NACA RESEARCH MEMORANDUM - NASA · PDF fileno rm l9t21a naca research memorandum experimental investigation of the effects of root restraint on the flutter of a sweptback, uniform,

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NACA

RESEARCH MEMORANDUM EXPERIMENTAL INVESTIGATION OF THE EFFECTS OF

ROOT RESTRAINT ON THE FLUTTER OF A SWEPTBACK,

UNIFORM, CANTILEVER WING WITH A VARIABLY

LOCATED CONCENTRATED MASS

By John E. Tomassoni and Herbert C. Nelson I Langley Aeronautical LabQp4tqry

M FILES Langley Air Force Base, Va. NAT

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NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

WASHINGTON March 31, 1950 I

https://ntrs.nasa.gov/search.jsp?R=19930086124 2018-05-23T19:21:33+00:00Z

NACA RM L9J21a

NATIONAL ADVISORY CONMITTEE FOR AERONAUTICS

RESEARCH MEMORANDUM

EXPERIMENTAL INVESTIGATION OF THE EFFECTS OF

ROOT RESTRAINT ON THE FLUTTER OF A SWEPTBACK,

Ifl1IFORM, CANTILEVER WING WITH A VARIABLY

LOCATED CONCENTRATED MASS

By John E. Tomassoni and. B:erbert C. Nelson

Data from 129 flutter tests conducted in the Langley 4.5--foot flutter research tunnel have been compiled and are reported. The investigation was carried out to obtain information which would test the validity of the assumption of root restraint used commonly in the flutter analyses of swept wings. This investigation was made with wings of 1450 and 600 angles of sweepback each having two different lengths. Each configuration included a'concentrated mass located at various spanwise positions and at two chordwise positions.

The data obtained provided results which indicate that the assump-tion of root restraint is fairly well Justified, at least for swept wings hating length—to—chord ratios of the order of 4 .5. However, none of the wings tested with the roots perpendicular to the leading edge showed exactly the same flutter trends over a range of spanwise weight positions as those obtained with the corresponding wing having the root parallel to the stream direction.

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The boundary conditions at the root of a sweptback wing make the problem of an exact structural analysis very complicated. In order to circumvent this difficulty, the following simplifying assumptions are sometimes made: that (i) the root is rigidly restrained normal to the elastic axis, and (2) the elastic axis is a straight line. With these assumptions and with the air forces, modified for sweep by the method of reference 1, a flutter analysis of a sweptback wing can be made.

2

NACA RM L9J21a

The purpose of this paper is to present experimental data on the flutter characteristics of weighted sweptback wings clamped, at the root to approximate the conditions of the previously mentioned. assump-tions. The models used in the investigation are similar to the swept models of reference 2 but are modified by root—stiffening plates and change of length. The lengths of the models were measured along the elastic axis which was located at the midchord.

By approximating the simplifying assumptions of theory in regard to root restraint and elastic axis, the data presented provide a means of evaluating the sufficiency of theory regarding structural representation and air—force evaluation.

w weight of wing section, pounds per inch

WW weight of concentrated weight, pounds

'1 length of midchord line, feet

b half chord of wing section measured perpendicular to the ntidchord line, feet

t thickness of wing section, inches

A sweep angle measured from an axis perpendicular to air stream in plane of wing to elastic axis, degrees, positive for sweepback

x distance from elastic axis to center of gravity of wing section, referred to half chord, positive rearward

ew distanbe from elastic axis of wing section to center of gravity of weight, referred to half chord, negative for forward weight location

ICG mass moment of inertia of wing section about its center

of gravity, inch—pound--second2 per inch

I mass moment of inertia of wing section about its elastic

axis, inch—pound—second2 per inch

NACA RM L9J21a 3

IW mass moment of inertia of weight about its center of

gravity, inch-pound--second.2

El bending rigidity of wing section, pound-inch2

(]J torsional rigidity of wing section, pound-inch2

rn mass of wing per unit length, slugs per foot

r. nandimensional radius of gyration of wing section

CEA about its elastic axis I

1

qf dynamic pressure at flutter, pounds per square foot

P air density at flutter, pounds per square foot

Vf stream velocity at flutter, feet per second

wing mass-density ratio at flutter ',t b

gh, g structural damping coefficient in bending and torsional degree of freedom, respectively

