENT RANK4 -053592E-06 2 013764E 020175252 02 5 4 -024892E-06 2-048029E-07 17 0175252 02 5 084664E-080181332 02 166 -018664E-06 4 018133F 02 6 0629572-090193702 02 337 0658832-0 11 019370E 02 7 0160102-08029392 2002 8a -08384E-O 1 025796E 02 022939E 02 8 02959E-06 I9 0713832-07 80287022 02 025796E 02 9 -0406042-07 Q10 -0139962-07 25 0287022 02 10 -0759132-08028944E 02 1811 -0883042-09 38 028944E 02 11 046]03E-090100962 02 12 -012140E-07 27 3
030096E 02 120316032 02019LE-08 2502 13 010699E-09 45 031603E 02 13 -01831S2-090323342 4002 1i -077401E-07 7 032729E 02 1s 0323842 02 14 011383E-07 25-030357E-04 34 032729E 02 15 011987E-08 310348362 02 16 0444702-09 40 034836E 020365783 02 17 16 023294E-11 490578352-07 13 036578E 02 17 -041263E-08 20033611E 02 18 0563632-07 14 0386112 02 18 0323122-08 2203Z819E 02 19 -033613C-07 19 0388192 02 19 -063355E-07041914E 02 320 314586E-060482252 02 21 050976E-07 15
5 041914E 02 20 0553512-07 7048225E 02 21 0165972-07 110493301 02 22 0184792-07 43 049330E 02 22 061729E-10 43051462E 02 25 -047961E-08 32 051462E 02 23O0S124E 02 -017185E-08 2724 030984E-10 47 052244E O 25 052124E 02 24 0118772-10 46014236E-09 44 05224E 02 25 055366E-10 4405 8392 02 26 071946E-11 48 0528392 02r 0529122 02 26 031037E-1127 0583032E-09 39 48
052912E 02 27 031925E-09055803E OZ 28 -0808752-08 30 3a 0553032 02011957C 02 34 28 -0920052-09 3z0351802-07 14 011757E 02 34 -055936E-07012446E 02 35 6040870E-09 41 012446E 02 35G6801E 02 -054F57F-09 3336 -0218982-06 3 016801E 02 36 -0570672-070173092 02 37 -0267172-08 35 3 0173092 02 37 -0147262-08 30020952E 02 38 -0653032-07 12 020952E 02 38 0584782-07023872E 02 39 -0132amp9c-06 6 40238721 02 39 031132E-070270202 902 40 -016376E-07 24 027020E 02 40 018599E-03 26029155E02 41 0329902-07 20
0300182 02 31 02915520 2 41 -O28606E-08 2442 0726122-08 030048E 020306002 42 020573F-09 3902 43 071090E-07 10 030500E 02 43 -0773092-080316359 02 1744 050161C-07 16 031635E 02 44 -012770E-07032753E 02 45 -0106552-07 28 12032753E 02 45 0147402-08 290331232 02 46 -020148E-07 23 033123E 02 46 034039[-080349202 02 47 -021846E-08 36 210369262 02 47 0321932-0 4S037883E 02 48 -0293212-07 21 037188E 02 48 -0621452-09 3403t871E 02 49 -0370272-08 33
043463E 02 50 038871E D2 49 -050649-09 36-0712552-07 9 043468E 02 50 -021672-7 10045841E 02 51 0282422-07 22 0458412 E 51 0525E0 2-07 13051102E 02 52 0122761-07 26 05253iE 02 53
051102E 02 52 0503242-03 19-0108 92-11 50 05 2272 052131E2Q 53 -0522732-12 5002 54 0249802-09 42 052227E 02 54 0101362-090594752 02 55 0115952-11 49
41 060748E 02 56 0b9475E 02 55 0424942-21 47090112E-08 29 06074E 02 56 011459E-07 140651353 02 5 0954112-10 46 065135C 02 57 -08402E-10 42067311E 02 50 0144522-08 37 067311E 02 50 029899E-08 23
RATE COEFFICIENTS
FREQUENCY MODE 0137642 02 017525E (2 0I833c O2 0193702 02 022939E 02 0257965 02
RESPONSE FROM
NO COEFFICIENT 4 026158E-08 5 066161E-07
-017206E-07 7 -011432E-06 8 -0347922-07 9 -0374822-05
028702E 02 10 -04807E-08 0894E 02 11 -0623Z9E-09 030096E 02 12 -053572C-08 031603E 02 13 027614E-08 032381E 02 14 0127002-07 032729E 02 15 0734442-09 034836E 02 16 0333802-09 0365788 02 17 099664E-08 038611E (2 18 051932E-07 038819E (2 19 -015411E-07 041914F 02 20 -068732E-08 048Z25E 02 21 0121712-05 0493302 (Z 22 -0497462-11 051462E 02 23 0551932-07 052124E Q2 24 -0609522-11 05244E 0Z 25 021149E-09 052839E 02 26 -049240E-l
w wA
052912E (2055803E 02
27 28
-O42209E-08 -059617E-08
011957E 02 34 -O44232E-08 0124462 02 35 068993E-08 0168012 02 36 -016398E-08 0173092 02 37 0177772-08 020952E G2 38 -019459-08 0238722 02 39 028907E-07 027020E 02 40 -0144202-07 029155E (2 41 -0110680-07 03D045E 02 42 -039285E-09 030800E 02 43 -091214E-09 031635C 02 44 -079694E-08 032753E 02 45 010249E-05 033123E 02 46 -059126E-08 036920E 02 47 -0781180-08 037888E 02 48 015758E-07 038871E 02 9 0094402-09 043468E 02 50 -015287E-09 0458412 02 51 -0237972-05 0511OZE 02 52 -0120IE-09 0521312 02 53 0207452-11 052227E 02 54 -052515E-12 059475E 02 55 -019401-10 0607482 02 56 -080298E-08 065135E 02 57 025068E-10 067311E 02 s 0103552-07
9026 INPUT FROM 2340393 RATE COEFFICIENTS
RANK 28 2 8 1 5
26
FREQUENCY 0137642 02 017525E 02 0181332 02 019370E 02 022939E 0 025796E 02
MODE
RESPONSE FROM shy
nO COEFFICIENT 4 00 5 00 6 00 7 00 D 00 9 00
23 028702E 02 10 00 39 020944E 02 11 00 22 030096C 02 12 00 27 0316032 02 13 00 12 03238(2 02 14 00 38 032729E 02 15 00 41 034836E 02 1G 00 14 036578E 02 17 00 4 038611E 02 18 00
10 038819E O 19 00 19 041914E 02 20 00 34 048225E 02 21 00 47 049330E O 22 00 3 051462E 02 23 00
46 052124E 02 24 001 4Z 05224 02 25 00 48 052839E 02 26 00 25 052912E 02 27 30 20 055803P 02 28 00 24 0119572 02 34 0269312-07 18 01246E 02 35 -9177V02-08 32 0168012 02 36 -0628I1E-07 31 017309E 02 37 054263E-08 30 009522 02 38 -090140E-07 6 0238722 02 39 016610E-06
11 027020E 02 40 049811E-08 13 029155C 02 41 011680C-07 40 030048C 02 42 -015603E-05 36 030800E 02 43 -0108 7E-07 16 031635C 02 44 -026769E-07 35 0327532 02 45 -0122682-08 21 033123E 02 46 -025570E-08 17 0169202 O 47 -0406692-08 9 0378882 02 48 -018294E-07
37 0388712 O 49 0167892-08 33 043468C 02 50 -0168878-08 29 045841E 02 51 -0178722-09 43 051102C 02 S2 -0122562-07 49 052131E 02 53 02110E-11 50 052227E 02 54 053322E-10 45 059475E 02 55 055687E-10 15 060748E 02 56 0338856E-07 44 065135E 02 57 026383E-07 7 0673112 02 58 -0820210-08
90044 INPUT FROM - 140391
RANK 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 33 32 31 30 29 2B 27 26 5 17 3
13 2 1
14 10 20 11 7
21 16 15 a
19 18 22
25 24 23 4 6
12
RATE COEFFICIENTS
FREQUENCY NODE (137640 02 4 017525E 02 5 018133E (2 6 019370E 02 7 0229392 C2 8 025796E 02 9 O287D2E 02 10 02894A 02 11 0300962 02 12 031603E 02 13 032384E 02 14 0327 9E 02 15 034836E 02 16 036578E 02 17 038611E 02 18 038819E OZ 19 041914E 02 20 048225E 02 21 049310E 02 22
051442E 02 23 052124 02 24 O522A4E 02 25 052819E 02 26 05Z912E 02 27 055803E 02 28 0119570 02 34 012446E 02 35 01630 1E 02 34 0173090 02 37 029952E 02 38 023872E 02 39 0270Z02 02 40 O2912SE 02 41 03048 02 42 030800E 02 43 031635E 02 44 0327530 02 45 0331232 02 46 0369202 02 47 037883E 02 48 038871C 02 49 043463E 02 50 045841E 02 51 051102E 02 52 052131E 02 53 052227E 02 34 059475E 02 55 060748 02 56 065135E 02 57 0673115 02 58
RESPONSE FROM -
NO COEFFICIENT 088156E-07 030552E-03 019928E-06 079930E-08 0i03162-05 021328E-06
-02(314E-06 0401qE-08
-0770172-07 055485E-08
-046183E-06 -02q58IE-07 -0179466-08 -033949E-08 -027512E-08 -01125EE-06 -O50953S-07 04944E-08 041562E-08
020295E-10 036492E-12 0582302-10
-075527E-11 -036828E-03 022759E-09
o0 00 00 00 00 00 00 00
00 00 00
00 00 00 00 00 00 00
00 00 00 00 00 00 00
90045 INPUT FROM - 140391 RATE COEFFICIENTS
RANK FREQUENCY MODE 7 013764E 02 4
18 0175250 02 5 5 018133E 02 6
12 019370E O 7 1 0229395 02 8 3 0257960 02 9 4 0287022 02 10
16 028944E 02 11 8 030096 02 12
13 031603E 02 13 2 032354E 02 14
10 (32729E (2 15 20 0348362 02 1d 11 0365780 02 17 19 038611E 02 18 6 03819E 02 19 9 041914E 02 20
14 04a2252 02 1 15 049330E 02 22 23 051162E 0Z 23 25 052124E 02 24 22 052244E 02 25
24 052839E 02 26 17 052912E 02 27 21 05SB03E 02 28 50 011957E 02 34
RESPONSE FROM -
NO COEFFICIENT 00 00 00 00 00 00 00 00 bO 00 00 00 00 00 00 00 00 00 00 00 00 00
00 00 00
-077354E-08 49 012446E 02 51S -046324-08 Aa 47
0158018 02 0 13092 02
36 67
-0138582-07 -001554E-08
46 020952E 02 38 -048037-07 45 021872E 02 19 -018380E-06 44 027020E 02 40 -017998E-07 43 02915SE 02 41 -040321E-08 42 0300A80 02 42 -010645E-08 41 030800E 02 43 -086357E-09 40 031635E 02 44 -038035E-07 59 03Z753R 02 S -0136420-06 38 033123E 02 46 -021440-08 37 036920E 02 47 -011143E-07 36 35
0378886 02 0338712 02
48 49
-056548[-07 -040705E-08
34 0414682 02 so -01704E-07 33 O4S861 02 51 -017552E-06 32 051102e 02 52 088247E-08 51 052131C 02 53 -090243E-11 30 052227E 02 54 -092479E-10 29 0594756 02 55 -050282E-10 28 060743E 02 56 -0176072-07 Z7 065135C 02 57 -051451E-07 26 0673110 02 58 -055032E-08
90046 INPUT FROM 140391
RANK 50 49 48 47 46 45 44 43 42 41 40 39 38 37 36 35 34 a3 32 31 30 29-r
28 27 26 z 14 16 10 13 S I 7
18 a1 22
6 20 P-9 19 11
3 17
8 2
12 25 23
4 9 4
is
RATE COEFFICIENTS RESPONSE FROM - 90044 INPUT FROM 140392 RATE COEFFICIENTS RESPONSE FROM - 90045 INPUT FRDM 140392
FREQUENCY MODE NO COEFFICIENT RANK FREQUENCY MODE NO COEFFICIENT RANK 0137642 02 4 00 50 013764E 02 4 -023666E-09 14 0175252 02 0181332 02
5 6
00 00
49 48
0175252 02 0181332 02
5 6
-0847202-11 0231972-09
19 15
019370E 02 7 00 47 019370S 02 7 -049082E-10 17 3Z232 02 8 00 46 0229392 02 8 -043357E-08 5 025796E 02 9 00 45 025796E 02 9 -04774C0E-09 11 0 702E 02 10 00 44 0287022 02 10 -042725C-08 6 028944E 02 11 00 43 0289442 02 11 081289E-11 20 O30096E 02 12 00 42 0300962 02 12 -OIOOOBE-08 9 0316032 02 13 00 41 0316032 02 13 -0794392-10 16 032384E 02 14 00 40 0323842 02 14 -0621312-03 3 0327292 02 15 00 39 0327292 02 i -0284352-09 13 034836E 02 16 00 38 0348362 02 16 025693E-11 22 0Z6578E 02 17 00 37 036578E 02 17 -011707E-08 7 0386112 02 18 00 36 0386112 02 18 -063942-08 2 0388192 02 19 00 35 0388192 02 19 -018070E-07 1 0419142 02 20 00 34 041914E 02 20 -044953E-08 4 0182252 02 21 00 33 0482252 02 21 030072E-09 12
09330E 02 22 00 32 0493302 02 22 0744932-09 10 0514622 02 23 00 31 0514622 02 23 -022736E-11 23
021242 02 24 00 30 052124E 02 24 0111432-13 25
0522442 02 25 00 29 052Z4E (2 Z5 U278002-11 21 0528392 02 26 00 28 0528392 02 26 0355042-12 24 052912E 02 27 00 27 052912E 02 27 001522E-02 a
0558032 02 28 00 26 0558032 02 28 018030E-10 18 011957E 02 34 -048784E-06 3 011957E 02 34 00 50
0124462 O 35 0172472-07 15 012446E 02 35 00 49 0italE 02 36 -02073CE-06 6 016DIE 02 36 00 48 0173092 02 37 -0378192-07 13 017309E 02 37 00 47
0209522 02 38 0182192-06 8 020952E 02 38 00 46 023872E 02 39 -0666642-06 1 02387aC 02 39 00 45 027020E 02 40 -0163112-07 17 0270202 02 40 00 44 0291552 02 41 061321E-07 11 0291552 (2 41 00 43 030048E 02 42 0171351-07 16 030012 02 42 00 42 030800E 02 43 0203002-06 7 030800E 02 43 00 41
031635E 02 44 023901E-06 5 031635E 02 44 00 40 0327532 02 45 0190472-08 21 032753E 02 45 00 39 0331232 O 46 010572E-07 19 033123E 02 46 00 38 0369202 02 47 0377662-07 14 036920E 02 47 00 37
037838E 0 48 0124532-06 9 037888E 02 48 00 36 038871E 02 49 -082219E-08 20 0358712 02 49 00 35 043468E 02 50 011205E-07 18 0434682 02 50 00 34 0158412 02 51 0141742-08 22 0458412 02 51 00 33 051102E 02 52 030716E-06 4 0511022 02 5 00 32 052131E 02 53 -O15143E-10 25 052131E 02 53 00 31 052227E 02 5 O48209E-09 Z3 0522272 02 54 00 30 059475E 02 55 0192622-10 24 0594752 02 55 00 29
0607482 02 56 0587872-06 2 0607482 02 56 00 28 0651352 02 57 -055184E-07 12 065135E 02 57 00 27 0673112 02 58 0932342-07 10 067311E 02 58 00 26
- 90044 INPUT FROM 140393RATE COEFFICIENTS RESPONSE FROM - 90046 INPUT FROM 140392 RATE COEFFICIENTS RESPONSE FRDM
FREQUENCY MODE NO COEFFICIENT RANK FREQUENCY MODE NO COEFFICIENT RANK 013764E 02 4 00 50 0137642 0Z 4 00 50 017525E 02 5 00 49 017525t 02 5 C0 49 010133E 02 6 00 48 0181332 02 amp 00 48 019370E 02 7 00 47 0193702 02 7 00 47 022939E 02 8 0 46 022939E 2 8 00 46 0257962 02 9 00 45 025796C 02 9 00 45 028702E 02 10 00 44 023702C 0 10 00 44 028944E 02 11 00 43 0239442 02 11 00 43 O3009E 02 12 00 42 0300962 02 12 00 42 0351603E 02 13 00 41 011603E 0 13 00 41 032382E 02 14 00 40 032384E 02 14 00 40 032729E 02 15 00 39 032729E 02 15 00 39 034836E 02 16 00 38 03336E 02 16 00 33
036578E 02 038611E 02
17 18
00 00
37 36
036578E 02 0336l1E 02
17 18
00 C0
37 36
038819E 02 19 00 35 0383192 0z 19 00 35 041914E 02 20 00 34 04k9l4E 02 20 00 34 043225E 02 21 00 33 04a2251 0 21 00 33 049130E 02 22 00 32 043302 02 22 00 32 051462E 02 23 00 31 0514622 02 23 00 31 052124E 02 24 00 30 0521242 02 24 00 30 052244E 02 25 00 29 052244E 02 25 00 29
wA 052839E 02 26 00 28 0528392 OZ 26 00 28 052912E 02 27 00 27 05 9122 02 27 00 27 0S5805E 02 28 00 26 0558(32 02 28 00 26 011957E 02 34 012012E-06 7 011957E 02 34 010919E-06 5 0124462 02 35 0449112-07 16 01 4462 02 35 0800023-07 20 01t0E 02 36 -047542-07 is 016801E 02 36 021309E-06 1 0173092 02 37 056840E-07 14 017309E 02 37 033221E-03 18 0209522 02 38 097094E-07 11 0209522 02 38 011254E-06 4 0Z3872E 02 39 0757662-06 2 023872E 02 39 016834-06 3 027020E 02 40 0589362-07 13 027020E 02 40 036114E-08 15 0291552 02 41 -021169E-07 17 029152E 02 41 0517402-07 7 030048E 02 42 0116902-07 20 030043E 02 42 034766E-08 16 008002 02 43 0161612-07 19 030800E 02 43 0400082-07 8 031635E 02 44 0339602-06 4 031635E 02 44 0635103-07 6 0327532 02 45 021180E-08 2z 0327536 02 45 0549733-03 13 033123 OZ 46 08e65E-05 21 033123E 02 46 0907463-08 12 0369202 02 47 010346E-06 10 036920E 02 47 025463E-03 19 0378882 02 48 038492E-06 3 037838E 02 48 0298142-07 10 038371E 02 49 0199343-07 18 0368712 02 49 -0365502-08 14 043468C 02 50 0118302-06 8 0434682 02 so 031939E-08 17 04584E 02 51 013921E-05 1 045841E 02 51 016578E-09 22 051102E 02 52 -0221172-06 6 051102E 02 52 -0140A92-07 11 05213LE OZ 53 064633C-10 Z4 0521312 02 53 -096025E-1 25 052227E 02 54 -O3611E-09 23 052227E 02 54 -093947E-10 23 0594752 02 55 -017392E-10 Z5 059475E 02 55 031043E-10 24 0607483 02 54 0266392-06 5 060743E 02 56 013013E-06 2 065135E 02 57 011175E-04 9 0651352 02 57 0349032-09 21 067311E 02 58 062589E-07 12 067311E 02 58 03 015E-07 9
= 90046 INPUT FROM 140391- 900A5 INPUT FROM - 140393 RATE COEFFICIENTS RESPONSE FROMRATE COEFFICIENTS RESPONSE FROM
FREQUENCY 013764E 02
MODE NO 4
COEFFICIENT -01857E-06
RANK 5
FREQUENCY 013764E 02
MODE NO 4
COEFFICIENT 00
RANK s0
0175250 02 5 -050026E-08 17 017525E 02 5 00 49
018133E 02 6 0459839-07 11 018133E 02 6 00 48
019370E 02 (2939E 02 025796E 02 02570ZE 02 028914C 02 030096E 02 031603E 02 032384E 02
7 a 9
10 11 12 13 14
-019297E-07 -083284E-06 -051629E-07 -025916E-06 0752031-09
-050186E-07 -040942E-08 -023947S-06
13 1 7 3
20 9
IS 4
0193700 02 0229390 02 0257960 02 0287020 02 028944C 02 0300960 02 0316030 02 032384E 02
7 8 9
10 11 12 13 14
00 00 00 00 00 00 00 00
7 46 45 44 43 42 41 40
032729E 02 15 -0101950-07 14 0327290 02 15 00 39
03q836E 02 036578E 02 033611E 02 0388190 02
16 17 18 19
037685E-09 -051121E-07 -013197E-06 -03079
2 0 6
1 a 6 2
034836E 0365780 038611E 038819E
02 02 02 02
16
17 18 19
00 00 00 00
38
37 36 35
0419142 02 20 -049622E-07 10 041914E 02 20 00 34
08225E 02 O933OE 02
21 22
-0277712-08 -0305535-09
19 22
048225E 0 93302
02 02
21 22
00 O0
33 32
051462E 02 052124E 02
23 24
-059835E-08 -011689E-11
16 25
051462E 02 052124E 02
23 24
00 00
31 30
0522 2 02 25 -011814E-09 23 05221E 02 25 00 29
0528392 02 052912E 02
26 27
0160975-10 0945512-08
24 15
052839C 02 0529120 02
26 27
00 00
28 27
055803E 02 28 -032273E-07 12 0558030 02 28 00 26 w 0119570 02 34 00 50 011957E 02 34 -031361E-07 9
0124E E 02 35 00 49 012446E 02 35 020B33E-08 21
016501E 02 36 00 40 0168010 02 36 0 47 013 EL07 7 0173092 02 020952E 02
37 38
00 00
47 46
017309E 02 020952E 02
37 38
-0499290-08 059973E-07
18 6
c
023872E 02 39 00 45 023872E 02 39 -0186270-DC 1I
027020E 02 40 00 44 027020E 02 40 -0130505-07 12
0291550 02 41 00 43 029155E 02 41 -017B61E-D7 11
0300480 02 42 00 4z 0300482 02 42 023718E-08 20
0308002 02 43 00 41 0308000 02 43 031850-D8 19
031635E 02032753E 02
4445
0000
40 39
031635E 02 032753E 02
44 45
097342E-07 0611352-08
3 17 C)
033121E 02 46 00 38 0331230 02 46 0761012-08 15
036920E 02 47 00 37 036920E 02 47 06976t2-08 16
037888 (32 038871E 02
48 49
00 00
36 35
037a889 0388715
02 02
48 49
0922472-07 088617E-08
4
14
0134680 02 50 00 34 04346E 02 50 0359830-07 8
045841E 0Z 51 00 33 0458410 02 51 0162812-06 2
051102F 02 52 00 32 051102E 02 52 010116E-07 13
052131E 02 53 00 31 052131t 02 53 040971E-11 25
052227E 02 059475E 02
54 55
00 00
30 29
0522270 059475E
02 02
51i 55
0162932-09 -029536E-10
23 24
0607480 O2 56 00 28 060748E 02 56 -081624E-07 5
065135E 02 57 00 27 065135E 02 57 -0706330-09 22
0673110 02 58 00 26 067311E 02 58 022822E-07 10
Table 4-3 POSITION COEFFICIENTS FOR CONVENTIONAL MODEL
POSITION tGYRO) COEFFICIENTS RESPONSE FROM - 90011 INPUT FROM - 5131 POSITION (GYRO) COEFFICIENTS RESPONSE FROM 90012 INPUT FPOM - 5131
FREQUENCY MODE NO COEFFICIENT RANK FREQUENCY MODE NO COEFFICIENT RANK 0137645 0Z 4 -041025E-08 6 C13764E 02 4 0541 8E-11 39 017525E 02 5 -05341E-08 0175250 02 5 -0138950-10 31
18133E 02 6 -0945560-08 3 (11330 02 6 061105E-10 26 0193706 02 7 018543E-09 22 019370E 02 7 -061447C-12 45 022939E 02 8 -029899E-07 1 022939F 02 8 015392amp-09 2L 025796E 02 9 -053363E-08 5 025796E 02 9 0e8445-10 27 023702C 02 10 -0293470-08 9 0287022 02 10 -08279E-10 2 028944E 02 11 -022034-08 10 (289440 02 11 011OOE-10 32 030056E 02 12 072821E-09 14 31056E 02 12 010917-10 33 031603E 02 13 -048140C-09 I 031603C 02 13 060931E-11 38 0323541 02 14 -0115960-07 2 0323611 02 14 -017106C-0 20 032729E 02 15 -0757512-09 13 032729C 02 15 -01038SE-l0 34 C348362 02 16 054170E-09 16 034836E 02 16 0616430-li 37 0365730 02 17 -0715440-10 25 036578E 02 17 066065E-11 35 C386116 02 18 011798E-08 11 033611E 02 18 0102982-09 23 038819E 02 19 030783E-08 8 038a192 02 19 -O1718E-10 30 041914C 02 20 0334260-00 7 0419111 02 20 -0195170-10 29 C4822SE 02 21 092496E-10 24 048225E 02 21 056799E-12 47 00330E 02 22 078547E-11 39 049330C 02 22 -062484E-12 44 (5142E 02 23 -050654E-10 29 051462C 02 23 066070-11 36 0E2I24E 02 24 022932E-13 49 052124E 02 24 -O50102E-15 5o 5224E 02 25 016132E-10 36 05 214E 02 25 -065340E-13 48
25230R 02 26 014864E-12 46 0528390 02 26 020503E-14 49 85291E 02 27 07086-11 40 052912C 02 27 057140E-12 46 052303E 02 25 0479830-01 41 055803E 02 28 -062847E-12 43 0119570 02 34 -087258-10 25 010957a 02 34 -033203E-09 17
w 012446E 02 35 -064262E-09 15 012446E 02 35 -036200C-07 3 03 016801C 02 36 -012316E-09 23 016801E 02 336 -023661E-07 5
017309E 02 37 -011609-05 12 017309E 02 37 -073773E-07 1 020952E 02 38 024735E-09 20 0209562 02 38 033066E-07 4 0238720 02 39 048885E-09 17 023822 02 39 03887E-07 2 027020E 02 40 -0721686-10 Z7 027020E 02 40 -076171E-05 8 029155 02 41 027721E-10 31 029155t 02 41 06668C-09 13 0300SE 02 42 021913E-11 A4 030018C 02 42 011v43E-09 22 039 030 02 43 -016657E-10 34 0308002 02 43 -06393(0-09 14 031amp35E 02 44 -074314E-10 26 031635E 02 41 -035ampq7-o8 9 032753E 02 45 010086E-11 45 0321530 02 45 02f57E-ID0 28 0332316 02 6 -O392151-10 30 033123L 02 46 -091372L-09 1z 036920E 02 47 -022112F-09 21 0369200 02 47 -0900W21-08 7 0378632 02 8 031673E-09 19 037888C 02 48 014576-07 6 013371E OZ 49 0222390-I0 32 0388710 02 49 -0zv0v9-o 10 0434 60 02 50 03216RE-11 43 043468C 02 50 0303222-09 18 045S41E 02 51 0947306-11 38 045841 02 51 018682E-09 19 051102E 02 052131F 02
52 53
-015196E-10 090711E-14
37 50
050102l2 02 052131 02
52 53
-022]12[-08 -086542E-12
11 41
052227E 02 54 -0306512-13 48 0522270 02 54 -0320dE0-11 40 059475E 02 55 016321E-12 47 059475E 02 55 085613E-12 42 060748F 02 56 -0I16S0E-10 35 0607482 02 56 -04476I0-09 16 065135E 02 57 016878E-10 33 065135E 02 57 0816050-10 25 0673116 02 58 0404520-11 42 067311C 02 58 04932E-09 15
