Prediction of the Vibration Levels Generated by Pyrotechnic Shocks Using an Approach by Equivalent Mechanical Shock

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David Wattiauxe-mail: [email protected]

Olivier Verlindene-mail: [email protected]

Calogero Contie-mail: [email protected]

Faculté Polytechnique de Mons,31 Boulevard Dolez,

7000 Mons, Belgium

Christophe De FruytierThales Alenia Space ETCA,

101 Rue Chapelle Beaussart,6032 Mont-sur-Marchienne, Belgium

il: [email protected]

Prediction of the Vibration LevelsGenerated by Pyrotechnic ShocksUsing an Approach by EquivalentMechanical ShockThis paper is concerned with the numerical simulation of mechanical structures subjectedto pyroshocks. In practice, the methodology is applied on the pyroshock test facility,which is used by Thales to qualify the electronic equipment intended to be embarkedonboard of spatial vehicles. This test facility involves one plate or two plates linked byscrew bolts. The tested device is mounted on one side while the explosive charge isapplied on the other side. The main issue of this work is to be able to tune, by simulation,the parameters of the facility (number of plates, material of plate, number of bolts,amount of explosive, etc.) so as to get the required level of solicitation during the test.The paper begins by an introduction presenting the state of the art in terms of pyroshockmodeling, followed by a description of the shock response spectrum (SRS) commonlyused to represent the test specifications of an embarked equipment. It turns out that thereis a lack of computational techniques able to predict the dynamic behavior of complexstructures subjected to high frequency shock waves such as explosive loads. Three sec-tions are then devoted to the simulation of the pyrotechnic test, which involves on onehand a model of the structure and on the other hand an appropriate representation of theimpulsive load. The finite element method (FEM) is used to model the dynamic behaviorof the structure. The FEM models of several instances of the facility have been updatedand validated up to 1000 Hz by comparison with the results of experimental modalanalyses. For the excitation source, we have considered an approach by equivalent me-chanical shock (EMS), which consists in replacing the actual excitation by a localizedforce applied on the FEM model at the center of the explosive device. The main origi-nality of the approach is to identify the amplitude and duration of the EMS by minimizingthe gap between the experimental and numerical results in terms of the SRS related toseveral points of the facility. The identification has been performed on a simple platestructure for different amounts of explosive. The methodology is then validated in threeways. Firstly, it is shown that there is a good agreement between experimental andnumerical SRS for all the points considered to identify the EMS. Secondly, it appears thatthe energy injected by the EMS is well correlated with the amount of explosive. Lastly, theEMS identified on one structure for a given amount of explosive leads to coherent re-sponses when applied on other structures. A parametric study is finally performed, whichshows the influence of the thickness of the plate, the material properties, the localizationof the EMS, and the addition of a local mass. The different obtained results show that ourpyroshock model allows to efficiently estimate the acceleration levels undergone by theelectronic equipment during a pyroshock and, in this way, to predict some eventualelectrical failures, such as the chatter of electromagnetic relays.�DOI: 10.1115/1.2827985�

Keywords: pyroshock, equivalent mechanical shock, shock response spectrum

IntroductionNowadays, the space industry uses more and more pyrotechnic

evices, such as pyrotechnic valves �Fig. 1� or mild detonatinguses �Fig. 2�, to carry out various operations such as separation oftructural elements �booster separation, etc.�, unlocking mecha-isms �unfolding solar panels, etc.�, or activation of onboard op-rating subsystems �Table 1�. The shock wave generated by thelast of these pyrotechnic devices produces severe vibrations in-ide the space shuttles. For several years, the effects of theseyrotechnic shocks �so-called pyroshock� have not been taken into

Contributed by the Technical Committee on Vibration and Sound of ASME forublication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received May 22,007; final manuscript received November 27, 2007; published online July 14, 2008.
eview conducted by Sotirios Natsiavas.
ournal of Vibration and Acoustics Copyright © 20

ded 23 Mar 2011 to 210.117.158.180. Redistribution subject to ASM

account because the manufacturers of electronic equipmentthought that the duration of the explosion was too short to damagethe onboard electronic devices. However, Moening �1� has shownthat many observed breakdowns on the American launchers werecaused by the pyroshocks.

At present time, the pyroshock resistance of the electronicequipment is mainly checked experimentally because of the diffi-culties to approach the problem with computational techniques,especially concerning the modeling of pyrotechnic excitation. Inpractice, simplified resonant fixtures, such as beam or plate as-semblies, are used to reproduce a vibratory environment equiva-lent to the actual one.

A new test campaign always begins by the choice of an ad-equate test facility. A trial-and-error process is applied on the test
assembly, loaded with a dummy of equipment, so as to satisfy the
AUGUST 2008, Vol. 130 / 041012-108 by ASME

E license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

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est specifications of the launcher. When the desired vibratory en-ironment is achieved, the nominal test is performed on the realquipment. Obviously, such a procedure is rather inefficient andxpensive. Consequently, it is useful to develop a mathematicalodel of the test facility to predict the vibration levels generated

y pyroshocks.