APPARATUS

The experimental results presented herein have been obtained in the Langley 4.5-foot flutter research tunnel with air used as the testing medium under atmospheric conditions. In this investigation models B-1 and 3-2 were the same as model B of reference 2 except as modified by the root stiffening plates and change of length. Models C-i and 0-2 were-of as nearly the same dimensions as model C of reference 2 as manufactured 0.090-inch aluminum sheet stock would permit and were

14. NkCA PM L9J21a

also modified by root stiffening plates and change of length. The

accompanying sketch shows how the Inch—thick root stiffening plates

were attached to the models.

tunnel wall

.root stiffening plate

midchord and

elastic axis L)-root torsion gage - -root bending gage 3-tip torsion gage - -tip bending gage

Small changes in the wing length were included to determine if a single effective length could be found which would give the seine flutter speeds as the corresponding model of reference 2. The following table lists the models with their respective lengths and sweep angles:

NACA EM L9J21a 5

Model2

(ft)A

(deg)

B (reference 2) 3.00 1 B-i 2.75 45 B-2 2.83 j

C (reference 2) 3.00 1 C-i 2.75 60 0-2 3.00 J

The section properties of the wings are as follows:

Chord, 2b, feet ....................... 0.667 Airfoil section ......... Flat plate

nondimensional ...... 0.01 (approx.)

nondimensional . ............. 0.005 (approx.) t, inches ......................... . 0.090 W, pounds per inch ...... . . . . 0.076 'CG' inch-pound--eecond2 per inch ..............0.000995

I, inch-pound--second2 per inch .............. 0.000995

El, pound-inch2 ...................o.005o6 x 106 GJ, pound-inch2 ...................o.008 x 106 ICcL, nond.imension.a.].. ............... 0.0

r,2, nondimension.a.]_ ........ . ......... . 0.3314

i/ic, (standard air density, no concentrated weight) . . . 314.1

Two weights which were essentially the seine were used in the tests. One was attached at various positions along the leading edge and the other along the inidchord line of each model. The weight properties are:

Item Leading-edge weight

Midchord weight

Ww, lb 3.12 3.12

.ew -1.0 0

I., in.-m--eec2 0.010 0.0098

6 NACA PM L9J21a

Strain gages cemented on the wings used in conjunction with a recording osciUo'aph provided a means for obtaining the frequencies and phase relationships of the torsional and bending strains at the gage locations. The positions at which the strain gages were attached to the models are shown in the preceding sketch. The gage traces on each of the oscilloaph records in figure 1 are numbered from left to right and represent the response of the root-torsion, root-bending, tip-torsion, and tip-bending gages, respectively. The fifth trace on the records is an imposed calibration frequency. The apparatus section of reference 2 gives a complete description of the method used to obtain the phase angles listed in table I.

The attenuation marked on each gage trace is a scale number obtained by electrical multiplication where the value of the attenua-tion is inversely proportional to the magnification of response. The amplitudes of the traces combine with the attenuation to give relative stresses, torques, or moments. These relative values are obtained in the following manner, the first two traces of a record being used as an example:

Stress (1) - (Attenuation (l)'1(Anrplitude (i) Stress (2) \Attenuation (2)JAmplitude (2)

TEST PROCB2JURE

An investigation at zero airspeed was conducted before each series of tests to obtain the first three natural frequencies for each span-wise weight position. Several spanwise positions of the concentrated weight for a constant chordwise station constituted a series for one model. During each test the airspeed in the tunnel was increased slowly. At the critical flutter speed the tunnel conditions were observed, and an osciflograph record of the model vibrations was taken. The tunnel airspeed was then reduced iniediately after the critical flutter speed was attained in order to prevent the model from being destroyed. The models were tested initially without any weight and each of the series of tests was accomplished by moving the weight progressively spanwise to the tip. After a series of tests was com-pleted the model was retested without the weight to provide knowledge of any possible damage which may have occurred. No difference was fouid to exist.