PCSITION (GYRO) COEFFICIENTS RESPONSE FROM - 90013 1NPUT FROM - 5131 POSITION (GYRO) COEFFICIENTS RESPONSE FROM - 90011 INPUT FRH 5132
FREQUENCY MODE NO COEFFICIENT -RANK FREQUENCY MODE NO COEFFICIENT RAN4K
013764C 02 4 -028259E-08 9 013764E 02 4 021171E-09 27
017525E 02 5 065495E-08 4 017525C OZ 5 D838621-08 4
018133E 0Z 6 - 134D5E-07 I 018133E 02 6 -050783E-07 1
019370E 02 7 014894E-09 31 019370E 02 7 D46358E-07 2
0221392 02 8 -059838E-08 6 0229391 02 8 072945E-00 5
0-5796C 02 9 0589692-09 20 025796E 02 9 090621F-O 3
025702E 02 10 064773E-08 5 028702E 02 10 -053645E-08 8
028944E 0Z 11 0248B0E-08 10 020944E 02 11 -0454239-08 9 0300962 C2 12 -096322E-09 16 30096E 02 12 -0543522-00 7
031603C 02 13 091475E-09 17 031603C 02 13 -031904E-00 10
0SZ84E 02 14 076998E-U8 z 032384E 02 14 068467E-08 6
032729E 02 15 049262E-09 23 032729E 02 15 057255E-09 19
03336E 02 16 -028709E-09 28 034836E 02 16 -062097L-09 18
036570E 02 17 -04969E-07 22 036578E 02 17 030436E-09 23
0336119 02 13 -039719E-08 8 038611E 02 13 -032914E-09 13
038319E 02 0419014 0
19 20
07382E-08 -052314-08I
3 7
060017C o 04191t o
19 20
-0207O02-0) -033w4)-09
20 22
046225E 02 21 -019229E-09 29 0432252 02 21 -053800E-09 20
049330E 02 22 OZO86E-I 40 049330E 02 22 0335701-10 39
051162E 02 052124E 02
23 24
-00451E-09 062762E-13
19 49
051162L 02 05Z124E 02
23 Z4
-079091C-09 04553a8-12
14 47
057244E 02 25 -014451E-10 42 05224E 02 25 -0209622-10 44
052539E 02 26 -032207E-l 47 052839C 02 26 022571C-12 48
052912s 02 27 -038731E-10 33 052912C 02 27 012101E-09 30 Lo 05803E 02 28 0403462-1D 37 055803E 02 28 097444E-10 33
011957E 02 0124460 02
34 35
1 -039435E-09 049771E-09
24 zi
011957F 02 0124169 02
34 35
-077527E-10 -026996E-08
35 11
016801E 02 36 011438E-G 13 016301E 02 36 -0219632-09 26
007309E 0 37 -036269E-09 25 017309E 02 37 -0703942-10 36
020952E 02 38 -019847E-08 11 070952C 02 38 -- 109972-09 32
0 2387ZE G2 027020E Z 029155E C2 03003c 02 0 30amp0E c2
39 40 41 42 43
-071480[-09 OIq209E-0S
-014025E-09 -0113942-10 033527E-10
18 12 32 43 35
023872E 02 0270206 02 029155E 02 U40001 OZ 030800E 02
39 40 Al 42 43
097507E-09 -023123E-09 0139672-09 U63S1L-10 030631C-10
12 25 29 42 40
03135E 02 44 032702E-09 27 031635E 02 44 068908-09 16
032753E 0 033123E 02
45 46
-056229E-11 016932E-09
45 30
032753C 02 033123E 02
45 46
02931452-11 035874E-09
49 21
036920E 02 47 099110E-09 i5 036920C 02 47 0629422-09 17
037533E 02 40 -099673E-09 14 037882 02 48 -075905C-09 15
03371E 02 49 -033252E-09 26 038871E 02 49 -039584E-10 3B
043468E 02 50 079544E-11 44 043468E 02 50 064582E-10 37 045341E 02 51 019154E-10 41 045812 02 51 0113111-09 31
C51102 12 52 046323E-10 36 0511022 02 52 -0287442-10 41
052131L 02 53 -053351E-13 50 0521312 02 53 -031012E-13 so
052227E 02 54 012513E-12 48 052227E 02 54 06880ampE-13 49 059475E CZ 55 -010975E-11 46 059475C 02 55 -099634E-12 46
06048E 02 56 012026E-09 33 060748E 02 56 -024805E-09 24
065135E 02 57 -02817E-10 39 065135E 02 57 088256C-10 34
067311E 02 58 -011897E-09 34 067311E 02 58 0260191-10 43
rOSITION (GYRUI COEFFICIENTS RESPONSE FRON 90012 INPUT FRDN 5132 POSITION (GYRO) COEFFICIENTS RESPONSE FROMI 90013 INPUT FROM - 5232
FRQUENCY NODE NO COEFFICIENT RANK FREQUENCY NODE NO COEFFICIENT RANK 013764E 02 4 -027943E-12 47 013764E 02 014583E-09 39
017525E 02 5 021816E-10 35 01752 E 02 5 -010283E-07 4
018133E 02 amp 032817E-09 21 018133E 02 6 -071923E-07 I 019370E 02 7 -015362E-09 23 019379E 02 7 037236E-07 2
0229398 02 8 -037552E-10 32 022939E 02 9 0101599-08 20
o 5796E 02 9 -002269E-10 28 029796E 02 9 -0]O0l4c-Oa 23
023701E 02 10 -015134E-09 24 020702E 02 10 01184UE-07 3 023944E 02030096E 02 1112 022693E-10-O82128E-ID 3429
028944E 02030096E 02
1112
051239E-08072554-08
8 6
031603C 02 13 OiEIE-ID 31 031603c oz 13 060248E-08 7
032334E 02 14 0o]0100E-09 26 032384E 02 14 -0466414-08 9 032729E 02 034836E 02
15 16
07849E-11 -070663E-11
38 40
032729E 02 03136C 02
15 16
-037234[-09 03290U-0
32 3q
036573E 02 17 -028104E-10 33 036578E 02 17 02114ZE-08 15 035611E 02 18 -072374E-10 30 038611E 02 18 027914C-08 13 034319E 02 19 011606E-11 46 038319E 02 19 -053481C-09 30 041914E 02 20 019765E-11 45 041914E 02 20 052977E-09 31
0482252 02 21 -033037E-Il 42 048225E 02 21 011134 -O8 22
049330E 02 22 -026705E-11 q4 049330E 02 22 087552-10 42 05162C 02 23 010311F-09 2S 051462C 02 23 -09438E-0 5
052124E 02 24 -099A90E-14 49 052124E 02 24 012463C-11 47 052244E 02 25 064904E-15 48 05224E 02 25 010779c-lt 4 0523392 O 26 00035SE-1 so 0528392 02 26 -016203C-12 50 052912E 02 27 B97578E-10 37 052912E 02 27 -066141E-09 28
055803E 02 28 -012763E-IU 36 0 011957C 02 34 -0295002-09 22 0119579 02 34 -8350J82-9 33
012446E 02 35 -0I207F-06 1 01246L 02 35 020508E-02 16 016801E 02 36 -042193E-07 3 016001E 02 36 0203972-06 17 0 17300E 02 37 -044733E-00 13 017309E 02 37 -021992E-10 43
020952t 02 0- 3 7E 02
38 39
-01696S-07 D7753 -07
a 2
02091r 02 023872E 02
30 39
08230C-09 -01 592-08
24 21
027020E 02 40 -024410E-07 7 027020E 02 40 045536E-08 10 029055E 02 41 0331489e-08 15 029155E 02 41 -0706612-09 27
030042F 02 42 0138682-Un 18 03000E 02 4z -0136 2E-09 37
030800E 02 43 011756E-08 19 030800E 02 43 -O1536OE-09 37 031635E 02 44 033100E-07 5 031635E 02 44 -0303972-0E 11 032753E 02 45 083133t-10 27 0 3275 c OZ S -016159-10 15 0331231E 02 46 0S3586Z-08 9 033123E 02 46 -015892-08 19 036920E 02 47 025601E-07 6 036920C 02 47 -028186C-08 12 037588E 02 48 -039440E-07 4 0378E 02 4iamp 0Z3P071-08 1 035716 02 49 -051474C-08 12 038071E 02 49 -059187E-09 29 043468E 02 so 060877E-00 11 043 68E 02 50 015970C-09 36 045841E 02 51 022306t-08 17 04541C 02 51 02871E-0 35 051102E 02 52 -041825C-00 14 051102C 02 52 O87621E-10 1 05213E 0 53 029537E-11 43 852131E 02 53 018240E-12 49 052227E 02 54 0720151-1 9 O5ZZE 02 54 -033099E-12 1 059475E 02 55 -0522ampqr-11 41 0T97C 12 55 06MUL-11 46 D60748E 02 56 -068625E-08 10 060748E 02 56 018437E-08 18 065135E 02 57 042671V-09 20 06515C 02 57 -014732E-09 38 067311C 02 38 032059t-08 1r 0673111 02 53 -V76 2L-0O 26
POSTTION (GYRO) COEFFICIENTS RESPONSE FROM 90011 INPUT FROM 5133 POSITION (GYRO) COEFFICIENTS RESPONSE FROM - 90012 INPUT FROM 5133
FREQUENCY MODE NO COEFFICIENT RANK FREQUENCY NODE NO COEFFICIENT RANK 013764E 02 4 -0139052-06 2 013764E 02 4 013353E-09 25 017525E 02 $ 056749E-00 7 017525E 02 5 0147626-It 36 018133E 02 6 -029177C-07 4 010133E 02 6 0188552-O9 24 019370E 02 7 093454E-10 31 019370E 02 7 -030969E-12 46 D 2739E 02 8 019466E-06 1 0229392 02 8 -0100212-08 16 025796E 02 9 -063076E-07 3 0257965 02 9 057263E-09 17 02570E 02 10 033707E-08 9 028702C 02 10 095093E-10 28 02amp944E 02 11 -O85768E-09 15 028944E 02 11 042849E-11 40 0300962 02 12 085076E-11 41 030096E 02 12 012754E-12 47 031603E 02 13 -013273E-09 29 031603E 02 13 0166961-11 43 032334E 02 14 010428E-08 1 03238 2 02 14 0153842-10 35 032729E 02 15 -03700E-09 19 032729E 02 15 -050729E-11 39 02 836E 02 03 573E 02
16 17
011602C-09 -O217Z6E-09
30 27
034E362 036578
oZ 02
16 17
0132)22-11 0200621-10
I5 34
335611E 02 is 028309E-09 24 038611E 02 18 024710E-10 33 035S|9E 02 19 021903E-08 11 033819E 02 19 -0121822-10 37 041914E 02 20 -014076E-07 5 04191C 02 20 0705IOE-10 29 048225E 02 21 079873E-08 6 048225E 02 21 049047E-10 30 0330E 02 22 0338842-09 20 049330E 02 22 -026955E-10 32 051462E 02 23 021569E-10 36 051462C (2 23 -0281451-11 41 0521211E 05 2244E
02 02
24 25
013350E-11 0124532-10
47 39
052124E (2 052244E 02
24 25
-029167E-13 -050137F-13
49 48
052339E 02 26 0030t0E-1Z 48 052039C 02 26 030112E-14 50 052912E 02 27 070306E-10 32 052912E 02 27 556691E-11 38 055 03E 02 28 025652E-09 25 055803E 02 25 -0335992-0 31 01157E Oz 34 04U343E-08 8 011957C 02 34 014505E-07 a Q1 446F 02 35 -032983E-09 21 0124462 02 35 -0185a02-07 9 0165D1E 02 36 -011133E-08 12 016amp51C 02 36 -021389E-06 2 017309E 02 37 023995E-09 26 017309E (Z 37 015248-07 10 023952F 02023372C 02
3839
030087C-08-0-IU 64c-u
1013
020952C (2023872C 02
3839 04102202-U4
-083197E-07 13
027020E 02 40 051250E-l 43 027020E 02 40 054100E- 18 029155E 02 41 019642E-0o 37 029155C 02 41 0470952-09 19 03004202 42 021589c-l 34 030048 02 42 O15O7E-U3 14 03033E 02 0316351 O3 032753E 02
43 44 45
027601E-11 -051314E-09 -O6903SE-1
46 17 42
0308002 02 031635C 02 032753E 02
43 44 45
O10593E-09 -024673E-07 -019557E-09
Z7 7
23
033123E 02 46 019316E-ID 38 033123C 02 46 045006E-09 20 036920E 02 47 -046047E-10 33 036920E 02 47 -01L729E-08 13 037835SE 02 40 -061560E-09 16 O378102 02 8 -031986E-07 5 033371E 02 49 -0221262-lO 35 030711 02 49 -U2773E-U 12 04446E 02 so -0310102-09 22 0434689 02 so -029231E-07 6 0 458411 02 51 -0854832-11 40 045841 02 51 -016859E-09 26 051102E 05211E
02 02
52 53
011362n-09 -01s2o-13
18 05110zc 02 0o0521311E 2
52 53
U6C91 E-07 014544E-11 44
052227E 02 54 033350E-11 44 052227E 02 54 0349042-09 21 059475[ 02 55 -036764E-12 49 0594751 02 55 -019205E-11 42 06078E 02 56 -021269L-09 28 060Al~t 02 51 -058841E-08 11 065135E 02 57 0287SIE-09 23 065135E 02 57 013901E-08 15 0673(1E 02 58 -028078E-11 45 067301L O 58 -034595E-09 22
POSITION (GYRO) COEFFICIENTS RESPONSE FROM 70013 INPUT FRM 5133 POSITION (GYRO) CfEFFICIENTS RESPONSE FRDM 90054 INPUT FROM 5131
FREQUENCY ODE NO COEFFICIENT -RANK FREQUENCY MIODE NO COEFFICIENT RANK 013764E 02 4 -095732F-07 1 013764E 02 4 (0 50
017525E 02 5 -069584E-08 11 0175252 02 5 C0 49
0181330 02 6 -041362E-07 2 018133e 02 6 00 40
019370E 02 7 0750641-10 38 019370E 02 7 00 47
__39E 2 0 038957E-07 3 022V39C 02 8 00 46 025796E 02 9 0697020-08 10 0257961 02 9 00 45 0ZSZ2E 02 10 -0743950-00 9 028702E 02 10 00 44 02944E 02 11 096845E-09 20 0209442 02 11 00 43 03G9E 02 12 -01153t-10 45 030096E 02 12 C0 42 031603E 02 13 025065C-09 30 031603E 02 13 00 41
0323C40 02 1 -071450-09 24 032384 02 14 00 40
032725E 02 15 024063E-09 31 032729E 02 15 C0 39 034536E 02 16 -061136E-10 40 034336E 02 16 U0 30 036578E 02 17 -015092E-08 18 0365780 02 17 00 37
038611E 02 18 -095304E-09 21 0386119 02 18 (0 36
035319E 02 19 0561400-08 12 0380190 02 19 00 35
0419104 12 20 0108990-07 6 0419140 02 20 00 34 040225E 2 21 -016604E-07 7 0432250 02 21 00 33 0491301 02 2z 0S037I0-09 22 049330E 02 22 00 32 05146E (2 23 02576-09 28 051462E 02 23 00 31 05124E (2 24 036538E-11 47 05212E 02 24 00 30 052244E 02 25 -011155E-10 46 0522440 02 25 00 29 052839E 02 26 -0596350-12 49 052839E 02 26 00 20
05291ZE (2 27 -030426-09 26 052912F 02 27 00 27
055303E 02 28 021569E-08 14 055803E 02 28 00 26 011997E 02 34 022102E-07 5 0119570 02 34 -01554BE-08 a 0144SC 02 35 0255450-09 29 0124460 02 35 019540E-03 7 O153OIE 02 36 010339E-07 a 016001E 02 36 044932-08 3
017309E 02 37 0749641-I0 37 017309C 0E 37 -0144702-08 9 0200522 02 38 -024120-07 4 0209520 02 38 -0780310-08 1 023c720 02 39 01b30OE-08 17 023872C 02 39 -020001E-08 6 027020E 02 40 -0100920-09 34 027020E 02 40 055922E-08 2 0291551 02 41 -099372E-10 35 0291552 02 41 -0550300-09 13 030D30 02 42 -011366c-09 33 030018E 02 q2 -0473-10 20 0308001 02 43 -013840a-10 43 030800E 02 43 032783E-09 16 031635E 02 44 022658E-08 13 0316352 02 44 012852E-08 11 031753002 45 036150-10 1 032730 02 45 -022057C-10 22 033123E 02 46 -0834001-10 36 033123[ 02 46 0663652-09 12 036920E (2037$3E C2 4742 0206202-0909373E-08 32is 0369202 02037B83E 02 4748 038860E-0-03S9155-08 54
033371E 02 49 -033034E-09 27 03181 02 49 -013131E-08 10 043460E 02 50 -076652E-09 23 043468E 02 50 0319110-X0 21 0453412 V2 51 -0172850-10 12 0458410 02 51 07562SE-10 19 0-1k02E 0205 i31 0O 5253 -0127610-08089693E-11 19 so 051102E 020521310 02 5253 011535E-09-0211900-12 1725
052227E 02 54 -013614E-10 44 052227E 02 54 0401110-12 24 0594750 02 55 0247221-11 48 059475C 02 55 -0429671-11 23 8607S5 02 56 0150096-08 16 060740E 02 56 046925E-09 14 065k352 02 57 -047991E-09 25 065135E 02 57 -0109430-09 18 067311E 02 58 0825780-10 37 0673110 02 58 -0463240-09 15
POS I1ON (GYRO) COEFFICIENTSZ RESPONSE FROM 90055 INPUT FROM 5131 POSITION (GYRO) COEFFICIENTS RESPONSE FROM 90056 INPUT FROM = 5131
FREQUENCY MODE NO COEFFICIENT RANK FREQUENCY MODE NO COEFFICIENT RANK
0137640 02 4 -O20634E-09 6 01376E 0 4 00 s9 017525E 02 5 -013474E-09 10 017S25E 02 5 00 49 018133E 02 6 -039314E-10 is 018133E 02 6 00 48 0193702 02 7 0116132-10 19 019370C 02 7 00 17 0l22390 02 8 015181E-09 9 022939E 2 a 00 q6 025796E 02 9 0374292-09 5 0257962 02 9 00 45 028702E 02 10 -020169C-09 0 020702E 02 i0 00 4 023914 02 1] 0236950-09 7 02394E 02 11 00 43 0300962 02 12 0230862-10 17 030096E 02 12 00 42 031603 02 13 094370E-10 11 0315031 02 13 00 41 03354E 02 14 -0827922-09 1 0323301 02 14 C0 cO 0317179 02 15 -05106ampE-10 13 032729C 02 1 00 39 034S362 02 16 037700E-10 16 034336E 02 16 C0 38 03578E 02 17 046772[-10 14 036570E 02 17 00 37 035611E 02 18 075238[-09 2 035611C 02 18 00 36 03819E 02 19 038159E-09 A 03819E OZ 19 00 35 C4Iq14E 02 20 -050750E-09 3 0119141 02 20 aamp 34 049275E 02 21 -082520-11 20 O4a2 r 02 21 00 33 049310E 02 22 -016047E-11 21 0493300 02 22 U0 32 051462E 02 23 -055942E-10 12 05146Z2 02 23 00 31 02124E C2 14 063614E-14 25 U5214E (1 2 00 30 0 5Z4[ 2 052837C 02
Z5 26
06924E-12 016742E-12
23 24
0022440 02 052939E 02
25 26
00 00
2 20
05Z9125 02 27 OI s55-o is 0529122 02 27 00 27 0 553030 0 28 086994E-12 22 0 558032 02 20 0 0 6
4 013957E (2 34 00 50 0119572 02 34 033966E-09 9 LO 01246E016301 02 356 0000 p4 0012446E 020161010 02 3536 0253002-08050563C-09 27
0 1-1n- 37 00 7 020173092 02 37 045791E-08 1 020552E 02 38 00 46 020952C 02 38 -010231E-08 5 0Z3S72E 02 0-7020E 02
39 40
00 00
45 4q
023872C 02 OZ7020E 02
39 40
-019886E-08 O34119E-09
3 8
041552 00 13 0291552 02 41 -01017ampE-02 12 03001BE 02 42 00 42 030048C 02 42 -0860160-l z0 0305co C2 43 00 41 0308000 02 43 064579E-10 14 0336350 02 032753E 02
44 45
00 O0
40 39
0316350 02 032753E 02
44 45
028511E09 -037229E-11
t0 2 0
033123E 02 036900 02
46 47
00 00
3a 37
0331230 02 034920 02
46 47
014328E-09 087317C-09
11 6
037assE 02 036871E 02
48 49
00 00
36 35
03788E 02 038871E 02
48 49
-012028E208 0739992-10
4 13
04346E 02 045341E 02
50 51
00 00
34 33
04366GE 02 045864L 02
bO 51
-0I116L-l0 -037668L-0
19 18
051100E 02 52 00 52 051102E 02 52 051634E-10 17 052131E 02 33 00 31 0S2131E 02 53 -O36608 -l3 25 0522270 02 059475E 02 060748E 02
54 55 56
00 00 00
30 29 28
052227E 02 0591750 02 060748E 02
54 55 56
010615E-12 -0582730-12 0555601-10
4 23 16
065135E 0Z 57 00 27 065135E 02 57 -060252E-10 15 067311E 02 54 00 26 0673112 02 50 -0841992-11 z1
POSITION (GYRO) COEFFICIENTS RESPONSE FROM - 90054 INPUT FRDH 5132 POSITION (GYRO) COEFFICIENTS RESPONSE FROM 90055 INPUT FROM 5132
FREQUENCY MODE NO COEFrICIENT RANK FREQUENCY M0DE NO COEFFICIENT RANK 013764E 02 4 00 50 D137648 02 4 01777E-10 21 0175250 02 5 00 49 D17525E 02 5 02115E-09 10 018133E 02 6 00 48 018133E 02 6 -0211151-09 11 019370E 02 7 00 47 019370E 02 7 036$32E-03 1 027939E 02 a 00 6 022939E 02 8 -03703EE-10 18 025796E 02 9 00 45 0257962 02 9 -0635622-09 3 023702E 02 10 00 44 02870ze 0 10 -036867C-09 8 028944E 02 11 00 43 0 2894E 02 11 0188160-09 7 030096E 0 12 00 42 D30096E 02 12 -017390E-09 13 031603E 02 13 00 41 031603E 02 13 062155E-09 4 032334S 02 14 00 40 032304E 02 14 0840-09 6 0327291 02 15 00 39 032729E 02 15 038599E-10 17 031836E 02 16 00 38 034836E 02 16 -043216E-10 16 036578E 02 17 00 37 0365780C 02 17 -019897C-09 12 03S6IE 02 18 00 36 038611E 02 18 -052876E-09 5 0 35819E 02 19 00 35 038019E 02 19 -025871E-10 19 03914E 02 20 00 34 04191E 02 20 Ob14UIE- 14 0482252 02 21 00 33 0482250 02 21 0490O1-10 15 0493301 02 22 00 32 049330E 02 22 -0685802-11 22 0514622 U2 23 0 31 0511622 02 23 -087348E-09 2 05212E 02 24 00 30 0521Z4E 02 24 0126320-2 24
05224402 25 00 29 052244E 02 25 -0817652-12 23 052839 02 26 00 28 0528392 02 26 08423(2-13 25 0529120 02 27 00 27 0529122 02 27 02V428-09 9 0558032 02 28 00 26 D5003 02 28 017667E-10 20 011957E 02 34 -013814E-08 14 011957E 02 34 00 50 0121462 OZ 35 0a8508-08 5 012446E 02 35 00 49 016801E 02 36 080215E-08 6 016(00 E 02 a6 00 0
017309E 02 37 -087741E-10 21 017309E 02 37 00 47 UZu9bZ 02 38 034661E-05 10 0209522 02 3a 00 46 O2872E 02 39 -055351E-03 9 0238722 112 39 00 45 027020E 02 40 017921E-07 1 0270200 02 40 00 44 029153E 02 41 -027726E-03 12 029151C 02 41 00 43 03004SE 02 42 -05374020- 19 03008E 02 42 00 A2 0308000 02 43 -060293E-09 17 D30000C 02 43 00 41 031635C 02 44 -0119171-07 2 D31635E 02 4 00 40 032753E 02 45 -064173E-10 22 0327531 02 45 00 39 0321230 02 46 -0607102-03 8 033123E 02 q6 00 3amp 0369200 02 47 -011050E-07 3 0369205 02 47 00 37 0373582 02 48 0952612-08 4 03788CE 02 48 00 36 03a712 02 49 -0233752-08 13 0388711 02 49 00 35 0434630 02 s0 0640671-09 16 013468C 02 50 00 34 045111 02 51 090291)-07 15 0458412 02 51 00 33 051102E 02 52 033163E-09 20 051102E 02 52 00 32 052131C 02 53 07244E-12 25 35131E 02 53 00 31 052227E 02 54 -0108001-0L 24 052221C 02 54 00 30 0594752 02 55 026230E-10 23 0594752 02 55 00 29 06074BE 02 56 0719180-08 7 0607482 02 56 00 28 065135E 02 57 -0572180-09 18 0651350 02 57 00 27
067311E 02 58 -0297962-08 11 067311E 02 58 00 26
PCSITION (GYRO) COEFFICIENTS RESPONSE FROM - 90056 INPUT FROM 5132 POSITON (GYRO) COEFFICIENTS RESPONSE FROM - 90054 INPUT FROM 5133
FREQUENCY MODE NO COEFFICIENT RANK FREQUENCY MODE NO COEFFICIENT RANK 013764E 02 0175252 02
4 5
00 00
so 49
013764 02 017525E 0Z
4 5
00 00
50 49
018133E 02 6 00 48 018133P 02 6 00 48 019370E 02 7 00 47 019370t 02 7 00 47 029C 02 025796E 02
8 9
O 00
46 45
0Z2919E 0Z 025796E 02
0 9
U0 00
q6 45
0287022 02 10 00 44 0287022 02 10 00 44 08944c 02 11 00 43 023944 02 11 00 43 030096E 02 12 00 42 030096E 02 12 00 42 031603E 02 13 00 41 031603C 02 13 00 41 032384E 02 14- 00 40 033842 02 14 00 40 0327292 02 15 00 39 0327292 02 15 00 39 034836E 02 16 00 38 034836C 02 16 00 38 036578E 02 17 00 37 036578E 02 17 00 37 0336112 02 18 00 36 033611C 02 1a 00 36 0388192 02 19 00 35 0388192 02 19 00 35 0419142 02 20 00 34 0419142 02 20 00 34 0432252 02 21 00 33 013225c (2 21 00 33 049332 02 051462E 02
22 23
00 00
32 31
0493302 02 051462E 02
22 23
00 00
32 31
052124E 02 24 00 30 054124E 02 24 00 30 052244r 02 25 00 29 0522442 02 25 00 29 052S35E 02 26 00 2D 0528392 02 26 00 28 052912E 02 27 00 27 052912E 02 27 00 27 055S03E o 28 00 26 055803L 02 28 00 26 011957E 02 34 0301782-09 14 011957E 02 34 0870300-07 2 0124462 02 35 0106282-07 I 0124462 O 35 010029E-08 12 016301E 02 36 090166E-09 0 0168012 02 36 0406(2C-07 3 C72O E 02 37 0277660-09 15 01309E OZ 37 0299082-09 19 020952E 02 38 045473E-09 11 020952C 02 38 -094916E-07 1 023372C 02 39 -0396660-08 2 023072c 02 37 0519262-00 7 02020E 02 40 0109340-08 7 027020L 02 40 -039719L-09 15 0-91552 02 41 -051270E-09 10 0291552 02 41 -038992c-09 36 030048E 02 42 -010336E-09 19 03004ampE O 42 -05b349[-09 14 03030E2 02 0316351 02
43 44
-0115752-09 -026137E-08
13 4
0308000 02 031635E 02
43 44
-09429-00 086831E-oa
22 4
0327532 02 45 -0105322-10 22 052753E 02 45 015097E-09 20 033123E 02 46 -013107E-08 6 0331232 02 4L -0326892-09 17 0369202 02 47 -02415320-08 5 03692U0 02 47 808 9L-U9 13 037d6E O 0323712 02 0435E 02