Overview of the State of the ArtThe numerical prediction of the vibration levels generated by

yroshocks requires an accurate dynamic model of the test facilitys well as a mathematical description of the excitation sources.

2.1 Modeling of the Structure. For simple configurations ofhe test facility, as for example an assembly of plates or beams,everal authors, such as Hampton et al. �3� and Sad �4�, suggestiscretized quasianalytical models, derived from a continuousnalytical model �Euler–Bernoulli theory�. Unfortunately, theseodels are not easy to implement, particularly for more complex

tructures.The finite element method �FEM� and the boundary elementethod �BEM� are the most conventional predictive tools and areidely used in low frequency range to predict the dynamic behav-

ig. 1 Pyrotechnic valve „left view: before activation-rightiew: after activation…

Fig. 2 Mild detonating fuses „MDFs…

Table 1 Pyrotechnic applications in astronautics †2‡

rogramNumber of installedpyrotechnic devices

ercury 46emini 139aturn �150pollo �CSM/SLA/LM� 314pollo �CSM/SLA� for Skylab 249

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ior of complex structures. FEM and BEM are deterministic meth-ods for which all parameters of the structure must be known ac-curately. FEM and BEM have good performances in the lowfrequency range. However, these deterministic methods havesome deficiencies at higher frequencies. As the wavelength de-creases with the frequency, the number of elements has to beincreased in the same way. This makes these methods, at highfrequencies, costly in memory resources, modeling work, andpostprocessing time.

At present time, the statistical energy analysis �SEA� is themost widely used theoretical framework for the analysis of thedynamic response of complex systems in high frequency range�5,6�. In the SEA method, the structure is modeled as an assem-blage of discrete subsystems that receive, dissipate, and transfervibrational energy. The SEA approach is based on two basic hy-potheses: the internal dissipation in a subsystem is proportional tothe subsystem energy and the energy flow between subsystems isproportional to the difference in modal energy. The main advan-tage of SEA is the small size of the model, which is not related tothe excited wavelengths, but only to the number of subsystems;consequently, the solution of a SEA model can be done at highfrequencies with a low computational cost. However, the majordrawback of SEA is the difficulty in establishing an appropriatemodel and particularly the choice of subsystems and the evalua-tion of the input parameters �coupling loss factors, internal lossfactors, modal densities, power inputs�, which are not directlyrelated to the physical properties that are commonly used in prac-tice. Another major drawback of SEA is the loss of information onthe spatial distribution of the vibrational energy inside each sub-system. Finally, the SEA method does not provide the time historyof the acceleration.

Several alternative methods to SEA have been developed inorder to try to overcome its limitations. Bodin �7� and Brevart �8�present a prediction method of the response of an electronicequipment assembly submitted to high frequency shocks. Hismethod combines the use of deterministic calculations and SEA.The FEM provides the low frequency content of the accelerationand SEA, coupled to a local random phase reconstruction concept,provides the high frequency content. This approach is similar tothe one followed by Dalton �9,10� but based on a distinct phasesynthesis. Dalton’s method uses a virtual mode synthesis �VMS�method, which assumes that the modes are distributed over fre-quency according to the modal density estimation and that thesemodes collectively produce the frequency response envelope ineach frequency band. The virtual mode residues are obtained bycomparing the Frequency Response Function �FRF� magnitude ofthe virtual system with the one obtained by SEA.

Because of the difficulty to verify the underlying hypothesesand to give a physical interpretation of the parameters of SEA andVMS models, we have decided, in this work, to only consider thedeterministic methods to describe the dynamic behavior of thepyroshock test facility.

2.2 Modeling of the Excitation Sources. The dynamic simu-lation of mechanical structures requires an accurate knowledge ofthe excitation forces. In the case of pyroshocks, these forces areunknown because they cannot be directly measured. Therefore, itis essential to have access to the applied forces. The most wide-spread identification procedures are the inverse methods, such asthe regularization methods which can be applied in the time andfrequency domains �11�. These methods allow in theory to iden-tify the unknown excitation forces from transient response mea-surements as far as a dynamic model of the structure is available.The drawback of inverse methods is their great sensitivity to mea-surement noise, which can produce an important drift of the iden-tified forces. Different drift reduction techniques, which consist inimposing constraints on the force profile, can be found in Ref.
�11�. Nevertheless, the application of these identification tech-
Transactions of the ASME


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iques to pyroshocks does not lead to accurate results; the differ-nce between experiment and simulation being greater than theolerances is generally admitted by the equipment manufacturers12�.