NACA RM L9J21a 7

PRESENTATION AND DISCUSSION OF RESULTS

This paper presents the experimental data obtained from flutter testing 450 and 600 sweptback wings with the roots modified by stiffening plates. In all plots the test results are presented as functions of the wing length 2.

The experimental results are compiled in table I. The dynamic pressure, flutter speed, Mach number, and the first three natural fre-quencies for each weight position and the corresponding flutter fre-quencies are listed. Also the phase relationships of the torsional and bending stresses at the gage locations for the second and third natural and flutter frequencies are given. The Reynolds number for each series of tests is given and the chord length used in its deter-mination was the length parallel to the air stream. A sketch of each model tested is included in table I with its corresponding data.

The oscillograph records taken at flutter for the various cases tested are shown in figure 1. The four traces on the records in the top row only, which represent the vibratory motions of the model, are numbered, but these numbers pertain in the same order to all records. Each is marked with its appropriate attenuation. The unusual type of flutter involving two frequencies simultaneously, as reported in reference 2, also occurred in a few cases during the present tests.

The flutter data of figure 2 show the validity of the commonly used assumptions regarding root restraint for the models tested. In general, -the differences between the data from a given unmodified wing and that from the corresponding wing having a modified root are small, indicating that the assumptions are fairly well justified.

The differences in the flutter speed when the concentrated weight was on the wing leading edge were small. This indicates that as the length of the wing with the modified root was increased (B—i to B-2 or C—i to 0-2) the flutter speed approached that of the unmodified wing (B or C, respectively) for the range of spanwise weight loca-tions 0 to 11-5 percent 1. From the 65 to about 100 percent spanwise weight range an opposite trend is noted. In the range from 45 to 65 per-cent 1 an irregular variation exists.

The data for the weight at the midchord line indicate that as the length of the wing was increased the flutter speed approached that of the unmodified wing over both the 0 to 45 percent and the 65 to 100 per-- cent spa.nwise weight ranges while the range from 45 to 65 percent was irregular.

8

NACA RM L9J21a

In figure 3 the first three natural and the flutter frequencies are plotted against spanwise weight position for each of the series of tests. These plots show the relation between the flutter frequency and the first three natural frequencies for each of the configurations tested.

CONCLUDING REMARKS

The structural assumptions usually made in the flutter analysis of swept wings, that the root is rigidly restrained and the elastic axis is a straight line at least for the uniform type of wing tested, appear to be fairly well Justified. Exceptions are noted for critical ranges of concentrated weight positions where small changes in the position of the weight produce relatively large changes in the experi-mentally determined flutter speed.

Langley Aeronautical Laboratory National Advisory Committee for Aeronautics

Langley Air Force Base, Va.

1. Barmby, J. G., Cunningham, H. J., and Garrick, I. E.: Investi-gation of the Effects of Sweep on the Flutter of Cantilever Wings. NACA PM L81130, 198.

2. Nelson, Herbert C., and Tomassoni, John E.: Experimental Investi-gation of the Effects of Sweepback on the Flutter of a Uniform Cantilever Wing with a Variably Located Concentrated Mass. NACA PM L9P2, 1949.

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0 0 CU0 In In H H H H -4 H CU CU In In .* - In CU H H H -1

oo c od o dd6d

- InIAOHCUInCOInNNOO'.0)CU'.0\OCU(0 4-. P. 4- 4-. N C) IA 0 H 0'. CU 0) CO N CU

0.4 CU N '1) '.0

.4 CU

N 0

.4 0'. CI) .4 In .4 0'. N In .4 '.0 In 0 IA CU CU -1 H H CU CU In In .4 IA .4 In CU H -1 H H N H

CUCU

IA '0

IA N

'.0 0

CI) IA

0'. 0 0 CU 0'. N

0 CO

0 IA

0 CO

0 N

'0

10

(0 '.0

H '.0

.4 CU

0 0

IA In In UI H

- - .9 CI) CU .4-4 -1 0'. -1 '.0 CU

IA CU

In H

'.0 In CU CU CU

00 0

H

4-

ID 0

H -

Fol 0

4I

V

16 NACA RM L9J21a

o o 0 - 0 0 ø N —

fl -i;-- H -;- Cu

-s- H0 -s- -- 0 ,-4 cu Cu H

- C\l Cu

N m 0 ol 0i0 cu 10 H H H C •'