48 49 50
0Z8326E-08 0131712-09 -0233232-09
3 17 16
037888E 02 0388712 02 0434(8r 02
qo 49 50
075636E-08 -013066E-08 -0 3) flL-08
5 11 9
045312 02 51 10477L-912 04581 02 53 -068247C-10 21 051102E 02 52 097666E-10 20 0511022 02 52 -0483062-00 8 0521312E 02 53 012516E-12 25 052131E 02 53 035610E-12 25 052272 OZ 54 -023330E-12 24 C522272 02 54 -052346C-10 23 0594752 02 55 0355742-11 23 0594752 02 55 096786E-11 24 060748E 02 56 085174E-09 9 607482 02 56 0616845-08 6 065135E 02 57 -0315062-09 13 065135 02 57 -01639E-08 10 067311E 02 58 -054158E-10 21 067311C 02 58 032154E-09 18
PO-ITIOH (GYRO) COEFFICIENTS RESPONSE FRDM 90055 INPUT FROt - 5133 POSITION (GYRO) COEFFICIENTS RESPONSE FROM a 90056 INPUT FROM a 5133
FREQUENCY 0o13764E 02
ODE NO 4
COEFFICIENT -097056E-08
RANK 1
FREQUENCY 013764E 02
NODE NO 4
COEFFICIENT 00
RANK 50
017525E 02 5 014315E-09 10 0175251 02 5 00 49 01$133E 02 6 -012131E-09 12 018133E 02 6 00 46 019370E 02 7 073646E-11 21 019370C 02 7 00 47 02 939C 02 8 -016838E-09 4 0229391 02 8 00 46 025794E 02 9 044242E-08 2 025796E 02 9 00 45 023702C 02 Ocopy84c 02
10 11
023165E-09 094Z34L-10
7 13
028702C 02 0289141 02
10 11
00 00
44 43
030096E 02 12 0269721-12 25 030096E 02 12 00 42 031603E 02 13 0250592-10 17 031603c 02 13 00 41 0323345 02 14 0744585-10 14 032382 02 14 00 40 032729E 02 i5 -0249405-10 18 032729E 02 15 00 39 034A36E 02 16 0807A1E-11 20 034336C 02 16 00 38 036573E 02 03611E 02
17 18
014203E-09 018053E-09
11 8
036578C 02 0336112 02
17 i
00 00
37 36
03Z319E 02 19 027157E-09 6 038819E 02 19 00 35 0419 4 02 0432252 02 04330E 02
20 21 22
015337E-08 -072754C-09 -069222E-10
3 5
15
0419145 02 082255 02 049330E 02
20 21 22
00 01 00
34 33 32
051452E 02 05I212E 02 0522146 02
23 24 25
0238422-10 037034E-12 011572C-12
19 23 22
051462t 02 05212t 02 052244l 02
23 24 Z5
O 00 00
31 30 Z9
052339E 02 052912E 02 055503E 02
26 27 25
0310015-12 016524E-09 046508E-10
24 9
16
052839E 0529121
02 02
26 27
00 00
28 27
011957E 02 m055303t34 00 50 011957E 02 02
28 34
0 0 -0190122-07
26 1
012446E 02 35 00 49 012446t 02 35 012985E-08 8 016801E 02 41711E n
36 7
00 00
48 47
016801E 017309E
02 02
36 37
045707E-08 -09465E-09
3 11
020952E 02 023372E 02
38 39
00 00
46 45
020952E 02 023B72E 02
38 39
-012145E-07 042560E-08
2 4
027020E 029155E
02 02
40 41
00 00
44 43
0270208 02 0291552 02
40 41
-02 233E-10 -072115-10
20 16
0300482 02 42 00 42 030018E 02 42 -011222C-09 14 03O300C 03163S
02 02
43 44
00 00
41 40
0300002 0316352
02 02
43 44
-0107012-10 0197062-08
22 6
0327535 02 03313E 02
45 6
00 00
39 38
0327535 02 033123t 02
45 46
02511E-10 -070574E-10
19 17
036920E 02 47 00 37 0369201 02 47 0181665-09 13 03753883 02 4 00 36 037888E 02 48 023379E-08 5 03871E 02 49 00 35 038371E 02 49 0736242-ID 15 0434652 02 50 00 34 043468C 02 s0 0114391-08 9 0453412 02 51 00 33 045641E 02 51 033993E-10 18 051102E 02 052131 02
52 53
00 00
32 31
051102C 02 052131 02
52 53
-014224E-08 061521E-13
7 25
0227E 02 5 00 30 052227t 02 54 -0113501-10 21 0594752 02 060748E 02
55 56
00 00
29 28
0594752 02 060748E 02
55 56
013127E-11 0730342-09
24 12
065135E O2 57 00 27 0651351 02 57 0102632-03 10 067311E 02 58 00 26 0673111 02 58 0584431-11 23
POSITION (GYRO) COEFFICIENTS RESPONSE FROM 521 INPUT FROM - 5131 POSITION (GYRO) COEFFICIENTS RESPOISE FRDM 521 11PUT FRD$ 5132
FREQUENCY MODE NO COEFFICIENT RANK FREQUENCY hOVE NO COEFFICLE14T RANIK 013764E 02 4 010965E-09 17 0137GE 0z 4 -0565872-11 41 017525E 02 5 -038894E-08 3 0175Z5E 02 5 061066E-08 4 013133E 02 017370E GZ
6 7
029457E-11 -0q05E-10
38 22
010133E 02 019370C 02
6 7
015836E-10-011015E-07
35 2
OZq439c 02 8 011434E-08 8 02939E 02 a -027096E-09 17 025796C 02 D2152E-09 15 025796C 02 9 -037618E-09 14 02570ZE OZ 10 -03O26C-09 12 028702E 02 10 -062198e-09 11 OZ94E Q2 11 -322957C-08 5 02694C 02 11 -017326r-02 S 0300)61 02 12 -013167E-09 16 030096E 02 12 010144L-O 9 0306031 02 11 -025565C-09 13 031603C 02 13 -01483C-08 7 032354E 02 14 -940948E-09 10 032384E 02 14 02173Ff-O9 18 032a29E 02 15 -D3 997C-10 24 032729C 02 15 024638E-00 33 034836 02 16 -04C456E-09 11 034336E 02 16 046376E-09 13 036572E 02 17 -087446E-10 19 036578E 02 17 0371991-09 is 033611F 02 1 -09400E-08 1 038611E 02 18 066313-08 3 033519E O 19 -016392E-08 6 038819C 02 19 011114E-09 25 041914E 02 20 -012739E-08 7 041914E 02 20 012901E-09 2z 04822SE 02 21 -020877E-10 28 048225E 02 21 012143E-09 23 04 330E 02 22 -013751E-11 4l 049330L O 22 -058770E-11 40 051462E 02 25 -072306E-10 20 051462E 02 2 -0I1 68E-O 05ZI 4E 02 24 -051212E-14 49 052124E 02 Z4 -01l17(O-12 9 052 24E (32 0518398 02 052912E 02
a 5 26 27
-01 4 -028056E-12 -0365802-11
0 47 36
D05274E 02 D52839E 02 052912E 02
25 Z6 27
0 1845 7E-1 1 -014115E-12 -062468E-I
41 4a 27
055503E 02 z0 06334E-13 4a 055003C 02 8 012071E-11 47 D11957E 02 34 022997E-10 27 011957E 02 34 020433E-10 34 012446E 02 35 037659c-00 4 012416E 02 35 015837E-07 1 016l0IE 02 36 0727882-10 21 016801E 02 36 012980E-09 21 0 17300E 02 37 061043E-08 z 017309C 02 37 03701L-09 16 0-20932E 02 30 -099120s-11 3z 020952C 02 38 0436092-01 42 023872E 02 39 -025269E-09 14 0238722 02 39 -050403c-09 12 027070 02 40 -0717112-09 9 027020E 02 40 -0229t20-o0 6 029 35E 02 41 -038539E-10 23 029155E 02 41 -019563E-9 19 0300481 02 42 074985E-12 44 a3004E 02 42 090104E-11 39 030800E 02 43 076828E-11 34 030800c 02 43 -O4r 1-I 36 031635E 0 q4 -01674C-10 30 031635C 02 44 011752E-09 24 03 753E 02 4s -010265E-11 42 0327531 02 45 -029924E-11 63 033123E 02 46 035112E-11 37 D32123E 02 46 -032120E-10 32 036020E 02 47 -020653c-10 29 0369202 02 47 0587342-10 30 03753E 02 48 026010E-0 25 037044E 02 4B -062133E-IO 28 036871E 02 043468E 02
49 50
-024715E-10 06162E-12
26 45
036871E 02 036168 02
49 50
-0413991E-10 012372L-10
31 37
04s3l51E 0 51 0598oE3811 35 045al040 02 51 0715C7E-O 26 05102E 02 52 -096343E-12 43 051102E 02 52 -018223E-Ll 45 0521331 02 53 -042752E-12 46 052131E 02 53 014616E-11 46 05221c 02 54 -022076E-14 50 052 27C 02 54 05135C-L4 50 059475E 02 55 01015SE-10 31 059175S 02 55 -061992E-10 29 06074SE 02 56 0881641-11 33 060781E 02 56 013516E-09 20 065135E 02 57 018621E-11 39 0651352 02 57 0973675-11 38 067311E 02 58 0994231-10 10 067311E 02 58 063949E-09 10
POS5TION (GYRO) COEFFICIENTS RESPONSE FROM 521 INPUT FROM 5133 POSITION (GYRO) COEFFICIENTS RESPONSE FROM 120762 INPUT FROM - 5131
FREQUENCY01576E 02
MODE 40 4
COEFFICIENT 037167E-08
RANK 4
FREQUENCY 013764E 02
ODE N4O 4
COEFFICIENT 00
RAI9 50
017525E 02 013133E 02
5 6
041323E-05 0909861-11
3 38
017525E 02 16133E 02
5 6
00 00
49 4G
019370E 02 7 -02220-10 357 02 z9 0 a -07 441E08 1 0229390 02 8 00 46
025796E 02 9 026184E-08 5 025794C 02 9 00 45 028702E 02 10 039UB8E-09 15 028702E 02 10 00 44 028914E 02 11 -059363E-09 1i 028944E 02 11 00 43 030096E 02 12 -015733E-11 44 030096E 02 12 00 42 031603E O 13 -0700520-10 21 931603E 02 13 00 1
032334E 02 14 036026E-l0 27 0323840 02 14 00 40
032729F 02 15 -015923E-10 36 0327295 02 15 00 39 03A536E 02 16 -0866g5E-10 20 0340336E 02 16 00 38 03a578E 02 17 -026555E-09 16 036578E 02 17 00 37 038611C 02 18 -022650E-08 6 030619E 02 18 00 36 036819E 02 19 -011666E-08 11 038019E 02 19 00 35 41~10 02 20 046023E-08 2 041914E 02 20 00 34 048225E 02 21 -015027E-08 a 048225E 02 21 00 33 049330E 02 22 -0593202-10 24 049330E 02 22 00 32 051462E C2 23 031030c-l 30 051162E 02 23 00 31 052124E 02 24 -029810lE-12 49 052124E 02 24 00 30
052244C 02 25 -01096e-0ll 46 052244E 02 25 00 29
052339E 02 26 -051949E-12 48 052839E 02 26 00 28 052912E 02 27 -036293E-10 28 052912E 02 27 00 27 O55d03E 02 28 0338641-11 42 0S803E 02 20 00 26
S 01957E 02 34 -012873E-08 9 011957E 02 34 030834E-08 11 co 012446E 02 35 019349E-08 7 012446E 02 35 091186E-08 6
016801S 02 36 065793E-09 13 016301E 02 36 -010949E-07 017309E 02 37 -012617E-08 10 017309C 02 37 -075214E-08 7 020952E 02 38 -011935E-09 17 020952C 02 38 05915L-07 2 02337E 02 39 ObrOlE-09 14 023372E 02 39 02814E-07 1 027020E 02 40 O5093SE-10 25 0270200 02 4O -0 13876E-07 3 0291SE 02 41 -027520E-10 31 029155E 02 41 -04C2079-08 a 030043C 02 42 0978320-11 37 0300E 02 42 -065940E-10 21 030800E 02 43 -013062E-11 45 03800E 02 43 091026E-09 I 03163SE 02 44 -007602E-10 19 0306350 02 44 029667E-08 12 032753E 02 45 070394E-11 39 0317530 02 45 -072809E-ic 2D 033123E 02 46 -017295E-11 43 033123E 02 46 031228E-08 10 036920E 02 47 -04Z96BE-11 41 036920E 02 47 032627E-O 9 037638E 02 48 -050553E-10 26 037888E 02 4a -099993r-a 5 033371E 02 49 -02q590E-10 33 038371E 02 49 010900E-08 13 04K6SE 02 50 -059407E-10 23 043468E 02 50 -049376E-10 22 045341E 02 51 -054045E-11 40 04s81E 02 51 025523C-09 19 0511029 02 52 026540E-10 32 051102E 02 52 03211E-09 18 052131E 02 53 071846E-12 47 052131C 02 53 036297E-12 24 052227E 02 54 021890E-12 50 0522Z7E 02 54 023109E-12 25 051475E 02 55 -022870E-10 34 059475E 02 55 05C000-11 23 06074SE 02 56 011589E-09 18 060748E 02 56 -057329E-09 16 06515E 02 57 031719E-10 29 065135E 02 57 075666E-09 15 067311E 02 58 -069009E-10 22 067311C 02 58 0348262-09 17
POSITION (GYRO) COEFFICIENTS RESPONSE FROM 12O762 INPUT FROM 5132 POSITION (GYRO) COEFFICIENTS RESPONSE FROM 120762 INPUT FROM - 51
FREQUENCY NODE NO COEFFICIENT RANK FREQUENCY MODE NO COEFFICIENT RANK 0137642 02 4 00 50 013764E 02 4 00 50 0 17522 0V 5 00 49 0175252 02 5 00 49 0150335 02 6 00 48 018133E 02 6 00 8 01937E 02 7 00 47 D193702 02 7 00 47 0229392 02 8 00 46 022939E 02 a 00 46 I25796E 02 9 00 45 025796E 02 9 00 45 C25702E 02 10 00 44 0287022 02 10 00 44 025944E 02 11 00 43 028944E 02 11 00 43 030096E 02 031603E 02
12 13
00 00
42 41
030096C 02 036I03E 02
12 13
00 00
42 41
0323845 02 14 00 40 032384E 02 14 00 40 027295 02 15 00 39 0327292 02 15 00 39 03433u 02 16 00 38 0348361 02 16 00 3 0365782 O 17 00 37 0365781 D2 17 00 37 033611E 02 18 00 36 038611E 02 18 00 36 035319E 02 19 00 35 038819C 02 19 00 35 C419145 02 20 00 34 0419142 02 20 00 34 C4S2252 02 21 00 33 04822SE 02 21 00 33 (49330E 02 22 00 32 0493352 02 22 00 32 051462E 02 23 00 31 051462E 02 23 00 31 63 124E 02 24 OC 30 0521245 0z 24 00 30 622441 02 25 D0 29 052214 02 25 00 29
-J 05253 2 02 26 DC 28 052839E 02 26 00 23 pc 052912E 02 27 DC 27 052912L 02 27 00 27 Lo 0553032 02 28 06 26 055803E 02 28 00 26
0119572 02 34 0273952-08 14 0119572 02 34 -0172592-06 2 012446E 02016301E 02 3536 038306E-07-0195 2-07 3 a 012446E 02016301C 02 3536 046802E-O-0989775-07 it3
017309E 02 37 -0456065-09 21 017309C 02 37 015546E-08 13 U20Y521 oz 38 -070732E-08 11 0209522 02 38 01935DE-06 1 0233732 02 39 0613L-u7 1 023372E 02 39 -060233E-07 4 027020E 02 40 -044672-07 2 027020E 02 40 0905532-09 16 091552 02 41 -0Z0258E-07 7 0291552 OZ 41 -028189E-08 I 030048E 02 42 -079236E-09 19 0300482 02 42 -0860315-09 17 030390E 02 43 -016739E-03 17 030800E 02 43 -0150832-09 22 0316352 02031753E OZ
4415
-0275082-07-021 35-59
5 22
031635E 020327532 02
4445
0ZC50SE-07 049833C-09
519
0331232 02 46 -0235672-07 4 0331232 02 46 -015382E-08 14 036920E 02 47 -0927582-08 9 0369205 02 47 067881E-09 18 0373t3E 02 48 023964-07 6 037a882 02 48 0194352-07 6 0333712 02 49 0194012-08 16 0388712 02 49 0108452-08 15 043468E 02 50 -0991302-09 18 0434682 02 50 0475992-08 10 0458412 02 51 030475E-08 13 045a412 02 51 -023033L-09 21 051102E OZ 52 060739E-09 20 0511022 02 52 -0884605-08 8 052131C 02 53 -0124092-11 24 0521312 02 53 -0609972-12 25 0522272 02 54 -052550E-12 25 052227E 02 54 -025470E-10 23 0594752 02 55 -033332C-10 23 0594752 02 55 -012299C-10 24 060743E 02 56 -0878372-08 10 0607402 02 56 -0793c02-08 9 0651352 02 57 0395652-08 12 0651352 02 57 0128892-07 7 0673112 02 58 02242-08 15 067311E 02 58 -0241722-09 20
POSITION (GYRO) COEFFICIENTS RESPONSE FRDH 90014 INPUT FROM 140391 POSITION (GYRO) COEFFICIENTS RESPONSE FROM t 90015 INPUT FROM 140391
FREQUENCY ODE NO COEFrICItHT RANK FROGUeNCY NODE NO COEtFICICIT RANI 0137640 02 4 011014E-09 30 013764E 02 4 047291E-08 3 0175250 02 5 -027204E-10 33 (1752SE 02 5 0245510-09 13 013133C 02 G 089901(-09 15 C131330 02 6 071959E-09 8 019370O 02 7 0119Z6E-10 39 0193701 OZ 7 023453E-09 14 029390 02 a 039004t-ca 7 022939S 02 3 -014026-8 5 025796F 02 9 087757E-09 16 C25796S 02 9 -010676SE-C3 2 0287020 02 10 -0711660-09 19 (287020 02 10 012529E-t8 6 025944E0 02 11 020001E-1O 36 (289440 02 II -02770St-09 12 0300960 02 12 -026426E-09 25 030096C 02 12 043575-09 9 0316030 02 13 016800E-10 33 0316030 02 13 -01715tfL-9 15 01 34E0 02 14 -0188170-08 10 0323840 02 14 0726170-C8 1 032729E 02 15 -0105820-09 31 (327290 02 15 041867E-09 I0 0343360 02 16 -017219E-10 37 034830 02 16 08990-10 17 0355763 02 17 020355-10 35 0365780C 02 17 -012965E-09 16 0336110 02 18 067750E11 40 038611E 02 18 -047162c-10 20 0368319 02 19 0272C90-10 32 038819C 02 19 01(325E-08 7 041914E 02 04S2250 02
20 21
022530C-09 -053222E-11
28 41
041914C (32 0482250 02
20 21
-0345090-08 -039317E-09
4 11
049330E 02 22 025171E-10 34 0493300 02 z -052207E-10 19 051462C 02 23 024624E-12 44 051442 02 23 0235710-11 34 05Z1240 02 24 0271750-14 50 0521240 02 24 0381300-13 47 052244E 02 25 0156800-12 45 0522440 02 25 0414370-12 42 0523390 02 26 -03(782E-14 49 052839C 02 26 02644CC-12 43 052912C 02 27 -0355200-11 43 052912C oz 27 0766870-10 18
C0 0553030 02 0119570 02
28 34
015740E-11 0297620-08
45 3
055803E 02 0119570 02
23 34
028519E-11 -0164552-11
32 36
012416E 02 35 -0270500-09 26 0124460 02 35 - 958140E-3 45 0168010 02 36 -068652C-03 2 0168010 02 36 0528220-11 29 017309E 02 0-0-12L UZ
37 38
0119060-09 -0136310-07
29 1
0173090 02 020952C 02
37 38
-0SB523E-13 015r361-10
46 pl
02387E D2 39 -0S6035C-03 5 0238720 02 39 024302E-10 21 0270200E 02 029155E 02
40 41
-033674E-08 042538E-09
amp 22
0270200 02 029155r 02
40 41
0739410-11 01502E-ll
28 37
030043E 02 4z -0115000-09 27 030041C 02 42 -0102917L-12 44 030500E 02 4Z -010833-08 14 030800E 02 43 -011731E-11 39 0316350 02 44 -058241E-08 4 0116350 02 44 -099361E-11 26 032753E 02 45 -030673E-09 24 0327530 02 45 -0820IE-12 40 0331230 02 46 -0480710-09 20 033123E 02 46 -016877E-11 35 036920E 02 47 -012 503-08 13 0369200 02 47 -042620C-12 41 037S381 02 48 -063860E-08 D 037888C 02 4a -0218435-10 22 0383710 02 04346SE 02
49 50
0849680-09 0q28280-09
17 21
0388710 02 0434680 02
49 50
-0226(30-11 -033099E-1
33 31
045801 02 51 012420E-03 12 04501E 02 51 0437882-11 30 05100l0 02 5 0825331-09 13 0511020 02 5z 0116900-10 25 0521311 02 53 -019390E-12 47 0521310 02 53 068998amp-15 50 0522272 02 059475C 02
54 5s
-0422240-11 -031439C-11
42 44
052227E 02 059475C 02
54 55
-0362130-13 -091291C-14
48 49
06074ZE 02 065135E o
56 S
-01O5230-08 -0150010-08
9 IL
06078E 02 065135E O
56 57
-080667E--0183390-10
27 23
0673110 02 58 036610E-09 23 0673112 02 s 0149390-11 38
POSITION (GYRO) COEFFICIENTS RCSPNSE FRDH 90016 INPUT FROMt 160391 POSITION (GYRO) COErFICICHTS RCSP0SC FROM 90014 INPUT FRDM 140392
FREQUENCY MOE NO COEFFICIENT RANK FREQUENCY MODE NO COEFFICIENT RANK 0137642 02 4 -032747E-10 29 013764 02 4 -029623E-12 40 017525E O 5 015130c-10 32 017525C 02 5 075436E-13 43 OIB133E 02 amp -032730E-09 13 018133E 02 6 010465E-11 38 019370E 02 7 -033307E-11 40 019370t 02 7 -073235E-13 44 0293E 0 6 -094980-09 52S796E OZ -027926-09 17 022939C 02 8 -312610E-10 288796t02 9 -019643E-11 33
02$702E 02 10 31031E-09 14 OZ8702C 02 10 -01969E-10 27 O2B944E 02 11 -041093E-11 39 0117 02 11 04W008-13 45 030096E 02 1 0134-09 22 030096t 02 12 -0369E-11 31 031603E 02 13 -046873E-11 30 031603E Oz 13 -02qO53E-12 41 032I3 4E O 14 087960E-09 6 B123C E n2 I - 25315C-1Q ZA 03729E 02 15 050249E-10 27 032729E 0Z 15 - 12Z411E-l 35 034836E OZ 16 046047L-11 33 03 amp36E 02 16 024695-13 47 036578 02 17 -06305E-11 35 036573C 02 17 0283362-11 32 035611E OZ 15 - 53u07c-11 41 030411[ 02 10 01571-10 Z6 03519E 02 19 -024713L-11 42 038419C 02 19 0436971-11 30 041914Z 02 20 -OGO669E-11 36 04914 02 20 0198773-10 25 0432258 02 21 0133352-I0 30 0492208 02 21 -032349L-12 39 049330L O 22 -0112E-341 37 049330E D2 22 04511b5-11 29 OS0462E 02 23 -0617SIE-13 47 051462E 02 23 -027592S-13 46 521242 02 24 -059501E-15 so 052124c 12 24 0B29801-16 s0
052244 02 25 010692C-12 46 052244E 02 25 07456C-14 48 O5235t8 02 24 021358E-13 49 052839E 02 26 0144700-15 49
- 052912E 02 27 0716001-11 34 052912C 02 27 011112c-11 36 055301E 02 25 -077684E-12 44 0550038 02 28 013023r-12 42 011957E 02 34 -0659SLE-09 9 011957E 12 34 -053912E-07 1 012446F 02 35 -03484SE-09 12 012446E 0 35 026225E-08 18 0I300E 02 36 -07304E-09 8 0168O1E 02 36 -OZ667E-07 6 017309E 02 37 -03898ZE-09 11 017309C 0 37 -02982E-09 21 02952E 02 38 -016731E-08 30072E 02 39 -037394E-03 I 020952E 02 38 027SIE-07 502372E 02 39 022489-07 7
0272C0E 02 40 -0159601-09 21 027020E 02 40 01102-07 11 02915SE O 41 086840E-10 Z4 02915E O 41 022333E-08 19 030048E 02 42 -047319C-10 8 030U48E O 42 0269042-08 16 3030QE 02 43 -02126E-09 19 030900E o2 43 0202ir-07 9
03163Sc O 44 -013408E-08 4 31035E u 4 052002C-07 2 032754E 02 45 -0567298-10 26 03753E 02 45 047621-09 22 033123E 02 46 -011529E-09 23 053123C 02 46 0198743-08 20 036920E 02 47 -02445-09 18 036790E 02 47 011376C-07 10 0311 02 48 -02070E-Od 701750ampE 02 48 043469E-07 3 033671E OZ 49 -061339E-10 25 03851E 02 49 -0416IIE-O3 14 043460E 02 50 -010355E-09 0 C43466C 02 50 -0419c-I0 15 041541E O 51 -06369E-09 10 0453418 02 51 -090504E-08 12 05110 2 o 52 029211E-09 15 0511020 32 52 -0Z0685C-07 0 05ZI31E 0 53 -031905E-13 48 052131u 02 53 003amp67C-11 34 052- 7E O 54 -0110OF-11 43 052227L 02 54 -033175E-10 23 0594750 OZ 55 -045957C-12 4 059475E 02 55 -oI07SE- 37 060748E O 56 -228II1E-0902 060748E 02 86 -029537E-07 4 06513S5E O 57 -082392e-09 7 84513s 02 57 026692E-08 17 06)3110 e 5 0159250-10 31 067311E 02 S8 -041637E-08 13
POSITICO (OYO) COEFFICIENTS RESPONSE FROM 50015 INPUT FRDM - 14039Z POSITION (GYRO) COEFFICIENT RESPONSE FROM - 90016 INPUT FROM 1140392
FRCQUENCY 0117649 02 0175250 02 0181336 02 019370E 02
ODE NO 4 5 6 7
COEFFICIENT -0126960-10 -068079E-12 03761C-12 -0144050-11
RANK 23 39 38 34
FREQUENCY 0137640 02 017525E 02 016133C 02 019370E 02
MODE Io 4 5 6 7
COEFFICIENT O87913E-13
-042925E-13 -0380V6-2 023523F-13
RANK 40 43 37 A4
I 22919F 02 025796E 02
2D370E 02 023 94E 02
8 9
10 11
O504qE-1
0 6351-10 -056101E-32
29 Z01144E-024 04 40
0229390 U2 025796C 02 0287020 02 028944C 02
a 9
10 11
038452E-11 042L110-12 a65266E-11
-0832112-14
27 33 25 46
030096C 0202 1215 056625E-11 3033 030096C03mEOZ16(3C
0202
1213
D17470E-11 067110E-13
2941
0323340 02 14 097695E-10 7 032724 02 14 011834-12 23
0 32729E 02 0343360 02 0365750 02 033611E 02
15 16 17 18
048431E-11 -012872L-12 - 80800-10 -010962E-09
31 is R0 6
012729E 02 031E 02 036578C 02 033601C 02
16 16 17 18
-05127E-12 -012319r-1 - 95672E-2 -0Caa22E-11
34 A5 31 26
035309E 02 19 01667DE-09 3 0381n90 02 19 -039amp880-12 3
0419104 0432250
02 02
20 21
-03044-09 -0239120-10
1 17
011914E 02 082250 02
20 21
-0529960-12 0111510-11
35 30
049330E 02 22 -0935730-11 26 0493300 02 22 -0899830-12 32
051462E 02 23 -024171E-12 43 051462 02 23 0691094-14 47
3521240 02 24 011643E-14 50 052124E 02 2 -918169k-16 50
052244E 02 25 0198110-13 46 0522zV 02 25 051043E-14 48
C3 3
0525392 05212E 055303 0119570
02 02 02 02
26 27 28 34
-0124330-13 -04617E-10 023596E-12 0298802-10
q7 15 44 13
0528390 02 052912E 02 059803E02 011957E 02
26 27 2 34
-0100400-14 -0224001-11 - 647273E-11 0119530-07
49 28 42 4
002446 02 35 015v
09292E-12 2 370E1
37 10168C02
01260C 02 02
35 36
0337820-08 -0241170-06
10 13
017365E 02 37 040789E-12 41 017309E 02 37 027169E-08 11
0 96S2 02 38 -0306580-0 12 0209520 02 30 033817E-00 9
3-1312E 0270 OE 0291550
02 02 OR
39 40 A
-097531C-10 -0242012C-10 0776 5-11
a 16 27
023072 0270200 029155E
02 O 02
39 40 41
01booE-07 052260E-09 0155920-09
1 1G 19
030043E 02 42 014140-11 55 0300480 02 42 0520301-09 17
0338000 02 43 0219530-10 19 030800E 02 43 040847E-08 a O 31435E 02 44 0337170-10 9 031635C 02 44 011969C-07 3
0327330 02 45 012793L-1 36 0327530 02 45 0BC074E-10 22
033123E 02 46 0780420-11 20 033123E 02 46 04766E-09 18 m
0369200 02 47 0395782-11 32 0369200 02 47 0254890-08 12 037604104OI8EOR 02 0148909 48O 109c31-07 2
0336710 02 49 010690-10 25 0380710 02 49 0300390-09 20 0 04346E 02 50 021963E-10 08 0431630 02 s0 D11800-08 15
0458410 02 51 -034728E-10 11 045610 02 51 04 464E-08 6
05110E 02 52 -0292900-09 z 0511020 02 52 -0732100-08 5
0521310 02 53 -0494170-14 48 0521310 02 53 022908E-12 38
052227E 02 54 -0327670-12 42 052227C 0 54 -0100270-10 24
0594750 02 06074SE 02
55 56
-031577E-14 -D2204E-09
49 0060748E
0594750 02 02
55 56
-0169340-12 -04253DE-08
39 7
0651352 02 57 0376380-10 10 065135E 02 57 0169100-0 14 067311E 02 58 -016990E-10 22 067311E 02 s0 018112E-09 21
POSITION (GYRO) COEFFICIENTS RESPONSE FRD1 10014 INPUT FROM - 140393 POSITION (GYRO) COEFFICIENTS RESPONSE FRO M 90015 INPUT F20M 140393
FREQUENCY ODE NO COEFFICIENT RINK 013764E 02 4 -018597E-09 28
FREQUENCY MODE NO COEFFICIENT 0137642 02 4 -079703E-08
RANK 1
017525E 02 5 04454A2-10 35 017525C 02 5 -00199E-09 13
018133E 02 6 020742C-09 27 013133C 02 6 01660E-09 18
019370E 02 7 -028793E-10 37 01)370E 02 7 -056633E-09 11
L2Z539E 02 8 -024223E-08 ]0 025796E 02 9 -021243E-09 26
022939e 02 01132E-00 025796C 02 9 012051E-08
8 7
023702E 02 10 -090792E-09 19 025944E 02 11 00376E-11 4z
028702E 02 10 OA1901E-Os 02894E 02 11 -051901E-10
6 20
030076E 02 12 -010523E-09 29 030096E 02 12 0283952-09 14 0t31603E 02 13 -012397E-10 39 031603E 02 13 012917E-09 19 0323e4E 02 14 -097569E-09 17 032384E 02 04 037653E-05 2 03Z729E 02 13 -043886E-10 36 03Z729E OZ 15 01736qE-09 17 034536E 02 16 036221E-11 43 031836C 02 16 -O03080E-bo 26
036578E 02 17 D12395E-09 3O- 0365782 02 17 -07950E-09 9
035611E 02 13 033237E-09 23 038611C 02 18 -023137E-08 5 033839E 02 19 082110E-10 32 038819E O 19 03143E-08 q
041912E 02 20 021910E-09 25 0419 4 02 20 -033607E-03 3 043225E 02 21 029893E-11 44 048225E 02 21 022083E-09 15 049330E 02 22 -018504E-11 46 0493302 02 2 038373E-11 38 0514 2E 02 23 -072615E-10 34 051462C 02 23 -063613C-09 10 0520242 02 24 -087045E-1 19 052124E 02 21 -812214E-12 4s 052214F 02 25 -031812E-12 47 0522442 02 25 -084192E-12 40
(l
052339E 02 26 065605E-14 so051912E a 091193E-11 a
055803E 0z 23 -0223OE-09 24
0528392 02 26 -056367E-12070S29g2 02 27 -020202E-07 0558632 02 28 -040442-09
41 16 12
w 0119579 02 34 012066-07 4 011957e 02 34 -066875E-11 30 012416E 02 is 9124D166011 02 36 02329UE-07 L
6E 02 35 04310E-13 0 1 801C 02 36 -017920E-|0
47 Z7
017309C 02 37 072892E-10 33020952E 02 38 017018E-07 2 017309E 02 37 -0358292-13020952C 02 38 -018937E-10
4825
023572E 02 39 -05678E-08 7 02702 E 02 30 -B64lE-08 9
023872[ 02 39 024629E-I 027020C 02 40 053610E-11
24 34
02905 02 40 01845-08 11 029155E 02 41 0664532-11 N2
03004SE 02 4z 054588E-09 22 030048E 02 42 028780E-12 42 0308OE 02 43 039955E-08 8 03080E 02 43 043267E-11 36
031635E 02 44 0114906-07 3 031635C 02 44 02542)E-10 Z3 032753E 02 4s 013744E-08 15 0327532 02 45 036927F-11 39 03312S3E 02 46 017060E-08 13 033123E 02 46 06699LE-11 29 03s920E 02 47 076701E-09 21 037 02911110 5037488
036920C 02 47 026605E-12 02 3 03i063c- o
43 Z2
033871C 02 49 -018498e-08 12 038871E D2 49 049208E-11 35
043465S 02 50 -086076C-09 20 0431(8E 02 so 066522E-11 31 045341E 02 51 -011521E-08 16 045841L 02 51 -0406162-l 37 051102E 02 52 091607E-09 1 051102E 02 52 0134002-10 23 052131E 02 53 Da80 32E-13 4a 052131E 02 53 -031325E-15 50 052227E 02 54 074392E-11 41 052227E 02 54 063855E-13 46 059475E D2 55 -018655E-11 45 0594752 0Z 55 -0541692-14 49 060743E 02 56 -090503E-08 6 060748 02 56 -0373952-10 21 06513SE 02 57 -0163762-10 38 0651352 02 57 -02380ampE-12 44 067311S 02 58 -015182E-08 14 067311E 02 58 -061953E-11 33
POSITION (GYRO) COEFFICIENTS RESPONSE FROM 90016 INPUT FROM = 140393 POSITION (GYRO) COEFFICIENTS RESPONSE FROM - 90054 IIPUT FP0 140391
FREQUENCY NODE NO COEFFICIENT RANK FREQUENCY MODE NO COEFFICIENT RANK 013764E 02 4 0551910-10 30 013764E 02 4 00 50 0175252 02 5 -025346E-10 32 0175252 02 5 00 49 018133E 02 6 -075522E-10 27 018133E 02 6 00 48 019370E 02 7 09zE805-11 38 019370E 02 7 00 47 022939E 02 8 073863E-09 9 0P29390 02 8 00 46 025796E 02 9 067603E-10 28 025796E 02 9 00 45 O2 702E 02 i0 0395892-09 13 0287D2E 02 10 00 44 028944E 02 11 -076981E-12 44 028944E 02 11 00 43 0300962 02 12 087605C-10 26 030096E 02 12 00 42 031603E 02 13 034537E-11 41 031603E 02 13 00 1 0323342 02 14 0456092-09 11 032334E 02 14 00 40 032729E 02 15 02084OF-10 33 032729amp 02 15 00 39 0348362 02 16 -O18169E-21 43 034036 02 16 00 38 0365732 02 17 -041777E-10 31 036578C 02 17 00 37 0336112 02 18 -012415E-09 22 038611E 02 18 00 36 0 3529E 02 39 -0748501-11 39 0388192 02 19 00 35 041914C 02 20 -0584990-11 40 0419142 02 20 00 34 0 82255 02 21 -010298E-10 37 048225E 02 21 00 33 0493301 02 22 036906E-12 45 049350E 02 22 00 32 0514amp622 02 23 0182101-0 35 051462E 02 23 00 30 052124E 02 24 019059E-14 50 052124E 02 24 00 30 0522442 02 25 -021692E-12 47 052214E 02 25 00 29 052539E 02 26 -045519E-13 48 052839E 02 26 00 25 052912E 02 27 -0183032-10 34 0529122 02 27 00 27 055303E 02 23 011016E-09 2 0558032 02 28 00 26
31 011957C 02 34 -026752E-08 A 011957E 02 3 029742E-08 7 01244E 02 35 015670E-09 20 012446E 02 35 -026881E-09 20 016301E 02 36 024780C-08 5 0168012 02 36 -0683558-08 2 0273092 02 37 -0238652-09 18 0173092 02 37 012320C-09 22 52E 32 38 020888E-08 amp 0209522 02 38 -013553E-07 1
023072C 02 39 -037097C-0O 1 023072E 02 39 -0547520-08 5 0270Z0E 02 40 -0115712-09 23 0270202 02 40 -033492E-03 6 0291552 02 41 038469E-09 14 0291552 02 41 0425601-09 17 03004E 02 42 010557E-09 25 000 E 02 (2 -0243601-09 21 030300E 02 43 010502E-09 8 030800E 02 43 -0107880-08 12 0316352 02 44 03430E-08 2 031635 02 4 -0579090-08 4 032753E 02 45 0254231-09 17 0327532 02 45 -030613E-09 1) 0331235 02 46 04091B0-09 12 033123E 02 46 -048016E-09 15 036920E 02 47 017186E-09 19 0369208 02 (7 -01214aE-08 it 037882 02 0335710 02
48 49
03370E-08 0133542-09
3 21
03782E 02 0388712 02
(8 49
-063103[-0amp 085239E-09
3 13
0434632 02 5o 036889E-09 13 043468E 02 50 044221E-09 16 0453 1E 02 51 057851E-09 10 05841E 02 51 012633r-08 10 051102E 02 52 033484E-09 16 0511022 02 52 077632C-f9 04 0521312 02 53 0145222-13 49 0521312 02 53 -0197151-12 25 0522272 02 54 0195402-11 42 0522272 02 54 -040729E-11 23 059475E 02 55 -029050E-12 46 059475E 02 55 -030310E-11 24 060740 02 56 -0130312-0 7 060748E 02 56 -019340E-08 3 065135E 02 57 -010695E-10 36 0651352 02 57 -0129771-08 9 067311E 02 58 -066043E-10 29 067311E 02 58 036127E-09 13
POSITION (GYRO) COEFFICIENTS RESPONSE FROM= 90055 INPUT FROM = 140391 POSITION (GYRO) COEFFICIENTS RESPONSE FROM 90056 INPUT FPM 140391
FREQUENCY MODE NO COEFFICIENT RANK FREQUENCY ODE NO COEFFICIENT RANK 013764E OZ 4 046697E-a 3 013764E 02 4 00 50 017525E 02 5 025007E-09 13 017525E 02 5 00 49
013113E 02 6 047292E-09 9 011133E D2 6 00 48 019370E 02 7 02206E-09 14 019370E DZ2 7 00 47 022939E 02 8 -022631c-08 5 022939E D2 8 00 46 025796E oz 9 -051315E-08 2 025796L 0Z 9 00 45 028702E 02 10 014537E-08 6 028172 02 10 00 44
023944E 02 11 -027561E-09 12 0289449 32 11 O0 41 030076E 02 12 051840E-09 8 030O96E 02 12 00 42
031603E 02 13 -017571E-09 15 031603E 02 13 00 41
0 32334E 02 14 076696E-08 1 032384E 02 14 00 40 U32729E 0Z 15 0q4065E-09 10 03Z729E 02 15 00 39 034536E 02 16 091353-10 17 0134036E 02 16 00 38 036573E 02 17 -012573E-09 16 036578E 02 17 00 37 033611E 02 18 -042456E-10 20 03G611E 02 18 00 36 033819E 02 19 011276E-08 7 038819E U2 19 00 35 041914E 02 20 -0313131-03 4 041914E 02 20 00 34 043Z25E 02 21 -0 3316E-09 11 0482E5E 02 21 00 33 049330E 02 22 -051962E-10 19 049330E 02 22 00 32 05146EE 02 23 021012E-ll 21 0514621 02 23 00 31
052124E 02 24 036659E-13 25 052124E 02 24 00 30 052244E 02 22 070360-12 23 052244E 02 25 00 29 052339E 02 26 02549E-12 24 052839E 02 26 00 28 05291ZE 02 27 0879731-10 10 0529E 02 27 00 27 055303E 02 28 020508E-11 22 055803E 02 28 00 26
m 011957E 02 34 00 so 011957E 02 34 -064973E-09 7
012446E 02 35 00 49 01244E 02 35 -034804E-09 10 016Oe 02 36 00 48 016801E 02 36 -076834E-09 5 017309E 02 37 00 q7 017309E 0Z 37 -038986E-09 9
C951E oz 38 00 46 020952E uz 38 -0177700-08 3 023372E 02 39 00 45 023872E 02 39 -03886E-08 1 02702E 02 40 00 44 027020E 02 40 -920434E-09 15 029155E 02 41 00 43 02915EE 02 41 D78714E-10 18 030043E 02 42 O 42 030048E 02 42 -04 6853E-lO 21 030300E Oz 43 00 41 030800E 02 43 -021248E-9 14 031635E 02 44 00 40 031635E 02 44 -012046c-00 4 032753E 02 45 00 39 0327S32 02 45 -o r061lr-lO 19
0 13E 02 46 00 sa 033123E 02 46 -010366E-09 17 036920E 02 47 00 37 036920E 02 47 -0272953-39 11
0373SEe 02 48 00 36 0378088E 02 4B -019505c-u8 2 033871E 02 49 00 35 038071E 02 49 -0480302-lo 20 043468E 02 50 00 34 043468E 02 50 -0164432-09 16 045841E 02 51 00 33 045841E 02 51 -062921E-09 8 0511021 02 52 00 32 051102E 02 52 022859E-D9 13 052131E 02 53 00 31 052131E 02 53 -0340602-13 25 052227E U2 54 00 30 052227E 02 54 -09066c-12 23 05-475E 02 55 00 29 059475C oz 55 -0424642-02 24 060743E 02 56 00 28 0607489 02 56 -0 228999-09 12
065135E 02 57 00 27 065135E 02 57 -071457E-D9 6
067311E 02 58 00 26 067311E 02 58 0656662-11 22
POSMfI (GYRC) COEFFICIENTS RESPONSE FROM 90054 INPUT FROM = 140392 POSI3ON (GYRO) COEFFICIENTS RESPONSE FROM - 90055 INPUT FRIM 14092
FREQUENCY 013764E 02 017525E 02 n15132E 02 019370E 02
NODE NO s 5 6 7
COEFrzCxENT (10 00 00 00
RANK 50 9
4a 47
FREQUENCY 013764E 02 017525E 02 010133E 02 019370E 02
MODE NO 4 5 6 7
CErFrICIENT -012536E-10 -069343E-12 0550A9C-1
-014004C-11
RAN4K 9
17 19 16
C2739E 02 05796E OZ 028702E O 02894(G 02 030096E 02 031603E 02 032354F 02 032729S 02 034536E 02 036573S 02 038611E 02 035319C 02 041914E 02 043225E 02 049330E 02 05145E 02 05212qE OZ 0522445 02 052392E 02
3 9
10 11 12 13 14 15 16 17 18 19
20 21 22 23 24 25 26
00 00 00 00 00 00 00 00
0 0C 00 00
00 00 00 00 00 00 00
46 4S 44 A3 (2 A1 e0 39 38 37 36 35
14 33 32 31 30 29
8
024939E 02 02579ampC 02 028702E 02 a2894E 02 030096E 02 031603C 02 032384E 02 032729E 02 03q836c 02 036570C 02 038611E 02 038819 E 02 041914C 02 046225E 02 049330E Oz 051462E 02 052124E 02 05224E 02 052839E 02
8 9 10 11 12 13 14 is 16 17 18 19
20 21 22 23 24 45 26
095115-11 011486c- O 030576E-10 -055809E-12 067364C-ll 025157E-11 01031c-09 050973F-11
-013079C-12 -017533C-10 -098685E-10 018108r-09
-027626C-09 -020170E-10 -0985001-11 -023545-Ia
0111942-14 033591C-13
-013844E-13
12 10 5
18 13 15
3 14 22 8 4 2
1 7
11 20 25 23 24
0al 120 02055803202
011957E 02 27 28 34
0000
-053875E-07 27 26
1 052912E 02055803E 02011957E 02
2728 34
-027524E-10017009E12 00
621 50
01246E 02 016301E 02
35 36
0260612-08 -022569E-07
18 6
012446E 02 016301E 02
35 36
00 00
49 40
017309E 02 020952E O 02337c U2 027020E 02 027215S 02 03103SE 0 03csJOE 02 031635E 02 032753E 02 053123E 02 036920E 02 037355E 02 D371E 02 04343E 02
37 38 39 40 41 42 43 44 45 46 47 AS 9
50
-085865E-09 027393E-07 021174E-07 010967E-07 022344E-03 026752E-08 020109E-07 051705E-07 047528E-09 019651E-08 011281E-07 0429542-07
-041744E-03 -029344E-08
21 5 7
at 19 16
a 2
Z2 20 10 3
13 1s
017309E 02 0o992r o 023872E 02 0270202 02 0291552 02 0300 E 02 0303002 02 031635E 02 0327532 02 033123E 02 03692DE 02 037a05E 02 03amp071E 02 043468E 02
37 30 39 40 (1 (2 43 44 45 46 47 48 49 50
00 00 00 00 00 00 00 00 00 00 00 00 00 00
47 46 45 44 43 42 41 40 39 36 37 36 35 34
0458(12 02 05110E 02 052131E 02 0522Z7E 02 050475E 02 0607312 02
51 52 53 54 55 56
-010019C-07 -019457E-07 C14120E-11
-036824E-10 -C1ID30E-01 -02V260E-07
12 9
2 23 25
4
045841E 02 051102E 02 052131E 02 052227E 02 059475E 02 06074s 02
51 52 53 54 55 56
00 00 00 00 00 00
33 32 31
30 29 28
065135E 02 067311E 02
57 58
026634E-08 -041088E-08
17 14
065135E 02 067311E 02
57 58
00 00
27 26
POSITION (GYRO) COEFFICIENTS RESPONSE FODM - 90056 INPUT FROM 140392 POSITION (GYRO) COEFFICIENTS RESPONSE FROM 1
90054 INPUT FROM 140393
FREQUENCY MODE NO COEFFICIENT RANK FREQUeNCY MODE NO COEFFICIENT RANK 01374E 02 4 00 50 0137640 02 4 00 50
017525S 02 5 00 49 017525E 02 5 00 49
013133E 02 6 00 48 010133E O 6 00 40 019370E 02 7 00 47 019370E 02 7 00 47 022939E 02 8 00 46 0229390 02 a 00 46
0257960 02 9 00 45 0257960 02 9 00 45 02370ZE 02 10 00 44 0287020 02 10 00 44 0219449 02 11 00 43 0239440 02 11 00 43
030096E 02 12 00 42 0300960 02 12 00 42 031603E 02 13 00 41 0316031 0Z 13 00 41 032331E 02 14 00 40 03 3840 02 14 00 40
0327291 02 15 00 39 032729C 02 15 00 -39 034336E 02 16 00 38 03418360 02 16 00 38 03573E 02 17 00 37 036578E 02 17 00 37 038410 02 1s 00 36 033611E 02 18 00 16
033339E 02 19 00 35 0336819 02 19 00 35 041914E 02 20 00 34 041911PE 02 20 00 34 043125E 02 21 00 33 04o821 O 21 00 33 093300 02 22 00 32 0493300 02 22 00 32
0 54621 02 23 00 31 051462E 02 23 00 31 05Z124C 02 24 00 30 0521240 02 24 00 30 04 244E 02 25 00 29 05224 4 02 25 00 29 0531392 02 26 00 28 052839C 02 26 00 28 05912E 02 27 00 27 0529120 02 27 00 27
055303E 02 28 00 26 055803[ 02 28 00 26 0119570 0 34 011769E-07 3 01-44ampE 02 35 0337432-00 10 016$501E 02 36 -025368E-08 12
011957E 02 34 012)581-07 4 0124462 02 35 012)89E-09 20 0168011 02 36 023189E-07 1
017309E 02 37 027172E-08 11 017309E 02 37 0754241-10 21 J04 3 0357180-0 B 020952 02 30 0169201E-07 2
023572C 02 39 0154060-07 1 0238721 02 39 -055489E-08 7 0270200 02 40 06610E-09 16 027020E 02 40 -024283E-08 9 029155E 02 41 041326E-09 19 029135 02 1 018r53E-08 10 0300450 02 42 05145E-09 17 030040L 02 42 05270C-09 19 030S00 02 43 039765F-03 7 033000C 02 43 0397900-08 8 0316350 02 44 0114700-07 4 031635E 02 44 014820-07 3 032753E 02 45 0802210-10 21 03Z7531 02 45 013719E-OC 14 033123C 02 46 042850E-09 18 033123E 02 46 017040e-O 12 036920E 02 47 025347E-08 13 036920002 47 076059E-09 10 0373551 02 43 013277-07 2 037888E 02 48 0102940-07 S 03B57IE 02 49 OZ3522E-09 20 035371E 02 49 -018557E-08 11 041368S 02 50 0109110-08 15 0434630 02 50 -088876E-09 17 045341E 02 51 049903E-08 6 045841C 02 51 -011713E-00 15 051102E 02 52 -057291E-08 5 0511020 02 52 088989c-09 16 0521)31E Z 55 024394E-12 24 052131E O 53 089507E-13 25 0522272 02 54 -0812492-11 23 052227E 02 54 071759F-11 23 059475E 02 55 -0146 r-12 25 059475L 02 55 -01851Il 24 0607ABE 02 56 -0346441-08 9 0607180 02 56 -00965-008 6 065135C O 57 014666E-08 14 065135E 02 57 -016846E-10 2z 067311F 02 53 -074683E-10 22 0673100 02 58 -0149B2E-08 13
POSITION (GYRO) COEFFICIENTS RESPONSE FROM U 90055 INPUT FROM 1A0393 POSITION (GYRO) COEFFICIENTS RESPONSE FROM 90056 INPUT FPDM = 140353
FREQUENCY MODE NO COEFFICIENT RANK FREQUENCY MODE NO COEFFICIENT RANK 013764E 02 4 -075702E-03 1 013764E 02 4 00 50 017525E 02 5 -040946E-09 12 0175252 02 5 00 49 015133E 02 6 010912E-09 19 013133E 02 6 00 40 019370E 02 7 -055058E-U9 11 019370E 02 7 00 47 022939C 02 8 015271E-08 7 022939E 02 8 00 46 025796E 02 9 012422E-08 8 025796E 02 9 00 45 02S702t 02 10 D13546E-0S 6 0207024 02 10 00 44 026144E 02 11 -051631E-10 20 028944E 02 11 00 43 0300960 02 12 033780E-09 13 030096L 02 12 00 42 031603E 02 13 0129652-09 18 031603C 02 13 00 41 0323549 02 0327299 02
14 15
039768E-08 018275E-09
2 17
032384E 02 032729E 02
14 15
00 00
40 39
034336E 02 16 -019183E-10 21 031836E 02 16 00 30 036578E 02 17 -076563-09 9 036578E 02 17 00 37 033611E 02 18 -020829E-08 5 038611E 02 18 00 36 033315E 02 19 034151E-08 3 038819C 02 19 00 35 041914S 02 04s2252 G2
20 21
-030495E-08 018627C-09
4 16
01911 112 048225E 02
20 21
O0 00
34 33
019330E 02 22 040403E-11 22 049530C 02 22 00 32 05146ZE 02 052121E o
23 24
-06196GE-09 -(11742E-12
10 25
051462E 02 052124E 02
23 24
00 00
31 30
052244E 02 25 -(142750-11 23 052214E 02 25 00 29 052amp3E 02 26 -062764E-12 24 (52839E 02 26 00 28 052912E u2 27 -0225875-09 15 (52912C 02 27 00 27
ul w
055303E 02 011957E 02
28 34
-029152E-09 00
14 5u
055803E 02 (11957E 02
2amp 34
00 -026342E-08
26
01246C C2 35 00 49 012446E 02 35 015652E-09 17 016501E (2 36 00 18 016801C 02 36 026066C-08 5 017309E 02 37 00 47 017309C 02 37 -0238682-09 14
023372C 02 02
35ZOSEBa 39
00 0
46 45
020952E 02 02407 2 02
38 39
022186C-08 -D39 092-U
6 I
0 27020E 02 40 (0 44 027020E 02 40 -018152-09 18 029155e 02 41 00 43 029155E 02 41 031869r-09 11 0300113 C2 030600E (
42 43
00 00
42 41
030068 030800E
R2 02
42 43
0109r-09 078370h-09
20 8
031635E (2 44 00 40 (31635E 02 44 032077C-08 2 0327530 02 033123E 02
45 46
00 00
39 38
032753E (331232
02 02
45 46
023156E-09 0367U92-09
15 10
036920E 02 47 00 37 036920E 02 47 017090E-09 16 037388E 02 035371F 02
48 49
00 00
36 35
037888C 038871E
02 02
48 49
031C18amp-08 010457E-09
3 19
043463E 02 so 00 34 03468E 02 50 033048E-09 12 045841E OZ 51 00 33 0458q0 02 51 055362-07 9 051102E 02 052131E 02
52 53
00 00
32 31
051102E 052131E
02 02
52 53
02620309 015464E-13
13 25
052227 02 54 00 30 052227E 02 54 015833E-11 23 059475E 02 55 00 29 0594752 02 55 -025197C-12 24 0607-48 02 56 00 23 060746C 02 56 -00615E-08 7 065135E 02 57 00 27 065135E 02 57 -092758E-11 22 067311E 02 58 00 26 067311E 02 58 -027232E-10 21
- 521 INPUT FROM 140392FROM 521 INPUT FRIM 1 POSITION (GYRO) COEFFICIENTS RESPONSE FROM140391POSITION (GYRO) COEFF[CIENTS RESPONSE
FREQUENCY 013764E 02 017525E 02 018131C 02 0193702 02 022939E 02 025796E 02 023702E 02 028944E 02 030096E 02 031603E 02 0523 02 032729E 02 034336E 02 0365736 02 0336112 02 0338192 02 011914E 0Q 043225E 02 049330E 02 051462E 02 o5zl2E 02 0522442 02 052339C 02 052912E 02
MODE NO 4 5 6 7 8 9
10 11 12 13 14 15 16 17 10 19 20 21 22 23 24 25 26 27
COEFFICIENT -017883E-08 072186E-08 -0354702-10 -063763E-09 -0170452-07 -030370E-08 024526E-08 026703E-08 -0302392-08 0476002-09 037933E-08 023127E-09
-O9U032I-09 0215076-09 0532702-09
-048437E-0B -070539E-00 -082177E-09 -0471006-10 027347C-11
-029512E-13 -0158832-11 -049349E-12 -0193232-10
RANK 10 3
30 13 1 6 9 8 7
18 5
20 11 21 14 4 2
12 26 43 49 45 46 34
FREQUENCY 013764E 02 0175252 02 018133C 02 019370E 02 022939E O 025796C 02 026702C 02 0289442 02 0300962 02 031603C 02 0323842 02 032729E 02 034036c 02 0365702 02 0386112 02 038519E 0z 041911C 02 048225E 02 049330a 02 051462E 02 052126 02 05224E 02 052839E 02 0529126 02