A ___ Cu Cu Cu Cu Cu Cu - —

A Tf 0+1

MC . 0 0 0 0 0 0 0 0 0 0 0 o -o

--

cu

---

NO

Cq

H ri H H H H H -

H - - -

C C -

0 IC\- 0 Cu H N 0 Q O H * IA 0

Cu 0 N

C DI ,1

II H cu H CU 0 CU 0' H O\ H QD H N H H N H C— H '0 H '0 H '0H 10 H

' °

04 R

cu cu cli cu cu m cu cli cu cu

I

cu

_E!_l 1 _______

0

o

H o

S

PIV 0

• ffI

Js 41 1/

18 NACA RM L9J21a

I!1IllhiIIiIINIIIPIIII 111111 EIODINE 1101,1111111 1111111 k III1IPJ1IIIGI

!!!1ll' IIp!qR

'IIO'O I! k

(b) Model B-1; A = 45° e = Puns /9-33.

Figure 1.— Continued.

50 130 20 20 - : : 50 3C

•1

20 NACA RM L9J21a

2 34 1 ? 3 4 50 50 20 20 : : r 50 50 20 20 : : 50 50 X 30 :

r

30 30

1. 20 20 I I 505O 30 : : 50 30 20 20

55

•1I-I 1 11111

( Model B-2 A45 eO Puns 52-66.


S 0 S 'S

4 I I!'

Lll

ill

21

/ 2 50 50

50 50

72

3030

30 30

30 30

34

NACA EM L9J21a

S

I

S

I5

4'0

r1 p Ibid

IRi

IOU, I

30 30 30 30 30 50 '30 30

76 ( '77

20 130 20 20 20130-, I 2020

J-,

791/ H a0

50 50 30 30 30 30 2020

L 82H!( IHHHiI liHi H 83 11W IHV!

(e) Mod/ C-I; A = 60*i 0., = - 1 Pur,s 67-83.


22

NACA EM L9J21a

1 2 3 4 1 2 34 1 2 34 50'f30 3030' 30 30 0 ; 0 30 30 2020

84 8"5 'fli 1 11 11

IftiIII1AII130 3020 1 20 30 3020 2011 30 I 30 20 20

0 IN 1 11

50 30 20 20 - 50 30 2020 5O 30 301 III

193 94

50 30 30 50 : :50 3030 50 II III (1) Model C1; A 60 eO

Runs- 8497.


/ 2 34

il

20 20

114

1)1

NACA RM L9J21a

23

/ 2 34

20 20 20 20

11311 p Hi

1llil 1fl1 fll V

20 t20 20

20 20 20

H

H I

1/2

115NA (9) Model C2; A = 60 0: e, = Puns 98-1/5.


2

NACA RN L9J21a

I1111'III 30 30 30 30 : : 30 30 30. 30 :

[L120 I

30 30 120 20 : 30 20 20- :

.fl30

I 30- 30 20 -20 50t 30 30 - 30 - - -30 30 30

L• /•

30 30 30 50- 30 '30 20 20 -

(h Model C-2,- A 600,- e = 0; Puns 116129.

Figure 1.— Concluded.

I .<

i

II

' \\

\

\ \

Ii

II

Model

B (reference 2) 3.00 -€

----- B-1 2.75

-------B-2 2.83

-10 0 10 20 30 40 50 60 70 80 90 100

Distance of weight from root, percent £

520

490

400

360

, 320

- 280

-4 0 0 -4

20

'a

200

160

120

80

40

0 -20

NACA RM L9J21a 25

(a) A=14.5°, e=—l.

Figure 2.— Variation of the flutter speeds with weight position for each of the models tested.

26

NACA RN L9J21a

320

280

214.0

200 4.4

43 • 160 0 H

4-3 120 4) H r.

80

LLO

IL.!

-0--)---*-.. -'- ---- ,.

- —<s,— - - -ø -0-- - 0-

Model 7,

-O -------B (reference 2) 3.00 2.75

--0--B-2 2.83

10 20 - 30 40 50 60 70 80

Distance of weight from root, percent 1

90 100

(b) A 1f5°, e=O.