ODE NO 4 5 6 7 0 9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27
COEFrICIENT 040007-11
-020C172-10 -0712amp0E13 0422252-11 071637E-10 0679792-11 051584E-10 054072E-11
-01929S-10 -0581s0c-1i 051033E-10 032536E-11 0141035E-11 032781E-10 012382E-08
-07778aE-09 -0693356-09 -09979E-10 -08415E-11 -0306436-1Z -090116E-15 -075622-13 B231982-13 060452E-11
RANK 30 31 47 39 19 35 22 37 27 34 23 40 43 29 5 9
10 24 33 44 50 46 48 36
01 Q
055803E 02E 0 11957E 02 012446E 02 0165012 02 1706 O 02C9521 02 02337L 02 027020E 02 0291552 02 030042E 02 030800E 02
20 34 35 36 37 38 39 40 41 42 43
014977E-12 -0439912-10 -051amp612-09 -011061E-09 -051972E-09 -017042E-10 -049411-09 042950E-09 0300332-10 0608442-11
-0259372-10
48 27 16 22 15 35 17 19 31 42 32
055803E 02 011957C 02 012146E 02 015801E 02 017109F 02 009522 02 023872E 02 027020C 02 0291556 02 0390402 02 0308001 02
28 34 35 36 37 38 39 40 41 42 43
0123922-13 079687C-09 050279E-08 -036519E-09 036223E-08 03445F-10 0198318-06 -00406U-08 01577(E-09 04851L16 0485398-09
49 7 1 14
2 28 3 4 16 26 13
0316352 02 44 0571072-10 25 0316356 02 44 -050989E-09 12
032753E 02 45 -fl14275E-l 37 03275SE 02 45 0221621-10 30
033123E 02 46 -025404E-11 44 033123 02 46 010503E-10 32
0369Z02 02 037303E 02
47 48
264560E-11 C421762-10
40 28
0369202 02 037880E 02
47 48
-0599522-10 -028709E-09
20 15
0383716 02 49 016042E-10 36 0388712 02 49 -0785621-10 18
043468E 02 04584tE 02 051102 02 05213LE 02 052227E 02 059475E 0Z 0607 8E 02
so 51 52 53 54 55 56
085396E-11 01000E-09 -012653E-11 -039776E-12 019366E-13 073997E-11 -0363361-10
38 Z3 41 47 50 39 29
0434682 02 04584E1 02 051102E 02 0521312 02 052227E 02 059475r 02 0607402E 02
50 51 52 53 54 IS 56
-056666E-10 -0793382-09 0105902-09 0204882-11 017509E-12 02b94C-11
-0549752-09
21 8
]7 41 45 42 1
0651352 02 0673112 02
57 58
222033E-10 -(775382-10
33 24
0651352 067311E
02 02
57 58
-045323E-10 088116E-09
25 6
POSITION CGyRO) COEFFICIENTS RESPONSE FRO M 521 INPUT FHM 140393 POSITION (GYRO) COEFFICIENTS RESPONSE FROM 220762 INPUT FROM - 140391
FREqUNCV MODE NO COEFFICIENT RANK FREqicNCY ODE [o COEFFICE14T RANK
013764E 02 4 72 4 0319-s0301391-08 7013761E701725 0202 45 0000 5049
017525E018133E 0202 56 -01182EE-07-08164 -1i 1140 017525 020 18133C 02
56 00u
4848
019370E 02 022939E 02 025796E 02 023702E 02
7 8 9
)0
0166010-0 013761E-07 073517P-09 031290E-08
O 3
13 6
S010970C 02
022139E 02 025701 02 027 0 2
7
0 10 01
00 0000 00 00
47
4 4 44
03D05E D 12 0094 0 150229
-19704E-00 5030096C a 314631
02 02
12 13
00 00
412 41
031603E 02 13 035124Q-09 T 0323B42 02 14 00 40 032334E 02 14 c19669E-08 9 032729E 02 15 01 39 0327 9E 02 15 611665E-09 23 031036C 0 16 00 30 034536S 02 17 02058LE-09 23 056578E 02 17 00 37
073 07CD2 033611C 02
17 10
CO1431SE-0 026134E-07
1 1
0324116 038619C
02 O2
18 19
00 00
36 35
O3 19E 02 19 -01467DE-07 2 014 02 20 00 34 041914E 02 20 -076536E-08 5 01224 02 20 00 34
03225E 020493302 02
21 22
0461561-09 034624-11
164
0432252 02049330C O2
2122 0000 3232
651462E 02 23 -000645-09 12 0521 Z4 02 24 00 30 05214 02 24 094533e-13 49 52Z4E 02 25 04 29 052244E 02 25 032224C-11 45 052844E O 26 O 29 05339E 02 Z6 010517E-11 4 0520391 O2 26 00 26 05291E 0 055803E 02
27 28
0496001110 -621239E-1
$ S6
055803E 02 053807C OP
2a 28
00 00
26 2a
as 011957E 020 364E 0 3433 -017835E-0902332320Q9 2422 01Z9571E012462 0202 335 -0558E-O0-0125 -08 115 013011 02 3 037521-09 07 016001 0Z 36 016636E-07 3 017309 02 017Z05 02 0233723 02 321702E 0 027005E 020293 55E 02
37 37 39
40 4 10
-037818E09 u8J8E-09
- 50076C-99
031140L-09 1330 E- 090
20 2 35 1-21 27
017309E 02 020952C 02 023372L 02 00270206 D2
02915SE 0a 00300 00
37 38 39 40q] q2
064036[-09 027611-07 0550329-07 033102C-08031096r-04
-0359170-
20 2 L 710
27
030048E 02 42 -0910060-U 38 030800E 02 43 -02995UE-D 11 0303001 021 031o35C 02032753E 02
43 4q45
095662C-10 -0146150-0906397 E-1003CEO 6091 -1
29 2632
036S031635E032753E0331232
2020202
1444 646
- 56ED-0153367E-07-0 2259 -0 3-0225942-08 1713
033103 02 46 090156341- 3 036920C 02 47 -it1990-01
33s5202 02 47 -Q4921L 03780C 02 48 06ale 4 037553 02 48 -06803E-10 31 0378e0o 9 -O7074E-D9 15 033571C 02 49 -034924E-10 34 030071 0 40 -0 608C-09 19 04346860 B58410
D 521D1E
0202
03
5051
52
-011163F10-092791E-10
- 4892-11
3710
41
U15a z045110E 02 0511020 02052131C 02
5520 5253
lfW304246 -O 0142163-08033770r-12
14 1425
o 51131 01 53 01005E-42 48 0522272 02 54 -0198102-11 24 D52227E 02 54 -034120E-13 so 059470 02 55 0397873-1 23
039475E 02 O 075c 02
55 56
CA3905211 -01605E-09
42 25
0607410 065135E
02 O
56 57
0236201-08 02973E-08
12 6
065135E 02 57 028667E-12 47 067111 02 52 02770-09 2 067311C 02 58 03215E6-09 19 U67311E 02 se -02726DE-09 22
- 120762 INPUT FROM N 140392 POSITION (GYRO) COEFFICIENTS RESPONSE FROM - 120762 INPUTFROM 140393POSITION (GYRO) COEFFICIENTS RESPONSE FROM
FREQUCNCY O13764E 02 017525E 02 0103133E 0 019370E 02
MO0E NO 4 5 6 7
COEFFICIENT 00 00 00 00
RANK 50 A9 40 47
FREQUENCY 013764E 02 017525E 02 018133E 02 019370E 02
NOVE NO 4 5 6 7
COEFFICIENT 00 00 00 00
RANK 50 49 48 47
322739E 02 025796E 02 O87020 02 026944E 02 030U96E 02 031603E 02
8 9 10 11 12 13
00 040 00 00 00 00
46 5s 44 A3 42 41
0229390 02 025796r 02 028702E 02 02amp944E 02 030096C 02 01603E 02
a 9
10 11 12 13
00 00 00 00 00 00
46 45 4 43 42 41
032334E 02 14 00 40 032384E 02 14 00 40
0327Z9E OZ 15 00 39 032729C 02 15 00 39
03 336E 02 16 00 38 03 36E O 16 00 38
36573E 02 335611E 02 033819E 02
17 18 19
00 00 00
37 36 35
036578E 02 0386116 02 036819C 02
17 18 19
00 00 00
37 36 35
T41711 043225E
2 02
zo 21
00 00
34 33
041911E 02 048225C 0
20 21
00 00
34 33
09330E 02 22 00 32 049330E 02 22 00 32
05146E 02 05212E 02 052244E 02
23 24 25
00 00 00
31 30 29
051462C 02 05212 E 02 052244 02
23 24 25
00 00 00
31 30 29
052339E 02 - SZ911E a 2627 0000 2827
052839E 02052912E 02
26 27
00 00
28 27
O3 055303E 02 28 00 26 055803E 02 28 00 26
bull- 011957E 1244S6E
02 02
34 35
010684E-06 012162E-07
4 14
011957E 02 012416 02
34 35
-023913E-07 056413E-09
6 20
16a8011 O 36 0549351-07 7 016801E 02 36 -05646E-07 1
0173090 02 37 -044431E-08 18 017309E 02 37 0392040-09 21
020952E 02 38 -0558692-07 6 020952E 02 38 -034509E-07 3 02357E 02 39 -022007E-06 1 0238723 02 39 055772E-07 2
027020E 02 029055E 02 0300SE 02
40 41 42
-0272125-07 0163251-07 03943C-B
11 13 19
027020E 02 0291550 02 03008c 02
40 41 42
060252E-08 0137752-07 080029C-09
11 7
18
030300E 02 43 056050E-07 5 0308OE 02 43 0110460-07 8
051635E 02 44 011935-06 2 0316350 02 44 034210-07 4
032753E 02 45 0156amp9E-03 22 032153C 02 45 0152a6c-0o 12
0331231 02 46 0931102-00 16 033123E 02 46 080183E-08 10
035-20E 02 47 094713E-03 i3 036920E 02 47 063859C-09 19
037836E 02 43 011037E-06 3 0370001 OZ 48 0264512-07 5
038711 02 49 036113-08 20 038871E 02 49 015403E-8 15
043468E 02 50 045403E-08 17 0434682 02 50 013752E-08 1
045341E 02 050102E 02
50 52
-033812E-07 -035630E-07
]0 9
045041E 02 051102E 02
51 52
-0395461-08 016296E-08
13 14
052131E 02 53 -0241875-11 24 052131E 02 53 -015332E-12 25
052227E 05475E
02 0
54 55
-017917E-10 01376ZL-11
23 25
O5zzz7 0z -05975
C 02
54 55
034916-11 02360ac-lI
22 24
060748E 02 56 035748C-07 8 060748 02 56 010953E-07 9
0651351 02 57 -018417E-07 12 065135E 02 57 011649E-09 22
067311E 02 53 030890E-O 21 067311E 02 5 011264C-08 17
50 CRITICAL RESONANCES FROM REALISTIC MODELS
The-determination of critical resonances for the realistic Space Shuttle
model at liftoff max q and SRB cutoff was accomplished by calculating
structural admittances for each of the inputresponse pairs previously
identified in Table 4-1 using postprocessor Option 6
51 SELECTION OF ANALYSIS FREQUENCIES
Ingeneral the admittance peaks do not occur at modal frequencies For
example the peak displacement admittance for a damped single degree-ofshy
freedom system occurs at a frequency g = IV and the acceleration admittance peak occurs at s=e AT r where w is the modal frequency and
C is the equivalent modal viscous damping ratio For a multi-degree-ofshy
freedom system the proximity of other modes causes further shifts in peak
resonances particularly when modal coupling is significant Therefore to
-find the resonance peaks for the Space Shuttle admittances must be calculated
for several frequencies in the viscinity of each modal frequency and between
modal frequencies
The analysis frequencies (B)chosen for each modal frequency (W)are as follows
72 tf+ 2 rpsa -- t +l
Some of these frequencies were omitted for closely spaced modal frequencies
and additional analysis frequencies were included between widely spaced
modal frequencies
52 CRITICAL RESONANCES
Displacement velocity and acceleration admittances (amplitude and phase angle)
for the inputresponse freedoms shown in Table 4-1 were calculated and ranked
using postprocessor Option 6 The complete set of tabulated data for liftoff
max q and SRB cutoff are contained in Section 30 of Volume II These tables
indicate which resonances are the primary contributors to the structural
response of each response freedom due to excitation at each input freedom
162
Selected responseexcitation pairs for the liftoff condition are used in
Section 60 for the comparison of the admittance technique with the conshy
ventional modal selection method
163
60 ADMITTANCE METHOD COMPARISON AND MODAL EXCITABILITY CRITERION
The ranking of critical resonances for the realistic model at liftoff using
the admittance approach was compared with the ranking of critical modes for
the conventional model There are significant differences in the rankings
resulting from the coupling introduced by discrete joint damping in the
structural model A criterion for assessing the effect of damping in strucshy
tural joints on the excitability of structural modes is presented
61 COMPARISON OF REALISTIC AND CONVENTIONAL MODELS
The most significant result obtained from the comparison of the realistic
and conventional models is that the damping in structural joints produces
significant modal coupling Figures 6-1 through 6-3 show displacement rate
and acceleration admittances for several response freedoms due to excitation
at one outboard Space Shuttle main engine (gridpoint 14039) and at one SRB
engine -(gridpoint 513) for both the realistic and conventional models The
frequency range was reduced for these comparisons to provide better definition
of frequency shifts resulting from modal coupling The curves shown in the
figures are displacement admittances for the position gyro in the Orbiter inertial
measurement unit (IMU) rate admittances for the SRM forward and aft rate gyros
and the Orbiter rate gyro and acceleration admittances for the aft dome of the
ET LOX tank and the crew compartment instrument unit for the realistic model
Shown as points on these curves are the admittances calculated for the conventional
model using two methods for comparison (a)using a uniform damping ratio of
01 for all the modes and (b)using the damping ratio determined from the diagonal
term in the coupled modal damping matrix
For some resonance peaks the conventional model using method (b)(damping
calculated from the diagonal term of the coupled modal damping matrix) comes
close to the realistic model admittances But for the resonance peaks which
show strong modal coupling the conventional model admittances are signifshy
icantly lower than the realistic model Infact the conventional model
admittances are zero for some resonances which are significant in the realistic
model As an example for the position gyro response in the pitch (ey ) direction
(Figure 6-1) the admittance peak at approximately 182 radsec isthe second
highest peak for the realistic model but for the conventional model the mode
at 181 radsec ranks fourth in criticality Therefore modal coupling due to
164
--
107
108 RESPONSE FREEDOM 90054 DUE TO 5133
7
3-
4
q
x
a
ADMITTANCE AT MODAL FREQ
CONVENTIONAL MODEL WITH
CONVENTIONAL MODEL USING DIAGONAL TERN OF BHH
= 01
44
0a _ ____
S_
1 0] l I t1 I
Ii
I i I II i
i It
16
I I-- IiF
)1------L PI FREQUENCY radsec
i 1
COMPARISON OF CONVENTIONAL AND REALISTIC MODELSFIGURE 6-I
DISPLACEMENT RESPONSE
165
8ADMITTANCE AT MODAL FREQ6_ s x CONVENTIONAL MODEL WITH 01
-- Q CONVENTIONAL MODEL USING 3__ PIAGONAL TERM OF BHH109N
- _
S
7
4
-
-shy
- -0------
C7-
-10
I0~Ia I01
FREQUENCY radsec
FIGURE 6-1 COMPARISON OF CONVENTIONAL AND REALISTIC MODELS DISPLACEMENT RESPONSE (continued)
166
10-98 - _7 DrD CCCD7= anr=nr r
7
o 108
8shy
011
i-9I
10shy
16
FREQUENCY radsec
FIGURE 6-1 COMPARISON OF CONVENTIONAL AND REALISTIC MODELS DISPLACEMENT RESPONSE (continued)
10-7
7 5-
4
bull
RESPONSE FREEDOM 90055 DUE TO 140391
ADMITTANCE AT MODAL FREQ CONVENTIONAL MODEL WITH C 01
CONVENTIONAL MODEL USING DIAGONAL TERM OF BHH
6
7 -
lt
3shy
3
-j
7-I -- I I
-10
10shy
110 I 1 20
10 1
10
1
2 1
16 18
1 1
20
FREQUENCY radsec
FIGURE 6-1 COMPARISON OF CONVENTIONAL AND REALISTIC MODELS DISPLACEMENT RESPONSE (continued)
168
RESPONSE FREEDOM 90055 DUE TO 1403930-7
_ ADMITTANCE AT MODAL FREQ
x CONVENTIONAL MODEL WITH t 01
a CONVENTIONAL MODEL USING PIAGONAL TERM OF BHH
HI
8
7shy
10 shy
10-t
10 12 14 16
FREQUENCY radsec
18 20
FIGURE 6-1 COMPARISON-OF CONVENTIONAL AND REALISTIC MODELS DISPLACEMENT RESPONSE (continued)
169
RESPONSE FREEDOM 90056 DUE TO 140392 10 7 _ 8 ADMITTANCE AT MODAL FREQ
5 CONVENTIONAL MODEL WITH
SCONVENTIONAL MODEL USING DAGONAL TERM OF BHH
c O1
10
8
6o1
5 -
0-9
I i1 I p
a
10 _I __L_ I- I I
Iri
I i
10-11 12
FREQUENCY radsec
FIGURE 6-1 COMPARISON OF CONVENTIONAL AND REALISTIC MODELS
DISPLACEMENT RESPONSE (continued)
170
-6
7
4-
3
5 ii I i
RESPONSE FREEDOM 9015 DUE TO 140391
x CONVENTIONAL MODEL WITH =01 0 CONVENTIONAL MODEL USING
DIAGONAL TERM OF BHH
6
8 I i I I rI I I I I i
10shy
0 - 1 2 _ 1 4 1 6 182 0
10 12 14 16 18 20
FIGURE 6-2
FREQUENCY radsec
COMPARISON OF CONVENTIONAL AND REALISTIC MODELS
VELOCITY RESPONSE
171
10-6 0-9
RESPONSE FREEDOM 9016 DUE TO 140391
7-
x
ADMITTANCE AT MODAL FREQ CONVENTIONAL MODEL WITH c = 01
3
o CONVENTIONAL MODEL USING DIAGONAL TERM OF BHH
ltC 1 -8___----_----- -_
9
I0I
10 10
FIGURE 6-2
1i2i 114 16 T382
FREQUENCY radsec
COMPARISON OF CONVENTIONAL AND REALISTIC MODELS VELOCITY RESPONSE (continued)
172
Uwjl)0BL~ryOF THES
-5A -- - RESPONSE FREEDOM 9024 DUE TO 5133
7 ====== ADMITTANCE AT MODAL FREQ
x CONVENTIONAL MODEL WITH = 01 4 o CONVENTIONAL MODEL USING
3 DIAGONAL TERM OF BHH
C -J
10
10 12 14 16
FREQUENCY radsec 18 20
FIGURE 6-2 COMPARISON OF CONVENTIONAL AND REALISTIC MODELS
VELOCITY RESPONSE (continued)
173
10-5 RESPONSE FREEDOM 9025 DUE TO 5133
7-- ADMITTANCE AT MODAL FREQ
5= CONVENTIONAL MODEL WITH 01
4 _=== CONVENTIONAL MODEL USING 3_ DIAGONAL TERM OF BHH
9
6
1 -- I I I -shy
4shy
10 ___-174
_
10 12 14 FREQUENCY
16 radsec
18 20
FIGURE 5-2 COMPARISON OF CONVENTIONAL AND REALISTIC MODELS
VELOCITY RESPONSE (continued)
174
10-95 RESPONSE FREEDOM 9026 DUE TO 5132 8
7 ADMITTANCE AT MODAL FREQ 5 CONVENTIONAL MODEL WITH 01
4 m CONVENTIONAL MODEL USINQ 3 DIAGONAL TERM OF BHH
7 6
$ -- I------- 1---------shy
10 -6_ _
4-7
F-
I I IIrI II I
10 12 1
FIGURE 6-2
FREQUENCY radsec
COMPARISON OF CONVENTIONAL AND REALISTIC MODELS
VELOCITY RESPONSE (Continued)
175
S RESPONSE FREEDOM 9025 DUE TO 140393 -5
ADMITTANCE AT MODAL FREQshy7
3
s 4
x CONVENTIONAL MODEL WITH
CONVENTIONAL MODEL USING DIAGONAL TERM OF BHH
=
S10shy
6 1 - 1
8_
S 10 ~ I I I
-LJ
7shy
4_
10
FIGURE 6-2
12 14 16 18 20
FREQUENCY radsec
COMPARISON OF CONVENTIONAL AND REALISTIC MODELS VELOCITY RESPONSE (continued)
176
_-5__ -RESPONSE FREEDOM 9026 DUE TO 140392
7 ADMITTANCE AT MODAL FREQ
5 XCONVENTIONAL MODEL WITH 01O 4 CONVENTIONAL MODEL USING 3DIAGONAL TERM OF BHH
709-
10shy
_ ______=__-
LuJ
7
3_
02
C6
I-I lO
W 2I1
W i I 16t
I 1 20
I- 77
717
1 S RESPONSE FREEDOM 90044 DUE TO 5133 ADMITTANCE AT MODAL FREQ
6
S CONVENTIONAL MODEL WITH c = 01 4 o CONVENTIONAL MODEL USING
3= = -DIAGONAL TERM OF BHH
10
0-shylt
10 I4It I I I I I-
ii I n II 1 I II g I u
10 12 14 16 FREQUENCY radsec
18 20
FIGURE 6-2 COMPARISON OF CONVENTIONAL AND REALISTIC MODELS
VELOCITY RESPONSE Ccontinued)
178
4
S FREEDOM 90045 DUE TO 513310-75RESPONSE
ADMITTANCE AT MODAL FREQ
B ___ CONVENTIONAL MODEL WITH = 01
q CONVENTIONAL MODEL USING
= =IAGONAL TER OF BHH
- 6
L444 0 I
1008
10 12 14 16 18 20
FREQUENCY radsec
FIGURE 5-2 COMPARISON OF CONVENTIONAL AND REALISTIC MODELS
VELOCITY RESPONSE (continued)
]79
10 RESPONSE FREEDOM 90046 DUE TO 5132
7 ADMITTANCE AT MODAL FREQ
S x CONVENTIONAL MODEL WITH =901 4-o CONVENTIONAL MODEL USING
DIAGONA TERM OF BHH
m10
1 L I ------------------------shy
6 -7 10=
10shy
10 12 14 16 18 20
FREQUENCY radsec
FIGURE 6-2 COMPARISON OF CONVENTIONAL AND REALISTIC MODELS
VELOCITY RESPONSE (continued)
180
I-rnanENCT0-5 7___^K 1
u-iN 006
I8shy
-- --shy7
10 12 14 16
FREIQUENCY radsec
18 2
FIGURE 6-2 COMPARISON OF CONVENTIONAL AND REALISTIC MODELS
VELOCITY RESPONSE (continued)
181
105 8=
4 3
106
4
C 7
-6I
7shy
10
FIGURE 6-2
RESPONSE FREEDOM 90046 DUE TO 140392 ADMITTANCE AT MODAL FREQbull
SCONVENTIONAL MODEL WITH c = 01 CONVENTIONAL MODEL USING DIAGONAL TERM OF BHH
12 14 16 18 20
FREQUENCY radsec
COMPARISON OF CONVENTIONAL AND REALISTIC MODELS VELOCITY RESPONSE Ccontinued)
182
--
-4 RESPONSE FREEDOM 521 DUE TO 140391O9
ADMITTANCE AT MODAL FREQ6
x CONVENTIONAL MODEL WITH c 01
0 CONVENTIONAL MODEL USING a DIAGONAL TERM OF BHH
10 7
S ___ ___--_--
-6shy
0 0_ltc2N 10 12 14 16 1820
FREQUENCY radsec
FIGURE 6-3 COMPARISON OF CONVENTIONAL AND REALISTIC MODELS ACCELERATION RESPONSE
183
C
DIAGONAL TERM OF BHH a
10 -4
7
6shy
-4shy
4 0 12 14 16 18
FREQUENCY radsec
FIGURE 6-3 COMPARISON OF CONVENTIONAL AND REALISTIC MODELS ACCELERATION RESPONSE Ccontinued)
184
RESPONSE FREEDOM 90012 DUE TO 5132-4
5
4
3
o
ADMITTANCE AT MODAL FREQ
CONVENTIONAL MODEL WITH c CONVENTIONAL MODEL USING DIAGONAL TERN OF BHH
01
102-- ----
CD
C
7-shy
6 10-
u-I
7-
O1 12 14 16 FREQUENCY radsec
18 20
FIGURE 6-3 COMPARISON OF CONVENTIONAL AND REALISTIC MODELS ACCELERATION RESPONSE (Continued)
185
RESPONSE FREEDOM 90013 DUE TO 51330-4
7 ====== ADMITTANCE AT MODAL FREQ
_ CONVENTIONAL MODEL WITH g 01 4 o CONVENTIONAL MODEL USING
3__ DIAGONAL TERM Of BHH
0-5
LI6 4shy
o 3- VF i-------CD
I2II
S10
--shy
10 12 14 16 FREQUENCY radsec
18 20
FIGURE 6-3 COMPARISON OF CONVENTIONALAND REALISTIC MODELS ACCELERATION RESPONSE (continued)
186
structural joints can have a significant effect on identifying the resonances
which are critical for dynamic analyses
62 CRITIERIA FOR THE EXCITABILITY OF MODES
The admittance matrix for selected responseexcitation pairs can be used
to identify critical resonant frequencies for points of interest throughout
the structure The frequency of the admittance peak is used to identify the
dominant mode associated with that peak The peak admittance amplitude is used to calculate an equivalent modal viscous damping ratio for this dominshy
ant mode For displacement admittances
lik~ Rk1
k-kk (42)
and for velocity admittance
(3k ik Rkl =k k iA Pl2k~m (43)
k kk
where wk = frequency of dominant mode
mk = generalized mass of dominant mode
Ik = kth mode shape for input freedom
R kth mode shape for response freedom
JACP)l =peak displacement admittance
JA(P)I = peak velocity admittance
k = equivalent modal viscous damping ratio for dominant mode
This method could be used as a criteria for the selection of a set of critical
modes for dynamic analyses and to establish the equivalent viscous damping
ratios to use with these modes
187
70 COMPUTER TIME ESTIMATES
Estimates of the computer time required to perform various parts of the
analysis are given in the following paragraphs The computer time is given
in computer resource units (CRU)
71 ORBITER
The incorporation of structural joints (23 BAR joints and 64 plate joints)
into the Orbiter finite element model using the preprocessor requires
approximately 250 CRUs This includes the generation of the additional
data necessary for the joint damping predictor (JDP) computer program The
calculation of 30 Orbiter free-free symmetric and antisymmetric modes with
125 retained degrees-of-freedom using NASTRAN is approximately 350 CRUs each
The joint damping predictor computer program used to calculate Orbiter damping
parameters for four damping sets required approximately 160 CRUs
72 SPACE SHUTTLE
The computer time required by the preprocessor to incorporate 33 BAR joints
and 77 plate joints in the Space Shuttle model and create the NASTRAN BULK
DATA set is approximately 300 CRUs (computer resource units) The original
NASTRAN calculation of 30 antisymmetric Space Shuttle modes with 292 retained
degrees-of-freedom and the generation of a special user tape containing these
modes is approximately 700 CRUs Approximately 800 CRUs are required to
calculate 30 symmetric modes (using NASTRANS restart capability) merge
these modes with the antisymmetric modes and calculate the coupled nodal
damping matrix (BHH)
The calculation of modes and the coupled damping matrix for additional mass
conditions required less computer time since the NASTRAN restart capability
was used and therefore the stiffness matrix and elemental damping matrix did not need to be recalculated Using the restart tape from the original
NASTRAN antisymmetric modes run approximately 300 CRUs are required for the
calculation of antisymmetric modes for a new mass condition-and approximately
188
600 CRUs are required-to calculate symmetric modes and the merged modal
damping matrix (BHH)
Postprocessor computer costs depend upon the option used For the conventional
model Option 1 requires approximately 30CRUs to calculate structural gains
for 50 modes and 180 responseexcitation pairs for each mass condition Using
Option 6 to calculate structural admittances for the realistic model the
computer time is primarily a function of the number of frequencies () for
which admittances are desired The number of responseexcitation pairs has
a much smaller effect on computer time The computer cost for Options 4 5
and 6 are given by the following expression
CRU = 10 + NBETA
where NBETA is the number of admittance frequencies (s)
189
80 CONCLUSION AND RECOMMENDATIONS
81 CONCLUSIONS
Significant differences were found in the dynamic responses at various points on the Space Shuttle structure between the conventional model and the realistic model (Figures 6-1 through 6-3) Equivalent modal viscous damping was used in the conventional model and the critical modes were determined using the unshycoupled modal response to calculate physical tramissibilities between the excitation and response freedoms The realistic model incorporated local damping effects due to structural joints and admittances were calculated
using the resulting coupled modal damping matrix
Results of this analysis show that coupling of modes through local joint damping is important and can significantly affect the identification of critical resonances for dynamic response studies Formodes whose frequencies
are close together and which are coupled the frequency at which the maximum admittance occurs will be different from the modal frequencies Therefore
frequencies between modal frequencies should also be used to locate the admittance peaks for each responseexcitation pair For example in Figure 6-2 (SRM rate gyro 9015140391) the two modes at 168 and 173 radsec are coupled to produce an admitthnce peak at 170 radsec which is more signifshyicant than either mode using the conventional model
The equivalent modal viscous damping ratios calculated for the SRB cutoff condition using the same joint damping parameters used for the liftoff conshydition are higher than expected for the primary modes Therefore it is necessary to recalculate the joint damping parameters for each flight conshydition to achieve realistic vehicle damping
82 RECOMMENDATIONS
It is recommended that distributed damping resulting from structural joints be included in dynamic analyses of complex structures to preclude the omission of critical resonances which could significantly affect the analytical results
It is also recommended that further studies be conducted to verify the
190
conclusions found in this study by comparing analytical results with test
data Studies should also be conducted to determine the practical limits
for the methods described herein ie how many structural joints are
required to obtain a sufficiently accurate representation of modal damping
over a given frequency range
Additional studies are required to investigate the cause of the higher than
expected equivalent modal damping for the SRB cutoff mass condition The
investigation should determine the effect of total mass on the joint damping
parameters This study may involve the previously mentioned study to determine
the number of structuraljoints required to give a realistic damping
representation over a range of frequencies (or masses)
191
APPENDIX I
PREPROCESSOR COMPUTER PROGRAM
Introduction
This program written in FORTRAN IVwas developed to incorporate strucshytural joint damping models at selected points in a NASTRAN finiteshyelement model The user specifies the location and properties of the desired structural joint The locations for joints are limited to the
ends of BAR and ROD elements and edges of QUADI QUAD2 QDMEM and SHEAR plates Gridpoints at the joints must be located either in the basic rectangular coordinate system or in an arbitrary cylindrical or rectangular coordinate system referenced to the basic system Displacements of the
joints must be defined-in the basic rectangular coordinate system The preshy
processor reads the NASTRAN BULK DATA deck for the original model and outputs a revised data deck containing additional BULK DATA card images necessary for the inclusion of the specified Voigt damping models The revised BULK DATA is used by NASTRAN to calculate modal characteristics of the structural model and the coupled generalized modal damping matrix using rigid format 3
The number of structural joints which can be implemented is limited to 1000 BAR joints ROD joints and 200 plate joints A maximum of 1000 cards for each of the various types of NASTRAN data (GRID CBAR PBAR C plate P plate
etc) may be stored by the preprocessor for joint implementation Ifthe original model has more than 1000 of any of these data cards the additional
cards will be passed through the preprocessor without modification Gridpoint element property and material identification numbers from 7000 through 9000 are used by the preprocessor for the gridpoints and elements of the joint
models and cannot be used in the orignal structural model
Input Description
The input data required by the preprocessor consists of a NASTRAN BULK
DATA card set describing a structural model and punched cards which describe the locations and properties of the structural joints to be incorporated into
192
the model The DMAP ALTER statements which must be included in the NASTRAN
EXECUTIVE CONTROL deck depend upon the purpose for which the results are
desired A complete list of ALTER statements is shown in Table I-I
Structural joint damping models for BAR ROD and plate elements are shown
schematically in Figure I-I The location of a structural joint is specshy
ified by giving the element identification and- gridpoint identification
numbers for the desired joint location The locations of the added gridpoints
are specified in terms of the locations of the gridpoints at the ends of the
structural elements
for BAR and ROD elements
iG(c) - G(a)l = KG IG(b) - G(a)I = KG-ab
for plate elements
JG(c) - G(a)I = KG IG(d) - G(b)J = KGTb
where G(a) G(b) G(c) and G(d) are the locations of gridpoints a b c and d
respectively KG is a factor specified either by the user or-by default and
b is the length between gridpoints a and b The formation sequence of the
added gridpoints are reidentified using the SEQGP feature of NASTRAN to improve
matrix bandwidth
Section properties of the revised elements are specified by multiplying the
original element section properties by appropriate factors specified either
by the user or by default
for BAR and ROD elements
A(k) = KA - A(j)
J(k) =KJ - J(j)
Il(k) = KII l(j) - BAR joints only
12(k) = K12 - 12(j) - BAR joints only
193
TABLE I-I NASTRAN DMAP ALTER Statements for the Preprocessor Computer Program
For calculating the damping set data as input to the joint damping predictor
ALTER 26 2 SMA1-CSTMmPT ECPT-GPCT-1-T-KGfGX 4GG GPSTV-N NOGE NLV N NO4GG--7tzr ALT R 28T9 SMA2 CST4M4PTECPTrGPCTDITMGGBXXVYWTMASS1CVuHtNOxGGVNwNOBGG
Vy COUPt4A SS V Y CP 8AkVY CPRODA IY PQUADIV Y CP1)tJAUV YCPTkIAIVYCPTP1A2vYCPTUBEYtCPQDPLTVYyCPTRPLTV YCPTRRSC S
SAVE-- NGMGG NOBGG ADD K4GGBXXBGG I MTRXIN CIATPOOL EQEXIr) SILPVCO PVCiPVOV NLUSETVNNOPVOOv
N NU)PVO 1V N NOPVO2--$ PPRTNM BGPVOC BGGCOCI-I $ CHK NT PVOOBGGOO sP ARTI+ -- - BG G Po10 BG G I1C- N-1-
ChKPIIT PVOIBGGGI -PARTgt BGGPV02 BGGO2CN-1 S CHKPN T -PV O2 GG0-$ MiTRXlN M4ATPOOLEQEXIISILPVO-3PVOtPV05VNLUSFTVNNOPVO3V
NIOPVO4VNNOPVC5SSGG - GP ARTNI ---- PV -3--- --1---
CHKONT PVO$GG03 $ PARTN BGGPV04 BGGO4CN-l $ CHKOT-PV04BGGO4 --PARTI SGGPVOS -GGO5C N-I $ CHiK 0 T PVOS0GG05 $ ALTER- 74--shyATGPR GPLUSETSILtMA-CNAS MATGP 4t G LUSETSILBGGCNGS ALTER --96 -- -
OUTPU TI PHIGiiC-1CN0 $ -I
ENDALTER
194
TABLE I-I NASTRAN DMAP ALTER Statements for the Preprocessor Computer Program (Contd)
For calculating symmetric or antisymmetric modes and writing on a user tape
ALTER 714 MATGPR GPLUSET SIL MAACNAA ALTER -946 OUTPUTI PFiIGrCN-IcNo s ENDALTER
For calculating symmetric modes merging previously calculated antishysymmetric modes and calculating coupled modal damping matrix
ALTER 26t26 -SMA---CSTMMPTECPTiGPCTiDIT-KGGX- K-4GG- GP S-TiV IiN4G-EN-V-f-NNUK-GG-ALTER 28t29 SMA2 CSTMMPTECPTVGPCI D1TMGGBXXVYWTMAS$nlOVNNOMGGVNtNOSGG
-V V-j COUPuMA Samp t-Ti-tPampBAR-V-Y--CpRjUYVfl-j-p 7UxAto-1v ryCgtQ t t-V-
YtCPTRIAIVYCPTRIA2VYCPTUBEVYCPCDPLTVYCPTRPLTV YCPTRBSC $
-SAVE--NCMGGNCGCG-1-- --ADD K4GGBXXBGG S CHKPNT BGG__$ ALTER 74 -MATGPR-GPL-USETi-S-tLMA-VOyN-A$ MATGPR GPLUSETSILBGGCNG$ ALTER 9596 --SDR1 US L T t P H IA-T fGO GM -KF S-PRI GX- --QG1- Pt--C-N-CF--s CHKPNT QG $ INPUTT1 PHIGYCN-1CNO $ -MERG E- -PhI IGX i P H IGY- -v-P tIGC---NT-k----$
CHKPNT PHIG $ MPYAD PHIG bGGXXCN ICNCN0 $ -MPYAt -XX -PHIG f8 HHC-N OC-i-N tIC- F CJ-PNT bHH $ MATPRN BHHi $ -fNDATER-shy
95OF THftol~ paI~eo
195
a k C j b -- X
4 IP BAR ELEMENTS
S ROD ELEMENTS WITH r VISCOUS DAMPING
z MPCS
A) BAR JOINT SCHEMATIC
a c b -
m
ROD ELEMENT WITH VISCOUS DAMPING
--------- V1SC ELEMENT
B)IOOJOINT SCHEMATIC
------ ROD ELEMENTS WITH VISCOUS DAMPING
V MPC (ROTATIONS OPTIONAL OUT-OF-PLANE)
C) PLATE JOINT SCHEMATIC
Figure I-1 NASTRAN Joint Damping Model Schematics
196
where A(j) J(j) l1(j) and 12(j) are the cross sectional area torsional
constant and area moments of inertia of the original BAR or ROD element (j)
Similarly for plate elements
bull= KA = A(bd)Mac) 2 ta tij (Gj)
C E-2 A ad) = A(bc) = KS 2 E
where t G and Ei are the membrane thickness shear modulus and elastic
modulus of the original plate element (J)
Damping values for the BAR elements are input by specifying the C1 (axial)
and C2 (torsional) damping constants for each ROD element denoted by m n
and p in Figure 1-1 input as if the RODS were VISC elements Damping values
for ROD joints are input as the damping constant of a VISC element between
gridpoints a and c Damping values for the plate elements are as if they
were Cl damping constants for VISC elements The following conversions are
performed to calculate the structural damping coefficient (GE) required for the
MAT1 card for all damping except axial damping with SHEAR plates
for axial ROD elements
EGEA = A(ac)
for diagonal ROD elements
EGED = A(ad)-
where ac and i are the lengths between gridpoints a and c and between a and
d respectively These structural damping coefficients are automatically
converted to viscous damping coefficients since the preprocessor sets
W4 = 10 on a PARAM card (Reference 15 page 16-3)
197
Detailed preprocessor input descriptions and examples for BAR ROD and
plate element joint damping models are shown in the following pages
The card format is the NASTRAN single-field format The $BAR $ROD
and $PLATE must begin in column one but the rest of the input may be
located anywhere within the 8 column fields The element ID and
gridpoint ID are integers and the rest aredecimal input The preproshy
cessor data cards may be placed anywhere in the NASTRAN BULK DATA deck
198
PREPROCESSOR DATA DECK
Input Data Card $BAR Joint Damping Element (BAR)
Description Defines a Voigt damping model to be included at the end of a
BAR element
Format and Example
1 2 3 4 5 6 7 8 9 10
J$BAR IDBR I IDGB Cim CnI Clp C2m C2n C2p abc
$BAR 801 185 8090 8090 8090 5129061 512906 512906 +D80l
I~c KG KA I KJ IKill K21MPCIDj 0MTBfI DSN0 I_ I+D8011 08 1 751 11 1l
Field Contents
IDBR Identification number of the BAR element to which a joint
is being added
IDGB Gridpoint identification number which defines the location
of the joint
ClmClnClp Translational damping constants for the joint in the
local element x y and z directions respectively
C2mC2nC2p Rotational damping constants for the joint in the local
element RX RY and RZ directions respectively
KG Joint length factor (default = 1)
KA Joint area factor (default = 10)
199
Field Contents
KJ Joint torsional constant factor (default = 10)
KIlKI2 Joint area moment of inertia factors (default = 10)
MPC ID Set ID into which generated MPCs will be placed
(default = 1)
OMTB Indicator used to include generated joint freedoms in the
OMIT set
OMIT - include joint freedoms in OMIT set
blank- do not include joint freedoms in OMIT set
DSN0 Damping set number
Remarks 1 Every input on the first card is required no default
values exist
2 The second card is optional default values are provided
for blank fields
3 Joint factors (KGKAKJKI1K12) are used to define joint
properties
length of joint = KG x length of original element
area of joint = KA x area of original element
etc
4 Freedoms generated for the joint should not be included
in the analysis set If an OMIT set is used for other
freedoms in the NASTRAN model input OMIT in field 8 of
card 2 If an analysis set (ASET) is used elsewhere in
the model leave this field blank
5 Identification numbers for the gridpoints element connecshy
tions properties and materials generated by the preprocessor
are in the range 7000-9000 These ID numbers may
therefore not be used in the original NASTRAN structural
model
200
6 Multipoint constraint sets must be selected inthe CASE
CONTROL deck (MPC = MPC ID)to be used by NASTRAN
7 DSNO specifies the damping set into which the joint
damping parameters are placed for use in the joint
damping predictor computer program
DSN0 = 0 if damping values are known
DSN0 = 12 --- if damping parameters are unknown
8 DSN0 must be input No default value is provided
9 All damping elements in a BAR joint are in the same
damping set
201
Input Data Card $ROD Joint Damping Element (ROD)
Description Defines a Voigt damping model to be included at the end of
a ROD element
Format and Example
1 2 3 4 5 6 7 8 9 10
[SR0D IDR IIDGR C] C2 KG KA jKJ I OMIT abcd
I$RD1 4 3 261 927 2 14 1MIT +R04Ibcd I I
DSN0 I - I J+R04 1 0 11111 I I I _
Field Contents
IDR Identification number of the ROD element to which a joint
is being added
IDGR Gridpoint identification number which defines the location
of the joint
ClC2 Axial and torsional damping constants for the ROD joint
KG Joint length factor (default = 1)
KA Joint area factor (default = 10)
KJ Joint torsional constant factor (default = 10)
OMIT Indicator used to include joint freedoms in the OMIT set
OMIT - include joint freedoms in OMIT set
blank - do not include joint freedoms in OMIT set
DSN0 Damping set number
202
Remarks 1 Joint factors (KG KA KJ)-are used to define joint
properties
length of joint = KG x length of original element
area of joint = KA x area of original element etc
2 Freedoms generated for the joint should not be included
in the analysis set If an OMIT set is used for other
freedoms in the model input OMIT in field 9 If an
ASET is used elsewhere in the model leave this field
blank
3 Identification numbers for the grid point ROD element
ROD properties and VISC element generatedby the preshy
processor are in the range 7000-7999 These ID numbers
may not be used in the original NASTRAN structural model
4 DSN0 specifies the damping set into which the joint
damping parameters are placed for use in the joint
damping predictor computer program
DSNO = 0 if damping values are known
DSNP = 12 if damping parameters are unknown
5 DSNO must be input No default value is provided
6 Both the VISC element if used and the damping in the
rod element are in the same damping set
203
_____
Input Data Card $PLATE Joint Damping Element (QUADI QUAD2 QDMEM
and SHEAR)
Description Defines a Voigt damping model to be included along
an edge of a quadrilateral plate element
Format and Example
1 2 3 4 5 6 7 8 9 10
IsPLATET IDPJ lOIGE I10GB IClIA I1 KG I KA I KSrJ bcJI j$PLATE I 805 186 188 2582 3591 1_1-75- I ti +805
+bc IMPG IDIOMTB MPCN2 D5NQD ID3NOAI MPCNl 1805 12 1 0_ 1j 1 1
___
_ 1_ _
FIELD CONTENTS
IDPJ Identification number of the quadrilateral plate element
to which a joint is being added
IDGAIDGB Gridpoint identification numbers which define the location
of the joint
CIA Translational damping constant for the joint in the axial
directions defined by gridpoints ac and bd of Figure I-1
CID Translational damping constant for the joint inthe diagshy
onal directions defined by gridpoints ad and bc of Figure I-1
KG Joint length factor (default = 05)
KA Joint axial area factor (default =10
204
FIELD CONTENTS
KS Joint shear area factor (default = 10)
MPC ID Set ID into which generated rotational MPCs will be