NACA RN L9J21a 21

600

560

520

zgo

400

320 > .4 C, 0

280 C.

c.. 2

200

160

120

80

40

0 -20

m 360

'(L \\ 1iI \\

-4 y

/ I \ \

I \

"I .1, \ - —&

- --1j___".( I \ S

/

I-

Model -o-----C (reference 2) 5.00

2.75 --0--C-2 3.00

-10 0 10 20 30 ko 50 60 70 80 90 100


(c) A = 6°, e = —1.


10 20 30 40 50 60 70


Ioo

280

320

go

00

•r

—0----

Model 1. --------o------C (reference 2) 3.00 -

C-1 2.75 --G--C-2 5.00

—go 90 100

240

200 '-I 0 0 -4 0

0

-4

160

120

28

NACA RM L9J21a

(d) A=60°, e=O.

Figure 2.— Concluded.

NACA RM L9J21a 29

14.0

36

32

16

12

—0--Natural frequency --a-Flutter frequency

I rd

-- ----

fl\0-

at

-----. -

00.

10 20 30 40 50 60 70 so 90 100


28

0

a 24

0 0

20

(a) Model B—i, A 4.50 , ew = —1.

Figure 3.- Variation of the first three natural frequencies and flutter frequency with weight position.

30

NACA P.M L9J21a

—e-Natural frequency --a-Flutter frequency

—o---.-

-----

----0

. -

10 20 30 kO 50 60 70 so 90 100


(b) Model B—i, A = 450, e = 0.

Figure 3.- 3.- ContInued.

32

2

2

20

0

o 16

a.

12

8

NACA RN L9J21a 31

—0--Natural frequency --fl--Flutter frequency

rd

0

------ N -- ---

—0---0--

-0— 0—

IV 4U JU fU U bu (06 0 90 100


(c) Model B-2, A = 450, e = —1.

FIgure 3.- Continued.

11-g

mo

36

32

28 m P. U

U 0

Sk U

20

16

12

00

32

2

2

20

16 w 0. 0

0 c 12 0 CS 0 0

ri..

32

NACA RM L9J21a

-e--Natural frequency --a-Flutter frequency

3rd

a--

nd -a-- ----o.--E .

—0-- -O

18t

0- >---

10 20 30 40 50 60 70 SO 90 100


(d) Model B-2, A = 45 0 , ew = 0.

Figure 3.- Continued.

00

NACA RN L9J21a 33

-0-Natural frequency I ---F1utter frequency

rd

—0---.

- —0-- —O-- - B - - -

—a-- —0---—o-- .

Lu eu 50 40 50 60 70 80 90 100

Distance of weight from root, percent

(e) Model C—i, A = 600, ew


60

56

52

36

o 32

0

I, r..

24

20

16

12

00

314 NACA RN L9J21a

ri

28

2

32

20

11-

00

3rd

-0-Natural frequency --0--Flutter frequency

- t- -- -

/•

- 1et

_0—

-

10 20 30 40 50 60 70 80 90 100


(r) Model C—i, A = 600, ey = 0.

Figure 3.— 3.— Continued..

16

A U

0 12

0•

r.8

NACA RM L9J21a 35

—0--Natural frequency --El--Flutter frequency

rd

N 2nd --- o-_

lot-

-0-----, —0---. - - - 130 50 60 70 80 90 100


(g) Model C-2, A = 600, e = —1.


56

52

11.8

11.0

36

32 0. 0

>. 0

0)

0• a)

24

20

16

12

8

00

10 20 30 ko 50 60 70 do 90 100

32

2

24

g

00

—0— Natural frequency --n--Flutter frequency

-3rd

-- _1-_ —e-

T ------- 2nd -0- -

N

-- --

U--.

lot N̂ACA

20

p. C)

36

NACA RM L9J21a


(h) Model C-2, A =600, e = 0.

Figure 3.- Concluded.

NACA-Langley - 2-10-54 -75

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NACA RESEARCH MEMORANDUM - NASA · PDF fileno rm l9t21a naca research memorandum experimental investigation of the effects of root restraint on the flutter of a sweptback, uniform,