placed a blank indicates no rotational MPC equations are
to be generated
0MTB Indicator used to include generated joint freedoms in the
OMIT set
OMIT - include joint freedoms in OMIT set
blank - do not include joint freedoms in OMIT set
MPCNl MPCN2
DSNOD DSN0A
Gridpoints to which added plate grids (NI amp N2) are to be
MPCd to provide out-of-plane stiffness The MPC set ID
is the same as MPCID if MPCID is blank MPCset default is 1L
damping set number into which the diagonal and axial damping
elements are placed
Remarks 1 Joint factors (KG KA KS) are used to define joint
properties
width of joint = KG x length of joint
axial area of joint = KA x axial area of original
element
shear area of joint = KS x shear area of original
element
2 Translational damping constants (ClA and CID) are input
as if the axial and diagonal elements are VISC elements
205
3 Out-of-plane translation and rotational MPC equationsare
optional for QUADl and QUAD2 plate elements but are required
for QDMEM and SHEAR plate elements unless BAR elements are
used as edge members Multipoint constraint sets must be
selected in the CASE CONTROL deck (MPC = MPC ID)to be used
by NASTRAN
4 Freedoms generated for the joint should not be included in
the analysis set Ifan OMIT set is used for other freedoms
in the NASTRAN model input OMIT in field 3 of card 2 If
an analysis set (ASET) is used elsewhere in the model leave
this field blank
5 Identification numbers for the gridpoints element connections
properties materials generated by the preprocessor are in the range 7000-9000 These ID numbers may therefore not
be used in the original NASTRAN structural model
6 DSN0 specifies the damping set into which the joint damping
parameters are placed for use in the joint damping predictor
computer program
DSN0 = 0 if damping values are known
DSNO = 12 if damping parameters are unknown
7 DSN0D and DSN0A must be input No default values are provided
8 Damping in the diagonal rods are always in the same damping
set
9 Damping in the axial rods are always in the same damping set
206
____________________________
Preprocessor Listing
STP2 EXEC FORTHCLGPARFORT=MAPIDt REGIONFORT=2OOKPARMLKED=IXREFLISTOVLY REGIGNGOz26OKTIMEG0=2
IFORTSYSIN 00 _
C C NASTRAN PRE PROCESSOR PROGRAM FOR CREATING FLEXIBLE JOINTS
__ C C
REAL8 CD BULK HOR(17)
INTEGER2 OMIT[NTEGER 2-OMTB
INTEGER OMP _____ COM CON IMAGE CDIIO)
COMMON BROD IDR(20) IDGR(201 RPARM(2O5) OMIT(20) NROO COMMON BGRID IGC(O00) IPCG(1000i GCD(IO003) NGD DUMM X IXCD(lOOO)tIXPS(lOOO) REAL8 IXCD IXPS COMMON BCROG I IORO(10004) NCRD COWVCN BPROD IDPRDOO00) IDMP1000) JPROP(IO00 41 NRPD COMMON BNEW - NGRO IDEX IPEX IEaCM IDCV IMEX COMMON BCOMM XC(35J 11 12 INCP COPYON BOEFLT AKGPO AKGSO AKMO AKAPO AKASO BKMD BKGPO_ _____
I 8KGSD BKAPD BKASD EKJPD BKJSD 8KIIPO BKIISD BKI2PD BKI2SO COMMON BSQGP I NWGRD(40) SEGMX(40)t NSQGP COMMON BIMG NIMG(2040) IMG
COPtON SCBAR IDB(1000) IPB(I000-A(iO0Oj-iBBiO0O) I IBREC(IO00) NBAR NBREC COMMON BOAR IDR(50) I1GB(50) BPARM(5012) ONTBL50- NBR CONPON BPBAR IDPB(iO0O) IPRECtOO0) NPBAR NPREC COMMONIBPLATEI IDP(200)IDGPLT(2002)PLTPRM(2005)MPCID(200) X OMP(200NPLT X MPCPAv2OObMPCPB(2o0) COMMONBCPLTI IDCP(IOOO)IPID(1000NG(10004)hTH(1000)INC(I000) X NCPLT COYWCNBPPLT IDPPIIOOO)INP10OO)THICK(1000)IMIDIIOOO)NPPLT COMMONBNAT1 IDMAT(lOO)E(IOQ)G(100)NMAT1 COMMONBCORO IDCOR(20)IFIOR2(2OXPP(20qNCORD DATA HR 8HSROD 8H$BAR 8HCROD 8HPROD
I 8HGRID 8HCBAR BHPBAR 8HPROD 8HGRID 2 8HCBAR 8HPBAR 8HPROD 8HGRID 4 8HCBAR -
3 8HPBAR H 8H8ENODATA ENDOATA REAL8 HDR2(20) DATA HDR2 8H$PLATE 8HCQUADI 8HCQUAD2 8HCQDMEM 6HCSHEAR
X BHPQUAU1 8HPQUAOI 8HPQUAD1l X 6HPQUA02 8HPQUA02 8HPQUAD2 X 8HPQOMEM 8HPQOMEM 8HPQODMEM X BHPSHEAR 8HPSHEAR BHPSHEAR 4 X SHMATI 8HMATI 8HMATI REAL8 HOR3(4) DATA HDR3 BHCOROIC- BHCORO2C SHCORDIR 8HCORD2R I
C 10 CONTINUE
C C READ NASTRAN DECK CARO IMAGES C
207
READI57000END=200 CD 15 CONTINUE
GO TO 30 20 CONTINUE
C C WRITE CARD IMAGE ON DISK DATA SET FOR INPUT TO NASTRAN
-- C WRITE(97000)
CD GO TO 10
-- 30 CONTINUE C C TEST CARO IMAGE FOR DESIRED BULK DATA SUBSET
DO 50 1 = 1 17
IFICD() EQ HOR(I]) GO TO 60 __ -50 CONTINUE
DO 56 K=120 IFCDII)NEHOR2(KI) GO TO 56
I=K _ GO TO 145
56 CCNTINUE DO 58 1=14shyIF(CD(1)NEHOR3(I)1 GO TO 58
C -_ C COORD SYS
C WRITE(97000) CD CALL RADJ(3IDX) CALL CORSYS(I) GO TO 10
58 CONTINUE C C NOT ONE OF DESIRED SUBSET C
GO TO 20 60 CONTINUE
IF(I GE 16) GO TO 10 IF(I GE 12) 1 = I - 4 WRITE(O7000) CO CALL RADJ(I IOX) --GO TO (130 140 90 100 80 110 120 100 80 110 120) 1
80 CONTINUE _ C GRID CARD ------
CALL GRIDO4DX I) GO TO 10
90 CONTINUE-- - - -- C CRO CARD
CALL CRD GO TO 10 _
100 CCNTINUE C PROD CARD
CALL PROD(I IDX-GO TO 10
110 CONTINUE C CBAR CARD
208
CALL CBAR(I GO tO 10
120 CONTINUE C PEAR CARD
CALL PBARLI GO TO 10
130 CONTINUE C $ $ROD CARD
CALL ROD GO TO 10
C SEAR CARD 140 CONTINUE
CALL BARLI GO TO 10
145 CONTINUE C
IOX L5 S200)
IDX E15 amp200)
IDX amp15)
C --PROCESS CARDS PERTAINING TO PLATE JOINTS C
IF(ILE5) GO TO 48
C THESE BULK DATA CARDS WILL NOT BE MODIFIED AND CAN C THEREFORE BE WRITTEN TOTHE NASTRAN FILE NOW C
WRITE(97000) CD 148 CONTINUE
K=1o IF(ILE6I K=3 IF(IEQ9 OR tEO12OR IEQ15 OREQAS)K3 IF(IEQ1) K=I WRITE(OTCOO) CD CALL RAOJ(KIDX) IFtINE1) GO TO 150
C SPLATE CARD CALL PLATE(ampIS) GO TO 10
150 CONTINUE rFCIGT5) GO TO 155
C CCUADICQUAD2CQDMEM OR CSHEARCARD CALL CPLATE(I) GO TO 10
155 CONTINUE IF(IGT17) GC TO 160
C PQUADIPQUAO2PQDEM
CALL PPLATE(I) GO TC 10
160 CONTINUE C 4 MAIL CARD
CALL tATI(I) GO TO poundO
200 CONTINUE C
OR PSHEAR CARD
C PRINT JOINT INPUT DATA C
WRITE(67OIO) NROD NBR NPLT IF(NRCOLEO) GO TO 212
209
OF TIlE
WRITEt671003
00 210 I=INROD WRITE(67110] 1 IDRI) IOGR(IRPARMiIJ)jJ=15)q OMIT
210 CONTINUE 212 CONTINUE
IF( NBRLEO2 GO TO 222 WRITE6120) DO 220 [ = 1 NOR WRITE6130) 1 IDBR(I) IDGBI) (BPARM(IJ) J=112) OMTB(I)
220 CONTINUE 222 CONTINUE
IF(NPLTLEO) GO TO 232 WR[TEIS7140--- -- -
DO 230 I=INPLT WRITEi67150) IIDP(I)-IDGPLTIl)IDGPLTCI2) X (PLTPRM(IJJ=s5)MPCID(I)OMP(I)MPCPA(I)MPCPB(II
230 CONTINUE 232 CONTINUE
C C CONVERT GRID COORDS FROM CYL COORO SYS C
CALL GCONV__-C C 4 CREATE NEW BULK DATA FOR PLATE JOINTS
-- C __ __ _ __ _
CALL PJ C C CREATE NEW BULK DATA CAROSFOR-OD JOINTS----C
CALL ROOJT C C CREATE NEh BULK DATA CARDS FOR BAR JOINTS C
CALL BARJT C C CLEAN UP C C C WRITE CBAR IMAGES ON DISK C
REWvIND 3 IRC = 0
300 CONTINUE - READ(3000ENO=350) CC IF(CD(1) EQ HOR(6)) GO TO 310 IFCOI) EQ HDR(IO)) GO T0_305_ IFCO(I) NE HDRf14)) GO TO 320
305 CONTINUE C DOUBLE FIELD IMAGE
IRC = IRC + I WRITE(07001) (CD(L)L=J3) IPBCIRC) IBACIRCI IBB(IRC) CD(1O) REA 0O7000 ) CD GO TO 320
310 CONTINUE C SINGLE FIELD IMAGE
210
IRC = IRC + 1 1RITE(O7002) (CD(L)L=IZ) IPB(IRCI IBA(IRC)t IBB(IRC)t X tCD(L)pL=6IO) READ1O7000) CO
320 CONTINUE C W WRITE CARD IMAGE ON DISK
IRITE(97000) CD GO TO 300
350 CONTINUE C C WRITE CROD IMAGES ON DISK C
IFNCRD LE 0) GO TO 450 00 400 1 = 1 NCRO WRITE(O70O4) HDR(3) (IDRD(IL)L=I4) IMG = 0 CALL STORE( 10 fRITEC97003) (NIMGL1)L=120)
400 CONTINUE 450 CONTINUE C C 4 WRITE C(PLATE) IMAGES TO DISK C
IF(NCPLTLEO) GO TO 480 DO 470 I=NCPLT NE=INCII) IF(NEEQ5) GO TO 460 WRITE(97005) HOR2(NE)IOCPCI)IPIOI)NGIJ)Jfl4)______
X TH(I) GO TO 470
460 WRITE(917005) -HORZ 5)iPC)LIPID(i) NGI(J)1 470 CONTINUE 480 CONTINUE
C C 4 PUT ENDOATA IMAGE AT ENO-OF- DATA SET ON DISK C
ImG = 0 WRITE(070001 HORI 16 CALL STORE( 2 2 WRITE(97003) (NIMG(-IjLL201 STOP
C
7CCO FORMAT[1OA8) 7001 FORMAT[3AB31t6AS) 7002 FORJAT(2A83185A8) 7C03 FORMATI2OA4) 7004 FORMAT(A8 418) 7005 FORM4AT( AS6I8F83 7010 FORrAAT(IH1IHO 65(2HLIIHO46X3BHNO ROD ELEMENT JOINTS TO BE
IMCODIF[ED 1447X38HNO BAR ELEMENT JOINTS TO BE MODIFIED 141 X 47X4OHNO PLATE ELEMENT JOINTS TO BE MODIFIED v12 2 IHO65(2H 2)
71C0 FORMATCIHO54X22HV ROD JOINTS 7110 FORMAT(ZOXT22110 5E135v 15) 7120 FORPATIIHO55X22H BAR JOINTS )
211
7130 FORMATIZOXI2 2110 5E135 IZ4X E135 5F133 AS 15) 7140 FORMAT(IH055X22H PLATE JOINTS 7150 FORWAr(13X12317 5F133 417
END BLOCK DATA
C INTEGER2 OMIT INTEGER2 OMTB COFCN BRED IOR(20) IDGR(20) RPARM(205) OMIT(Z01 NROO COMMON SGRID IGD(LOOOhIPCG(000) GCOIOOO3) NGD DUMM X IXCD(loooItXPSs(100) REAL8 IXCO tXPS COMMON BCROD IDRD(10004) NCRD COMMON BPROD IDPRD4l000) IDMP(lO00i JPROP(IOOO4) NRPC COMMON BNEW NGRO IDEX IPEX IECM IDCV IMEX COMPON BCoMm XC135) II [2 INCP COMMON BOEFLT AKGPD AKGSDt AKMD AKAPO AKJPD BKMD BKGPD 1 BKGSO UKAPD BKASD BKJPO BKJSD BKIIPD BKIISD BKIZPD BKI2SO COMMON BSOGP NWGRD(40) SEGMX(40) NSQGP COMMON BIMG NIMGC20401 IMG COMMON BCBAR 103(1000) IPBIO00) IBA(I000) TBBCIOoo) 1 IBREC(IOOG) NBAR NBREC -----
COMMON BEAR IDRRCSO) IOGB(50)t BPARM5012) OMTB(50sI NBR COMMON BPBAR IDPB(10001 IPREC(IOO) NPBAR NPREC
C DATA NROO OMIT 210 DATA NGD 0 DATA NCRD 0 DATA NRPD 0 DATA NGRD IDEX IPEX IEDCM IDCV 7000 7300 7500 7600 7700 DATA IMEX7000 DATA AKGPO AKJPD AKNO AXAPO 01 100 01 100 -
DATA bKGPO BKAPD BKJPD BKIIPD BKI2PD 1 01 100 100 100 100 DATA BKMO BKGSU BKASD BKJSD BXIISO BKI2SD I 1 01 01 01 01 01 01 DATA NSOGP 0 DATA NBAR NBREC 0 0 DATA NBR I 0 DATA OMTB 500 -0
DATA NPBAR NPREC 0 0 DATA RPARM t00-LO DATA bPARM 600-I0 COWMCNBMAT1 IDMAT(100)E(100)G(lOOhNMAT1 COMMONBCPLT IDCP(1000)IPIDOIOOO)NG(10004)TH(IOOO)INC(10001
_x NCPLT COMMONBPLATE IOP(200)IDGPLT(2002)PLTPRM(2005)MPCID200) X OMP(200)NPLT x MPCPAi2O0JMPCPB(20 COMMONBPPLTI IOPP(lDOOINP(IOOO)TTHICK(1000)-IMID-I-0)NPPLT DATA NMAT1NCPLTdPLTNPPLT O00O I COMMONBCORD IDCORL20)tIFORZ[20XPP(209)NCORD-__ DATA NCOROO E NO SUBROUTINE RADJIII IX)
212
C C RIGHT ADJUST NASTRAN BULK DATA IN FIELD C-
LOGICAL1 CD CCI64J DMY(4) BLNK CONMCN IMAGE I CD(80 DATA DMY lHO 1H 1HI IH- I DO 10 1 = I 64 CCII = BLNK
10 CONTINUE C C t TEST FOR SINGLE OR-DOUBLE-FIELD C
IF(II GT 7) GO TO 20 C 4 SINGLE FIELD
IDX = 8 IDY = 8 GO TO 30
20 CONTINUE C DOUBLE FIELD
tDX = 4 rDY = 16
30 CONTINUE C
READO(07000) CD C C 4 RIGHT ADJUST DATA IN FIELDS C
DO 100 J = 1 IDX IBLNK = 0 K2 = J TOY K1 = K2 + 8
100 50 L = - IDY IF(CDKI) -EQ BLNK) GO TO 40 IBLNK = I CC(1C2) =COIKI)
BLNK I i 1
-
K(2 =K2 - 1
50 CONTINUE IFIT GT 2) GO TO 100 IFIBLNK NE 0) GO TO 100 DO 60 L It 4 CCCK2)- = OMYL) K2 = K2 - 1
60 CONTINUE 100 CONTINUE
DO 120 J = 1 64 CD(J+8) CCIJ)
120 CONTINUE WRITE(O7000) CD RETURN
7000 FORMAT(BOAl) 7010 FORMAT(26X 80A ) _ - --
END SUBROUTINE SEQGENIIDG IGC) COPMON BSQGP NWGRDf40) SEQMX(40) NSQGP
213
REAL8 TLC DATA TLC 8HSEQGP IFINSOGP EQ 0) GO TO130 DO 120 L =1 NSQGP IFLIOG -NE- NWGRO(L)) GO TO 120 LS = L GO TO 140
120 CONTINUE 130 CONTINUE
NSQGP = NSQGFLplusmn__ NWGRD(NSQGP) = LOG SEQPX(NSQGP) = LOG LS = NSQGP
140 CONTINuE SEOC = SEQMX(LS) + 01 SEQYXILS) = SEQC WRITE(07000) TLCIGC SEQC CALL STORE 6 1 RETURN - ----
C 7000 FORMATAS 18 F81)
END
SUBROUTINE GRID(IIX II) DIMENSION a(51 REAL8 BB(41 ACONT CONMCN IMAGE CARO(2O) COMMON BGRID IDG(1000) ICP(10001 GCD(100D3) NGD DUMM X IXCD(1000)IXPS(1000 REALt8 [XCD IXPS K J DATA MAX 1 -1
C IP(IOX EC 41 GO TO 20 READiC7001) A B K J GO TO 50
C C DOUBLE FIELD CARD C 20 CONTINUE
REAOt 07002) A BB CONT 00 30 1 = I 4 B(I) = 88(1)
30 CONTINUE IF(B(2)LE0) WRITE(970001 CARD REAO(57000ENO=200) CARD WRITE(O7000) CARD CALL RADJ(I LOX) READ(07004) A 8(5)t K J
50 CONTINUE C C STORE DATA IN COMMON C
NGD = NG I IF(NGD -LE 10001 GO TO 75 IFMAX GE 0) GO TO 100 MAX =
214
__
WRITE(67003) GO TC 100
75 IOG(NGO) = B(1) ICP(NGD) = S(2) GCD(NGO11 = 8(31 GCD(NGD2) = B(43 GCO(NGO31 = B(51 IXCDNGD)=K IXPS(NGD)=J IF(ICP(NGO)GTO3 GO TO 108
-- 100 WRITE(9700O) CARD 108 CONTINUE
RETURN C -SUBROUTINE-GRID -INSERT 200 CONTINUE
WRITE(67001 A 8B CONT STOP
7000 FORVAT(2OA4) 7001 FORMAT(A8 SF80 ZAS) 7002 FORMATIA8 4F160 AS) 7003 FORMAT(1HO22X86H MORE THAN 1000 GRID POINTS NO MORE WILL B
IE STORED FOR JOINT PRE-PROCESSOR IHO) 7004 FORMATCA8FI6028XAI) 7010 FORmAT(1HOt46X40H END OF FILE ON INPUT IN GRID
1 26X AS 4FI65 AS)-END SUBROUTINE OMTC(N OMTI OM) INTEGER2 OTI(1) LOGLCALl OM(8) OMT(4)BLN DATA OMTC BLNK 4HOMIT IH EQUIVALENCE tOuIT(L)_t OMTF)
KI =8
K2 = 4 65 IFKI EQ 0) GO TO 100
IFCOM(KI) -EQ 8LNK) GO TO 70 OMT(K2) = 1(KI) KZ = K2 - i IF(K2 -EQ 0) GO TO 80
70 KI =K - 1 GO TO 65
80 CONTINUE
IFOMTF EQ OMTC) OMTI(N) =1 C
100 CONTINUE RETURN END SUBROUTINE ROD INTEGER2 OMIT COMMON BROD IDR(20) IDGR(20) RPARH(205) OMIT(20) NROD DIMENSION B19) LOGICALl O(8)
READCO7000) B OM
215
C
NRCD = NRCD + I IF(NROO LE 20) GO TO 50 WRITE(6700l) NROD B OM GC TO 100
50 IOR(NROD) = B(3) IDGR(NROD) BM(4 DC 60 I = i 5 RPARM(NRUDI) = B(1+4)
60 CONTINUE CALL OMTC(NROD_OMIT -OM---------shy
10C RETURN 7000 FORMATiZA4 TF80 8AI)
7001 FORMAT(HO_39H-_THNUMBER OF ROD ELEMENT JOINTS12j 1I6HEXCEEDS 20 2X2A4 7F84 SA1i
END SUBROUTINE BARLLL_ID-A INTEGER2 OMTB LOGICALlI CARD PLUS LOGICAL1 Ci8 BLNK CODPON BBAR-I IDBR(50) IDGB(50) BPARMt5O12J OMTB50) NBAR COMON IMAGE CARD(80I
-REAL8 A DIrErSION B(8) BO(6) EQUIVALENCE (BM) BOl)) DATA PLUS IH+ 1 DATA BLNK IH I
C READO7000) A BC-N2AR = NBAR + I IF(NBAR LE 50] GO TO 25 WRITE(670L0) NBAR B GO TO 200
25 CCNTINUE EDBR(NBAR) = 8(1) - EOGB(NEAR) = B(2) DO 40 1 = 1 6 BPARM(NBAR1) = 8(1+2)
40 CCNTINUE C C CONTINUATION CARD -
C REAO(57001END=3001 CARO IF(CARDfI] NE PLUS) RETURN I WRITE(070013 CARD CALL RADJ(II IOX) READ(O7002) A BC_C-
DO 125 1 = 16 BPARM(NBAR1t6) = 6(1)
125 CCNTINUE CALL OMTC(NBAR OMTB C)
200 RETURN C C V CONTINUATION CARD EXPECTED - END OF FILE ON INPUT DATA SET C
300 CONTINUE
216
WRITE(67020) At Bf C STOP
7CCC FORMAT(A8 8F80 8At) 7001 FORMAT(BOAUJ 7002 FORMAT(A8 5F80 AS SAl) 7010 FORMAT(IHO39H THE NUMBER OF BAR ELEMENT JOINTS IZ
117H EXCEEDS 50 2X8F8) 7020 FORMAT(1HO46X39H END OF FILE ON INPUT IN BAR
126XA8 8F64 8Al)END SUBROUTINE CRO REALt8 A COMMON IMAGE I CO(20) COMMON BCROD Iot t004--NCRO DIMENSION B(8) DATA MFLGI-_
__
READ(07000) A a 11 = -4
o-- CONTINUE I1 = I1 + 4 IF II GT) GO TO 75 IF(B(fl+) EQ 00) GO TO 75 NCRD = NCRD + 1 IF(NCRD GT -1000I GO TO 50 DO 25 1= 1 4 ID(NCRDO) = B(I11)
25 CONTINUE GO TO 10
50 CONTINUE c C TABLE FULL C
[F(MFLG -GE 0) GO TO 75 WRITE(67010) CO MFLG = i
75 IF(MFLGGT0) WRITE(9700U)__CD - ICC RETURN 7000 FORMAT(A8 8F80) 7001 FORMATCZOA4) 7010 FORPAT(IHO31Xamp6Ht CRO0 STORAGE FULL - NO MORE CRO CARD DATA
I WILL BE STORED 126X ZOA4) END SUBROUTINE PROD(II lOX) COMMON IMAGE I CD(201 COMMON SPROD IDP(OOO) _IOMI1OOOPROP(004)_NPRD REALt8 A DIMENSION B(61 DATA MFLG__I shy
READ(070001 A B NPRD = NPRD + I_ IF(NPRD GT 1000) GO TO 200 IDP(NPRD) = BMt) IDM(NPRD) = 8(2)
217
DO 25 1 = 1 4 PRDP(NPRD[) = 8 1+2)
25 CONTINUE GO TO 250
200 CONTINUE IF(MFLG GE 0) GO TO 250 WRITE(67010) CD MFLG = I
250 CONTINUE C C WRITE PROC IMAGE ON DISK C
WRITE(9700 ) CO 300 RETURN 7000 FORMATCAS 6F80 7001 FORMAT(2OA4) 7010 FORPAT(lIHO31X69H PROD STORAGE FULL - NO MORE PROD CARD DATA
1 WILL BE STORED 26Xg20A4) END SUBROUTINE CBZR(II IDX j 3 LOGICALfl CO PLUS STAR COMMONI IMAGE( CD(80) COMMON SCEAR IDB(lOOOjt IPBIIO0O) IBAtIOO|) IBBE OO 1 IBREC(1000) NBAR NBREC REAL8 A 86(4) DIMENSION B43 DATA PLUS STAR IH+ H1 1 MFLG -I
IFIIOX EQ 4) GO TO 20 C SINGLE FIELD CARD
READ(07001) A_B GO TO 40
20 CONTINUE -_ C DOUBLE FIELD CARD---
REAOLO7002) A B8 DO 30 1 = 1 4 B(1) = BE(1)
30 CONTINUE 40 CONTINUE
NSAR = NSAR + L --IF(NBAR LE 1000) GO TO 75 IF(FLG GE 0) GO TO 60 wRITE(67010 CD MFLG = I
60 CONTINUE - RTE(T7000)_CD___
RETURN 75 CONTINUE
IDS(NBAR3 = B (1) IPB(NBARI = 8(2) IBA(NBAR) = B(3) IBB(NBAR) = B(4) IBRECINBAR) = NBREC + I
C C SEARCH FOR CONTINUATION CARDS
218
C 80 CPNTINUE
NBREC = NBREC + 1 WRITE(37000) CD READ(57000END=200) CD IF(CDI) EQ PLUS) GO TO 100 IFICD() EQ STAR) GO TO 100 RETURN I
100 CONTINUE hRITE(O7000) CD CALL RAOJ(II IDX) GO TO 80
2CC CONTINUE C C END OF BULK DATA SET C
RETURN 2 7000 FORMATt8OAL) 7001 FORMAT(AS 4F80) 70C2 FORMAT(AB 4F160) 1010 FORMAT(IHO35X61H CBAR TABLE FULL
1E SAVED 26X_80A1) END SUBROUTINE PBAR(II lOX 3 LOGICAL1 CD PLUS STAR-COMMON IMAGE CD(80) COMMON BPBAR IOPI00) IPREC(IO00) REAL8 A DATA PLUS STAR MFLG i 1R IH -I
C IFIOX EQ 4) GO TO 20
C 4 SINGLE FIELD CARD READ(OZO0lf Ar I GO TO 40
20 CONTINUE READ(O7002) A I
40 CONTINUE NPBR = NPBR + 1 IF(NPBR LE 1000) GO TO75 F(MFLG LTO) GO TO 50 WR[TE(67010) CD MFLG = I
50 CONTINUE WITE(9-7000) CO RETURN
75 CONTINUE IDP(NPBR) = I [PREC(NPBR) = NPREC +I
80 CONTINUE C C iRITE PSAR IMAGE ON DISK
WRITE(97000) CDC -I
C SEARCH FOR CONTINUATION CARDS
- NO MORE CBAR DATA WILL B
NPBRt NPREC
219
C NPREC = NPREC + I WRITE(47000) CD READ[57000END=tO0) CD IFICD1I) EQ PLUS) GO TO 90 IF(CO(I) EQ STARI GO TO 90 RETURN I
90 CONTINUE WRITE(07000) CO CALL RAOJ(IIIOX)_ GO TO 80
100 CONTINUE
C END OF BULK DATA SET C
_
7000 FORMAT(8OAI) 70C1 FORYAT(AS 181 7002 FORMAT(A8 [16) 7010 FORMATHO35X61H- PBAR TABLE FULL - NO MORE PBAR DATA WILL B
IE SAVED 126X80AL)
R E T U R N 2 -- --
END
SUBROUTINE RODJT LOG[CALfl CD INTEGER2 OMIT COMMON IMAGE C(80) COIMCN BROD I IDR12O) IDGR(20) RPARM(205) OMIT(20) NROD COMMON BGRID IGDN(1000) IPCG(IO00) GC(I0OO03)NGD COMMON BCROD IDRO(IO004) NCRD COMMON BPROD IDPRD(1000) IDMP(1000) PRDP(10004) NPRO COMMON BNEW NGRD [DEX IPEXIEDCH IoCV
X IMEX COMMONSMATI IDMAT(1O0)E(IO0)G(IOOhNMAT COPON BCOM XC(35) 11 12 INCP COMMON BOEFLT I AKGPD AKGSD AKMD AKAPD AKJPO COMMON BSQGP NWGRD(O) SEQMX(401 NSQGP COVItON BIMG I NIMG(2040) IMG REAL8 TLC09) OATA TLC 8HGRID 8HCROD 8HCONM2 8HOIT8
I 8H 123456 8HSEQGP BHPRtOO BHCVISC _ SHPVISC- _
C IFNRO0 LE 0) RETURN
C C START LOOP THROUGH NO OF ROD ELEMENT JOINTS TO BE MODIFIED C
DO 500 NR = 1 NROD--IMG = 0 IDE = IOR(NR) IDG= IDGR(NR) ------
CI=RPARM(NRI) C2=RPARM(NR2)
DO 20 L = 1 NCRO [FIDE NE IDRD(LI)) GO TO 20 LL = L GO TO 30
220
- -
------
20 CONTINUE WRITE(67010) IDE
GO TO 500 30 CONTINUE
IGA = IORD(LL3) [GB = IDRD(LL4) CALL CCORD(IGA IGB 1OG AKGP = RPARM(NR3) IF(AKGP LT 00) AKGP = AKGPD
TOP = IDRO(LL2) IF(IDP EQ 0) TOP = IDE
C SEARCH FOR PROD CARD IMAGE C
O0 L50 L =it NPRD IF(ITOP NE IDPRO(L)) GO TO 150 LP = L
GO TO 160 150- CCNTINUE shy
WRITE(67020) lOP
GO TO 500 -- 160 CONTINUE
AKAP = RPARMINR4) IF(AKAP LT 00) AKAP= AKAPD AKJP = RPARMCNR 5)
IF(AKJP LT 00) AKJP = AKJPD AC = AKAP PRDP(LPl)
X (AKGP(1-AKAP) + AKAP) TC = AKJP PROP(LP2)
X (AKGP(-I-AKJP) + AKJP) MID=IDMP(LP) IF(CILEO) GO TO 175
C CHANGE MATERIAL PROPS TO INCLUDE DAMPING COEFF
-XE=E(MIO) -- - - - - - - - -
XG=G(CMID) NID=IMEX IMEX=IMEX+ 1
XL=SQRTfI XC(I2)-XC 1I)) 2 +--
X (XC22)-XC(21))2 + (XC (32)-XC (31 )) 2 ) X
GE=CIXL(ACXE)CI-AKAP+AKAPAKGP) WRITE(07008) MIDXEXGMID CALL STORE( 20 ) WRITE(07009) MIOGE CALL STORE( 18 )
175 CONTINUE- -shy C
C CHANGE ROD TO REFERRENCE NEW PROPERTY CARD AND WRITE NEW CARD
_ C
IORDLL2)=IPEX IPEX MIDt AC TC (PRDP(LPL)L134)WRITE(07005) TLC(7)
CALL STORE( 14
221
IF(C2LEO) GO TO 180 C C GENERATE CVISC CARD IMAGE C
WRITE(O7006) TLC(s)- rCVy IDCV IGA IGB CALL STORE( 10
C
C GENERATE PVESC CARD IMAGE C
C2=C21(l-AKJP+AKJPAKGPI WRITE(O7011) IDCVC2IDCV CALL STORE(20) WRITE(Q7012) _ID--CALL STOREI2)
180 CONTINUE WRITE(67O5O)_NRL _ WRITE(67080) 00 -200 L = It IMG WRLTE(97002) NIMG(KL)K=I20L NRITE(61090L(NIMG(KL)K=20
200 CONTINUE IDEX = IDEXt1
IPEX = IPEX + 1 IDCV = IOCV - 1
5Cc CONTINUE--------------------- RETURN
C C FCRFATS C 7001 FORPAT(AB 218 3F82) 7002 FORVAT(2OA4) 7C3 FORMAT(A8 818) 7004 FORAT(2A8 718) 7005 FORYATLA8 218 F
7CC6 FCRlAT(AS418) 7007 FORMAT(A8 18 2F81) 7008 FORPAT( 8HMATI 1162El6616X 3HM1t [5 7CCY FORMAT( 3Hf 15 48X E166 ) 7010 FORMATIHC33X31H SPECIFIED ROD ELEMENT I 1539H DOES NOT
IMATCH ANY CROD ELEMENTS ) 7011 FCRIVAT( 8HPVISC I1614X2H0E16816X 3HPV 15 1 7012 FORMAT( 3H PV 151 7020 FORAT(IH032X24H SPECIFIED PEAR ID 1538HOOES NOT MATCH AN
IY PEAR ELEMENTS ) 7050 FORMAT(IHI47X28H ROD ELEMENT JOINT - 12 8H I) 7080 FORMAT1IHO46X39H NEW CARD IMAGES 1 7090 FORMAT2OXI21OX2OA4)
END SUBROUTINE BARJT
LGGICAL I CO STAR INTEGERt2 OMTB COMJON IMAGE I CD(80) CCNMON BCBAR IOB(I000) IPBtIOOOI IBA(10001 iBBio000 1 IBREC(1000I NBAR NBREC COMMON BOAR IDBR(5)- IDGB(50) BPARM(5012) OMTB(50) NBR
222
C
COMCN BGRID IOGN(OGOO) ICP(IO0O) GCD(O003) NGO COMMON BOEFLT RDFLT(5) BKMD BKGPD BKGSO BKAPD BKASD I BKJPD BKJSD BKIIPD BKIISD BK12PD BK12SD CO N CN BIMG NIMG(2040) IMG -f NC_ _
COMMON BCOMM XC(351 11 12 INCP COMMON BNEW NGRO IDEX IPX 1EOCM IDCV
X [MEX COMMONBMATI IDMAT(100)E(100)G(100I)NMAT COMMON BPBAR IDPB(lOO) IPREC(IO00) NPBAR NPREC REAL8 TLC(6) BB(4) Al AZ REALt8 RLC(2) DIMENSION B(8) DATA RLC SHOMITI DATA TLC 8HGRID I 8HCVISC 8HPVISC DATA STAR t IH DATA CNE OFLT 4H
[F(NBR BLE O) RETURN
RH vHCSAR 8H SHPBAR
8 123456
1 4H-10
C START LOOP THROUGH BAR ELEMENT JOINTS
DC 400 NB = 1 NBR ImG 0 IDE = IOBR(NB) IDG = IDGBINS) DO 20 L = 1 NRAR IF IDE NE IO8(L)) 001020 LL = L GO TO 30
20 CONTINUE WRITEI67010) IDE GC TC 400
30 CONTINUE IGA = IBA(LL) IGB = IBB(LL) CALL COORD(IGA IGB IOG amp40O-BKGP = BPARM(NBt7) IF(BKGP LT 00) BKGP = BKGPD
CC COMPUTE NEW GRID POINT -- COORDINATES
00 40 L = 1 3 XCtL3) = XC(LII) + BKGP (XC(L12) XC(LI1))
40 CONTINUE IGC = NGRO NGRO NGRO -I WRITE(07001) TLC(IU [GC INCP (XCIL3)L =13) CALL STORE(16)
C C ESTABLISH GRID POINTS E amp F C
IGE = NGRD IGF = NGRO + I NGRO = NGRD + 2
223
C
CALL SEQGENI[OG IGC) CALL SEOGEN(IDG tGE) CALL SEQGENLIDG IGF)
C C TEST FOR CMIT CARD GENERATION C
IF(OMTB(NBI EQ 0) GO TO 50 WRITECO7O03) RLC(t) RLC(2 IGC IGE IGF CALL STORE(I -shy
50 CONTINUE C
C CALCULATE E amp F COORDINATES C
- CALL-EFC[-LLt_B_BB_A4001 C
WRITEO700) TLCLI) IGE INCP (XC(L4)L=I3) CALL STORE16 I----WRITE(O700 ) TLC(I) IGF INCP (XC(L5 L=31 CALL STORE(16)
- C C INSERT NE14 GRID POINT 160 IN ELEMENT LL C
IF(I1 NE 1) GO TOt6 - -shyIBA(LL) = IGC GO TO 70
60 IDB(LL) = IGC 70 CONTINUE
C C GENERATE ELEMENT CARD FOR NEWARELEMENT C
13 = B(8) IF113 EQ 2) GO TO 87 WRITEOt7002) TLC(2) IDEX IPEX TOG IGC (B(L+43L=14) GO TO 89
87 CONTINUE [OP = B(5) WRETE(07009) TLC(2) IDEX IPEX IDG IGC IDpt 13
S9 CONTINUE-------------
C CALL STORE( 18
C ESTABLISH PROPERTIES OF THE NEW ELEMENTS -
C IOP = IPBILL IFCIOP -LE O IDP IDE---
C = SEARCH FOR PBAR IMAGE 00 90 L = 1 NPBAR FCIDP NE IDPB(L)) GO TO O
LP = L GC TO 100
90 CONTINUE WRITE(670203 IOP GO TO 400
100 CONTINUE
224
NRECD = IPREC(LP) REIIND 4 DO 120 L = I NRECD REAO(47004) CO
12C CONTINUE WRITEiO700) CD IF(CO(5) EQ STAR) GO TO 140 IF(CO(B) EQ STAR) GO TO 140
C = SINGLE FIELD WORD READ(07005) Al B GO T iaO
140 CONTINUE C DOUBLE FIELD WORD
READ(07006) Ali 88 DO 145 L = 1 4 8L) = 8B(L)
145 CONTINUE READ(47004) CO WRITE(O70043 CD READ(07006) Ali BB DC 150 L = 1 4 B(L 4) = B(L)
150 CONTINUE NRECD = NRECD + 1
180 CONTINUE BKAP = BPARM(NB8] 87JP = BPARM4NB92 BKIIP = BPARM(NB10) BKI2P = BPARM(NE11) IF(BKAP LT 00) BKAP = BKAPD IF(BKJP LT 00) BKJP = BKJPD IF(BKIIP LT 00) BKILP = BKILPD IF(BK12P LT 00) BKI2P = BKI2PD13 = B(2) _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
B(1) = B(3) -BKAP 8(2) = B(4) SKEIP B(3) = 8(5) BKI2P------------------------- B(41 = 8(6) BKJP
C WRITE( 070Z1) rPEX13BIJB(2Ia3-PMX CALL STORE(20) WRITE(07022) IPEXB(3B(4) CALL STORE(10)
C C GENERATE RODS WITH DAMPING FACTORS ON MATL CARD
C
DO 184 L=INMATI IF(IDMATL)NE13) GO TO 184 XE=EIL) XG=G(L) GO TO 185
184 CONTINUE STOP 231
[85 XL=BKGPSQRT((XC(11)-XCCI2))2 + X (XC(21)-XCIZ21 2
225
x (XC(31)-XCt32)f2 SUMC=O D 187 L=16
187 SUMC=SUMC+BPARMINBL) GE=XLSUMC(XEIE-SB(1) MID=IMEX IMEX=IMEX+I WRITE07C11) MIDXEXGMIO CALL STORE[ 20 ) WRITEtO7012) MIOGE CALL STORE( 18 FI=XLCXEGE) F2=XL(XGGE) XAN=F1BPARMCNBI) XAN=FIBPARtICNO2) XAP=FIBPARMN3) XJM=F2BPARMCNB4) XJNzF2BPARM NB 5) XJP=F2BPAR(NB6) -----shyWRITE(O7013) IDEXIPEXIDGIGC CALL STORE( 10 ) WRITECO7014) IPEXMID_XAMXJMIPEX-CALL STORE( 20 ) WRITEO7015) IPEX CALL STORE( 2 3----------------- IDEX=IDEX+l IPEX=IPEX+1 WRITE(070l3) IDEXIPEXIDGIGE -- CALL STORE( 10 ) WRITE(07014) IPEXMIO XANXJNIPEX CALL STORE( 20 )- ---- - -hRITE(07015) IPEX CALL STORE( 2 IDEX=IDEX+I -- - - - IPEX=IPEX+1
WRITE(O7a13) IDEXIPEXIOGIGF CALL STORE( tO ) WRITE(070143 IPEXMIO XAPXJPtIPEX CALL STORE( 20 ) WRITE(O7CI51 IPEX CALL STORE( 2 1 IDEX=IDEX+I IPEX=IPEXf1----------
C C GENERATE PULTIPOINT CONSTRAINT CARDS C
HIO = BPARMNB 12) IF(HIO EQ DFLT) HI = ONE CALL MPCGENCIGC IGE_IGEtJHIOJ___
C
C PRINT OUT JOINT INFORMATION AND NEW BULK DATA CARDS C
WRITEI69IO0) NB WRITE(67L30) 00 300 L = 1 IMG
226
WRITE(900I (NIMG(KL) K=I20) WRITE67140) L (NIMG(KL1K=1201
3CC CONTINUE IDEX = IDEX + I IPEX = IPEX + 1
40 CONTINUE RETURN
C C FORMATS -C 7000 FORMAT(2OA4) 7001 FORMAT(AB218 3F822(7XIHO)) 7002 FORMAT(AB418 4F83) 7003 FORMAT(2A8 718) 7004 FOR$AT(BOAL) 7005 FORMAT(A8 8F80) 7006 FORMAT(A8 4Ft60) 7007 FORMAT(A8 418) 7008 FORMATIA8 18 2F81) 7009 FORMAT(A8 518 124) 7010 FORMAT(IlHO28X31H SPECIFIED BAR ELEMENT 1O I
140H DOES NOT MATCH ANY CBAR ELEMENTS ) 7011 FORMATI 8HMATI 1162E16616X 3HM1 15) 7012 FORNATI 3HM1 15 48X E166) 7013 FORMAT( 8HCROD 418 shy7014 FORMATI 8HPROD 2116 2E168 3HPRi15) 7015 FORMAT( 3HPR E5 I 7020 FORMAT(IHO25X36H SPECIFIED PROPERTY ELEMENT 10 _15
140H DOES NOT MATCH ANY PBAR ELEMENTS 1)) 7021 FORMAT( 8HPBAR 2116 2E168 3HPB153 7022 FORNAT( 3HPB 15 ZE168 ) 7100 FORMAT(IHI47X28H BAR ELEMENT JOINT - IZ 8W )
7130 FORAT(IHO46X39H NEW CARD IMAGES 4 4 4 1 7140 FORfAT(20X12 LOX 20A4)
END SUBROUTINE EFC( LL B 8B 3 COYON BCBAR IDB(1000) IPB(1000) IEA(IO0) 1BB(1000) 1 [BREC(1OCO) NBAR NBREC COMMON BGRID IDGN(1000) ICP(COOO) GCD(1O003) NGD COMWON SCOMM I XC(35) 11 12 - ------
COMMON IMAGE CO(80) LOGICAL1 C0 STAR REAL8 At 8B(4)_ DIMENSION 8(8) VI33 V2(3) V3(3) DATA STAR IH f
C W SEARCH FOR CBAR C
IOP = IBRECILL) _ _ _ _ _ _ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ _ _ _ _ _ _
REWIND 3 00 10 L = I IDP READ37000) CD
10 CONTINUE IFICD5) EQ STAR) GO T1 30 IF(CD(8) -EQ STAR) GO TO 30
227
__
-SLODU~UJTYOF- -- THE C SINGLE FIELD CARD
WRITE(O7000) CO READ(O7001) Al B GC TO 50
30 CONTINUE C DOUSLE FIELD
READ(37000) CD WRITE(07000) CD READ(Q7002) Al BB
- - DC 40 L = ft4 BL+4) = BB(L)
40 CONTINUE - 50 CONTINUE
IDP = B(8) IF(IDP -EQ 2) GO TO 60 V2(1) = 8(5) V2(2) = B(6) V2t3) = B(7)
- - GO TO 70
60 CONTINUE IDP = B(5)00 65 L = I NGD _____ - ---------
IF(UOP NE IDGN(L)) GO TO 65 V211) = GCD(LI) - XC(1I1) V2(2) = GCO(L2) - XC(21I V2(3) = GCD(L3) - XC(311) GO TO 70
65 CONTINUE WRITE(67010) LOP RETURN 1
TO CONTINUE VIM) = XCtV12) - XC(II1) V112) = XC(212) - XC(2It) Vl(31 = XCC312) - XC1311)
C
C F CCOROINATES C
AC=SQRT((XC(13)-XC(IIl))2+(XCi23)-XC(2I1))2+(XC(33-XC(3
1111 )2) V3(1) = V1(2J V2(31 - V1(3) V2(2)- V3(2) = V1(3) V2(11 - VII) 2M13) V3(31 = Vl(1 V2(2) - V112) V2(1) AMG=SQRTIV3(1)2+V3(2)2 V3(3)2) XC(L5) = XC(1I1) + V3(1)ACAHG XC(25) = XC(2I1) + V3(2)ACAMG XC(35) = XC13l) + V3(3)ACAMG
C C E CCORDINATES C
V42(1) = V4312) VI1M3 - V43(31 VIM1(2 V22) = V3(3) V1(1) - V3(1) V1(3) V2(3) = - V3(1) VI (2) - V3(2) VI(1L AMG=SQRT(V2(1)2+V2(2)2V2(3)21 XC(14) = XCriII) + V2(l)ACAMG XC(24) = XCIZ11) + V2(2)ACAMG
228
XC(341 = XC(3I1) + V2(3)ACAMG RETURN
7CC0 FORMAT(8OAI) 7001 FORMAT(A8 8F801 7002 FORMATCA8 4F160) 7CIO FORWAT(lHOL3X94H COULD NOT LOCATE GRID POINT FOR REFERENCE
ICOORDINATE SYSTEM- SUBROUTINE EFC - GRID NO 15 6H ) END SUBROUTINE COCRD(IGA IGB IDG 3 COMMON 3GRID IDGR(1000) ICP(1000) GCD(10003) NGO COMMON BCOMM XC(35)--I1 INCP
C
C COMPARE INPUT GRID POINTS FOR VALIDITY AND ORDER C
II =I
12 2 IF(IOG EQ ISA- GO-TO-20 11 = 2 12 = I TF(IDG EQ IGB) GOTO 20 WRITEC67000) IDG IGA IGB RETURN I
20 CONTINUE C C SEARCH GRIDTABLE FOR COORDINATES
00 30 L = 1NGD [FIGA NE IDGR(L)) GO TO30 DO 25 K =1 3 XC(K II = GCO(LKI
25 CCNTINUE 1F(i EQ I INCP ICP(L) GO TO 40
30 CCNTINUE WRITE(67010) IGA RETURN I
40 CONTINUE DC 50 L = 1 NGD IF(IGB NE IDGR(L)) GO TO 50 C0 45 K I 3 XC(K 2) = GCO(LK)
45 CONTINUE IF(12 EQ 1) INCP = ICPELI- - GO TO 60
50 CONTINUE WRITE(670OO) 8IGS RETURN I
60 CONTINUE RETURN
7000 FORIATCIHO29X72H ELEMENT GRID POINTS 00OTCOMPARE WITH SP IECEFEED GRID POINT 38XL2HSPECIFIED = 15 IOX12HELEMENT1 shy
2 A 15 7H B 15 _ 7010 FORMAT(IHOI8X48H= NO MATCH FOUND FOR THE ELEMENT GRID POINT
I 1542H IN THE GRID POINT COORDINATE TABLE 11 END
229
_ _
- SUBROUTINE MPCGEN(IC IE IF HID) COMMON BCOMM XC35) [ 12 DIMENSION C0) DIMENSION TLC(tO) )
DATA TLC 4HMPC 4H I 4H MPC 4H+MPC 4H I 4H 2 4H 3 I 4H 4 4H 5 4H 6
DATA LCNT Al A2 990_a - C
11 = IE
DO 100 1 1 2 C
___~ NI =5 N2 = 3 N3 = 10N4- 9
N5 = 2C
0D 10 Is2 __ _ __ L-= -3-_ _ _ __
C(L) = X(L3 XCL12) _ _ _ __
10 CONTINUE
C
DO 50 J = 1 3 ICNT = ICNT + 10
C C FIRSTTHIRDFIFTH CARD IMAGES C
WRITE(O7001) TLCCI) HID II TLCCNlI Al IC TLC(NI) 1 A2 TLC(3) ICNT CALL STORE( 20 1
C C SECGNDFOURTHISIXTH CARD IMAGES
ICNTIl ICNi ICNT = ICNT + 10 WRITE(07002 TLCt4) ICNTI IC TLC(N4) CN2) IC TLC(N31CUN5) CALL STORE( 18
C
NI = NI + 1 IF(J GT 1) GO TO 40 N5 = N5- I N4 = N4- 1 C(33 = -C3) GO TO 50
40 CONTINUE N3 = N3- i N2 = N2- 1 c ii = -c mI _
C(2) =-C(2) 50 CONTINUE
C
C SEVENTHEIGHTHNINTH CARD IMAGES C
D 75 J = 8 10
230
WRITE(O700) TLCI2) HID I TLC(J) Al IC TLC(J) A2 CALL STORE( 16
75 CONTINUE 11 IF 12 = 5
C
ICC CONTINUE RETURN
7001 FORMAT(A4 A12 18 A8 FBI I8 A8 F81 A12 14) 7CC2 FORMATCAA 14 16 A8 F83 18 AS F83 A12 14)
END SUBROUTINE STORE( N CCMON BIMG NIPG(2040) IMG DATA IBLNK-41-i
C
ING =1G + 1__ IFN - 20) 20 40 10
10 CONTINUE C N GT 20 NCT PERMITTED
N = 20 GO TO 40
20 CONTINUE C BLANK OUT UNUSED PART 0F IMAGE
11 = N + I DO 30 L = 11 20 NIMG(LIMG) = IBINK
30 CONTINUE 40 CONTINUE
C o READ IN CURRENT CARD IMAGE
REAO(O7000(NIMG(L IMG) L= 1N) RETURN
7000 FORMAT(2OA4) ENO SUBROUTINE MATI[KI
C C ROUTINE TO STORE MATERIAL PROPERTIES EANO G C
COMMONBATI IOMATl0O)E(100)GI100)NMAT1 IF(IMATIEQ10I STOP 30 NVATI=NMAT+I1 IF(KNE B) GO TO 20 READ1U7001) IDMATINATI) E(NMAT13 XGXNU
701 FORMAT( aX i8 3F80 GO TO 30
20 READ(O7002I IDMATNMATIENMATi)XGXNU 7C2 FCRAT( aX (16 3F160
30 CONTINUE IF(XGGTO3 GO TO 40 IF(XNUGTO1 GO TO 33 XG=O GO TO 40
33 CCNTINUE XG=E(NMATI|C 2(+XNUI)
40 CONTINUE G(NVATI)=XG RETURN END SUBROUTINE CPLATECNE)
C C ROUTINE TO PROCESS A CQUADICQUAD2 OR CODMEM ELEMENT- c CONNECTION DEPENDING IF NE=23 OR 4 STORE INFO SO C THAT CONNECTION CARDS CAN BE ALTERED IF JOINTS INTRODUCED C -- _ __ _ -___
COYPNBCPLT IDCP(IDOOOLIPIDIIOOOhNG(OOO4)THIOO0)INCIOOO) X NCPLT DATA IFMSG-l COMMONIMAGE C0(20) IF(NCPLTEQ1000) GO TO 80 NCPLT=NCPLT+t - REAOIO7000) IDCPCNCPLT)IPIDNCPLT)(NG(NCPLTJ)J=4)
X TH(NCPLT) 7000 FORMAT( aXbIS -F8_J
INC(NCPLT)=NE GO TO 90
80 IF(IFMSGGTOL S-BA IFMSG=I WRITE(67002) CD
7G02 FORMATI129HO PLATE CONNECTION TABLE FULL ALL PLATE CONNECTIL XONS FROM FOLLOWING CARD ON ARE NOT CONSIDERED BY PREPROCESSOR t X 20X 20A4
86 CONTINUE WRITE970041 CO
7004 FORPAT( 20MA I 9O CONTINUE
RETURN END SUBROUTINEPLATE12 _
C C THIS ROUTINE PROCESSES THE SPLATE CARD AND STORES C THE INPUT DATA IN COMMON BLOCk BPLATEJ c
COMMONBPLATE IDP(200)IDGPLT(ZOO2)PLTPRMI2OO5)MPCID2O) X CNP(2OO NPLT X MPCPA(2001MPCPS(ZOO) COMMONIMAGE CD(8O) DATA PLUSIH+ INTEGER OMP DIMENSION A(12)READOiOTOO0) AI
70o FORMAT(X8F80) REAO(5TO01) Co
7001 FORMATI BOAII WRITE(OlOOt) CO IF(CO(1)EQPLUS) GO TO 20
C C CONTINUATION CARD NOT GIVEN c
00 8 [=612
232
8 A(I)=0 A(6)=05 A (7)=5 A(8)=5 REAO(O70021(CO(I11=120)
7002 FORMAT( 20A4 J=-GO TO 30
20 CONTINUE C C PROCESS CONTINUATION CARD C
CALL RAOJ(IIDX) REAO(O7000) (Atf -pound-i=-21 IFIA(6)-EQ-1) A(6)=05 IF(A(7)EC-I) A(7)=5 IF(A(81EQ-j) A(8)=5 IF(A(9)EQ-) A(9)=O IFCA(1O)EQ-1) A(10)=OIFA(11)EQ-I) A(111=0IF(A(it)EQ-I) A(12)=O
J=O
30 CCNTINUE IF(NPLTLT200) GO TO 35 wRITE(67009)
7009 FORNAT( 49iO-THE NUMBER-OF-EXCEEDS 200 GO TO 80
35 CONTINUE NPLT=NPLTi IOPINPLT)=AC ) IDGPLT(NPLT1)=A(2) IDGPLT(NPLT2I=A(3) DO 40 I=i5
40 PLTPRM(NPLTI)=A(I+3) MPCID(NPLT)=A(9) OMP(NPLT)=A(10) MPCPA(NPLT)=A(II) MPCPB(NPLT)=AI12)
80 CONTINUE IF(JNEO) RETURN RETURN END SUBROUTINE PPLATE(NP)
C -C RCUTINE TO STORE PLATE THICKNESS AND MATERIAL CODE FROM C PROPERTYCARDS__________________________________ C
CONCNIBPPLT (OPP(IOOO)INP(1000)THICK(jOOO)IMIDg1000)NPPLT COMMONIMAGE CO(20) IF(NPPLTLT1000) GO TO 8 WRITE(6000) CD
-- 7C00 FORMAT( 55H0 _PLATE PROPERTY TABLE FILLED CANNOT CONTINUE X 20X 20A4 I STOP 20
8 CONTINUE
233
NPPLT=NPPLT+1 EFtNPEQ6 OR NPEQ9 OR NPEQ12 OR NPEQA5) GO TO 20 REAO(07002) IDPP(NPPLT)IMIO(NPPLT)THICK(NPPLTJ
7002 FORMAT( 8X 2116 F160) GO TO 30
20 READCO7004) IDPP(NPPLT)IMIDINPPLT)THICK(NPPLT) 7004 FORMAT( 8X 218 F80 2 _ _
30 CO1TINUE K=5 IF(NPGE6 AND NPLE8) K=2 IF(NPGE9 AND NPLE11)K=3 IF(NPGE12 AND NPLE141 K=4 INP(NPPLT)=K RETURN END
SUBROUTINE PJ - _ C C PRODUCE PLATE JOINTS C
CCMMONBNEW-UNGROIDEXdtPEXtEOCI4IDCVIMEX CCIPCNBCIJM XC(35I1112INCP CCNONSPLATEI IDPD(200)1DGPL 202LTPRML(20tN5-vPMPCIDO20 X O$P(200)NPLT X MPCPA(2OO)vMPCPB(200) COONBCPLT IDCP(1000)IPID(OO0)NG(10004)TH(1000)INC(IO0) shy
x NCPLT COMONSPPLT IDPP(1000)INP1000bTHICKfOOOihIMIDIIOfO NPPLT C0VIONBATI IDMAT(IOOEIOO)GO(100NMATI COYMON BCROD EORD(IOOOt4) NCRD COHYON EPROD [OX1IOGO) 0IO(1O0O) PROP(10004) NPRD CO$CON BCBAR IDB(1000) IPB(IOOO) IBA(IOOO) 188(1000) I [BREC(1O0) NBAR NBREC COH ON BPBAR IDY(IOOO0 IPREC(IO00) NPBR NPREC LOGICAL NEWGAPNEWGBP- INTEGER GAtGBGCGDGAPGBP DOUBLE PRECISION 88(10) INTEGER EDGE2003) DATA KSTRIH DATA IPLSIH+f DIMENSION AX(5 REAL8 CC(10)dW(I) IF(NPLTLE0) RETURN LEDGE=O ------------IvRI TE(96999)
6999 FORMATV 1SHPARA W4 1 1 DO 800 KK=LNPLL__ J=IDP(KK) KA=IDGPLTIKKL) KB=IDGPLT(KK ) OC 10 I=fNCPLT IF(IDCPtIl)NEJ) GO TO 10 K=1 -
KKK=I
GO TO 12 10 CONTINUE
234
GO TC 800 12 CONTINUE
D 20 1=14 IFtNGCIJEtQKA) Jt=I IF(NGCKI)EQKB) J2=I
20 CONTINUE JA= INO(JIJ2 _
JB=MAXO(JIJZ) IF(NOT(JAEQ1ANDJBEQ4)) GO TO 21 JO=2 JC=3 GO TO 22
21 CONTINUE JD=J A-I IFIJDEQ0) JO=4 JC=JB+ IF(JCEQ5) JC=I
22 CONTINUE
GC=NGCKJC)
GO=NGKJO)C
C CHECK TO SEE IF EDGE A-D ALREADY HINGED AND THE EDGE B-C C
NEWGAP-TRUE NEwGBP=TRUE IF(LEOGEEO0 GO TO 206 00 205 [ItLEDGE IFtNOT(GAEQEOGE(iI)ANOGDEQEDGEI2)))GO TO 205 GAP=EDGE(13) NEhGAP=FALSE GO TO 207
205 CONTINUE 206 CONTINUE
GAP=NGRD NGRD=NGRD+I LEDGE=LEDGE+I EOGE(LEDGE1)=GA EOGE(LEDGE2)=GD EDGE(LEDGE3)=GAP
207 DO 208 I=LEDGE IF(NOT(GBEQEOGE(11)ANDGCEQEDGE(I2|l)GO TO 208 GBP=EOGE(13) NEWGSP=FALSE GO TO 209
208 CONTINUE GBP=NGRD NGRO=NGRO I LEOGE=LEDGE+1 EDGE(LEDGE1 =GB
__ EDGECLEDGEt2)=GC
EDGE(LEDGEt3)=GBP 209 CONTINUE
NGCKJA)=GAP
235
NG(KJB)=GBP C C SEARCH ROD TABLE FOR RODS ALONG EDGES GA-GD OR GB-GC C IF FOUND CHANGE TO BE- GA-GAP-GD OR GB-GBP-GC C
IF(NCROLE0) GO TO 42 NCROX=NCRD------------- DO 40 [=INCROX IF(NOT(IDRD(13)EQGAANDIDRD(I4)EQGO))GO TO 24 IF(NOTNEIGAP) GO TO 40 IDRDCI3)=GAP GO TO32
24 IFINOT(IDRD(I4)EQGAANDIDRDI3)EQGD))GO T0_26 IF(N0TNEWGAP) GO TO 40 IORD(14)=GAP GO TO 32
26 IF(NOr(IORD(13)EQGBANDIDR(I41EQGCI)GO TO 28 IF(NOTNEWGBP) GO TO 40
--OIDRD(13)=GBP GO TO 30
28 IF(NOT(IDRD(14)EQGBANDIDRD(I31EQGC))GO TO 40 - IF(NOTNEGBPLGOIOSO
IDRDI4)=GBP 30 CONTINUE
JI=GB - -J2=GBP GO TO 34
32 JI=GA - J2=GAP
34 CONTINUE NCRO=NCRDOI IF(NCRDGTt000) STOP 98 IDRO(NCRDI)=IDEX IDEX=IDEXl IORD(NCRQ2)=IDRD(I2) IORD(NCRD3)=J1 IDRC(NCRD4)=J2
40 CCNTINUE 42 CONTINUE-
C C SEARCH BAR TABLE FOR BARS ALONG EDGES GA-GD OR GB-GC C IF FOUND CHANGE TO BE GA-GAP-GD OR GB-GBP-GC C
IF(NBARLEO)GO TO 75 REWIND 3 DO 70 I=INBAR
43 CONTINUE READ(37000) 3B WRITE(O7OO0a 5B(1) REAC(07030) K IF(KEQIPLS) GO TO 43
7000 FORMAT( IOAB ) IF(NOT(IBA(ILEQGAANDIBB(I)EOGD))GO TO 44 IF(NOTNEWGAP) GO TO 70 IBAiI =GAP
236
GOC TC 52 44 IF(NOTCIBB(l)EOGAANOIBA(t)EQGO)GO TO 46
IFLNOTNEWGAP) GO TO 70 [BB(I)=GAP GO TO 52
46 IF(UNOT(IBA(1)EQGBANDIBB(IIEQGCV-)GO TO 48 IF(NOTNEWGBP) GO TO70O IBACI )GBP GO TO 50
48 IF(NOT(IBB(I)EQGBANOIBA(I3EQGCI)GO TO 70 IFtNOTNEWGBP) GO TO 70 IBB( IIGBP
50 CONTINUE Ji=GB J2=GBP GO TO 54
52 JI=GA JZ=GAP
54 CONTINUE __ _
C OUTPUT NEh CBAR CARDC
WPtTE(97OO1)BB(1I)tDEXBfI3)j1J2taaJ)J=691 7C1 FCRMAT( A818tAS2184A8 I
IDEX=IDEX+1 70 CONTINUE 75 CONTINUE
C C SEARCH FOR RODS OR BARS ALONG EDGE GA-GB IF FOUND HALVE - --
C THE PROPERTIES AND ALSO PUT SAllE ALONG GAP-GOP C
IF(NCRULE) GO TO 740 DC 730 I=1NCRO IF(GAEQIDRD(I3)ANDGBEQIORD(It4)) GO TO 708 IF[NOT(GAEOIDRDU(4ANOGBEQIDRDOU3)) GO TO 730
708 J=IR(I2) IDRDII2)=IPEX DO 710 K=INPRO IF(JNEIXCK1J GO TO 710 JJ=K GO TO 712
710 CONTINUE 712 CCNTINUE
00 720 K=14 720 AXCK)=05PROP(JJK)
WRITEIT7004) IPEXICMJJ)(AX[K)K=13_ WRITE(97003) IUEXIPEXGAPGBP IDEX=IOEX+IPEX=IPEX+L ________ ________________
GO TO 740 730 CONTINUE 740 CCNTINUE
FINBARLE0) GO TOe-85 REWIND 3 00 780 I=INBAR
237
7A3 CONTINUE READ(37000) WW WRITE(O7000) WW(I) REAO(07030) K IF(KEQIPLS) GO TO 743 IF(GAEQIBA(I)ANDGBEQIBB(I1) GO TO 748 IF(NOTGAEQIBB(IANDGBEQIBA()]) GO TO 780
748 J=IPB(I)IPBI)=IPEX
-- RE IND __ D 750 K=1NP8RshyIF(IDY(K)NEJ) GO TO 750
__JJ=IPRECK_-_ GO TO 752
750 CONTINUE __ 752 IF(JJ LE 0I GO _T__758
DO 756 K=lJJ 756 REAO(47000) 8B 758 READ47000 _BB
REAO(4r7000) CC WRITE(O70O0) CCt(1
- - REAOO7030_K 7030 FORMATI Al )
IF(KNEKSTR) GO TO 762 C
C DOUBLE FIELD PROP CARDS C
WRITE(O7000) BB REAO17031) MID(AX(K)K=I2)
7031 FORMAT( 24X1162F16O) WRITE(O7000) CC REAO(O7032) (AX(K)tK35)
7032 FORMAT( 8X4F160) GO TO 766
762 CONTINUE C C SINGLE FIELD PROP CARD - C
WRITEO7000] BB REAO(O7033) MEO(AXK)K=L5) -
7033 FORVAT( 16XI85F8O) 766 CONTINUE
DO 767 K=15shy767 AX(K)=O5AX(K)
WRITE(970341 IDEXIPE XGAPGBPP(WWK)hK=69) -- 7034 FORMAT[ 8HCBAR _f418_4A8 )_ - _ -
WRITEC97035) IPEXMIDAX(I)AX(2)IPEXIPEX(AXIKIK=35) 7035 FORPATA 8HPBAR 21162EL68 3HPB 15 3HPB 15 3E168 )
IPEX =IPEX+I IOEX=IOEX-GO TC 785
780 CONTINUE 785 CONTINUE
C C GET MATERIAL PROPERTIES AND THICKNESS FOR CPLATE K
238
c J=IPID(KKK) NE=INC(KKK 00 80 [=1NPPLT IF(IDPP(IlNEJ) GO TO 80 1FfINP([)NENE) GO TO 80
GO TC 82 80 CONTINUE
STOP 97 82 CONTINUE
T=THICKCIP) -- J=IMID(IP
0D86 I=liNMAT1 IF(IOMAT(I)NEJ) GO TO 86 IM=I ir-ra 88
86 CONTINUE STOP 96
sect-88CONTINUE EE=E(IMP GG=G(IM)
C GET CCORDS OF GRIDS A AND 5 CALC DISTANCE BETWEEN - - CALL CdORb(GAGBGAamp800
XAB=XC(12)-XC(11) YAB=XC(22)-XC(21) ZAB=XC32)-XC(31) XLAB=SQRT(XAB2+YAB2+ZAB2) AAP=PLTPRM(KK3)XLAB IF(NOTNEWGAPJ GO TO 89
c
__ C CALC POSITION OF GRID GAP BETWEEN GRIDSA AND 0 C
CALL COOROIGAGDGAamp800) XX=XC(t2)-XCCIll YY XC(22)-XC(2t) ZZ=XC(32)-XC(31) XL=SQRTIXX2+YY2+ZZ2) XP=XC(1l)+AAPXXXL YP=XC2-I)+AAPYYXL ZP=XC131)+AAPZZXL
C C OUTPUT GRID GAP
C WRI TE97002 VGAPI NCPP YPZP
7002 FORMAT( BHGRID 218 3F83 2(TXIHO)) C C IF NORMAL O0F IS TO BE MPC-ED CALCULATE COORDINATES OFNORMAL C
lDMPCA=0 IF(NOTAPPCPA(KK)EQGA OR MPCPB(KKIEQGA)I GO TO 89 ANORMX=YYZAB-YABZZ ANORMY=ZZtXAB-ZABXX
239