The investigations of Brossard et al. �13� and Dharaneepathy etl. �14� on the effects of air blast on shell structures, such asoncrete plates or cooling towers, show that the pressure waveoad can be described by a sine-exponential model depending onwo parameters: the angle of the incident shock � and the reducedarameter �, which represents the ratio between the radial dis-ance R from the center of the explosion and the cube root of thehemical energy E. Their model has, unlike the inverse methods,he advantage to take into account the propagation of the pressureave along the structure. However, the model is exclusively us-

ble for reduced parameters � between 0.35 and 12, which lead,or typical pyrotechnic explosives �penthrite�, to distances from.07 m to 2 m between the explosive and the structure. Com-only, this condition is not verified during pyrotechnic campaigns

iven that the explosive device is fixed straight on the test facility.In this paper, we suggest an identification procedure of the py-

otechnic excitation using an approach by equivalent mechanicalhock EMS. The EMS method replaces the actual excitation by aocalized force applied on the FE model at the center of the ex-losive device. The amplitude and duration of the force are tunedo as to generate equivalent acceleration fields. It is not unreason-ble to envisage such a method given that several investigations2,15–17� have shown that the use of metal-metal impact devices,uch as dropping mass, air gun or pneumatic actuator, allows toeproduce experimentally the acceleration levels of the far-fieldyroshocks �distance between the pyrotechnic device and thequipment higher than 15 cm�.

Fig. 3 Single degree of freedom system

Fig. 5 Examples of typical pyro
Space ETCA…
ournal of Vibration and Acoustics


3 Test Specifications

3.1 Shock Response Spectrum. The pyroshock specifica-tions are generally expressed in terms of the shock response spec-trum �SRS�. The principle of the SRS consists in replacing the realstructure by an array of independent single degree of freedomsystems and to calculate the maximum response of each resonatorwhen its foundation is animated by a motion corresponding to theshock time history �18,19�. The motion of each single DOF sys-tem �Fig. 3� is characterized by the following classical differentialequation:

� + 2��0� + �02� = − y �1�

where ��t�=x�t�−y�t� represents the relative displacement, �0

=�k /m the natural pulsation, and �=c /2m�0 the damping ratio,which is generally fixed to 5% for pyroshock specifications �2,20�.

The SRS is the plot of the absolute maximum of the relativedisplacement ��t�, denoted by Sd, in relation to the natural fre-quency f0=�0 /2�.

The pseudoacceleration spectrum Spa is generally used �21� todefine pyroshock specifications. The pseudoacceleration spectrumSpa is obtained by multiplying the displacement response spectrumSd by �0

2:

Spa = �02Sd �2�

The pseudoacceleration Spa has the units of acceleration but itdoes not represent the absolute acceleration of the mass m, exceptfor a zero damping coefficient.

Fig. 4 Examples of SRS specifications

ck test facilities „Thales Alenia
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3.2 Examples of Test Specifications. Equipment specifica-ions are commonly expressed in terms of acceleration SRS speci-ed from a low frequency limit of a few hundreds of hertz to aigh frequency limit of 10 kHz �Fig. 4�; sometimes, this superiorimit can reach 25 kHz. The acceleration levels are generally de-ned in the three orthogonal directions and can vary widely fromne specification to another one. Figure 4 shows some examplesf SRS specifications for the direction perpendicular to the equip-ent mating plane. Vibration levels are often more difficult to

chieve for in-plane directions. Nevertheless, a small difference isenerally admitted between observed and required SRS. A typicalxample of tolerance is given in Ref. �21�:

• �6 dB for natural frequencies �3000 Hz• +9 dB /−6 dB for natural frequencies 3000 Hz

Thales Alenia Space ETCA sometimes considers a toleranceand of �3 dB about a straight-line approximation of the SRSpecifications.

Thales Alenia Space ETCA Pyroshock Test Facility

4.1 Test Facility Description. The pyroshock test facilitiessed by Thales Alenia Space ETCA �Charleroi-Belgium� are reso-ant fixtures, which can be excited either by an explosive charger by a mechanical impact �dropping mass, sledgehammer, airun, or pneumatic actuator� �2,20�. The resonant fixtures are madef steel or aluminum plates supported by a tubular structure withteel cables. Different configurations can be considered: simplelate or double plate linked by screw bolts either in vertical or inorizontal orientation. The tested item is screwed on the test fa-ility and is submitted to the shock wave generated by the exci-ation and to the response of the fixture. Figures 5�a� and 5�b�how two classical configurations of the test facility used by Tha-es Alenia Space ETCA.

Among the parameters influencing the SRS, the most importantnes are the following:

• the configuration of the test facility �number of plates andtheir orientation in space�

• material, area, and thickness of the plates• the intensity of the shock• the location of the shock device

Fig. 6 View of the pyrotechnic device

Fig. 7 Arrangement of explosive device for

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4.2 Shock Devices. The excitation of the test facilities can becarried out by a mechanical impact or an explosive charge. In thecase of mechanical shock, the impact device is a pneumatic ac-tuator, which is screwed on the test fixture �Fig. 5�b��.

In the case of pyrotechnic shock, the excitation is generated byan explosive device composed of a nonelectrical �NONEL� deto-nator and a detonating cord �12 g /m penthrite� assembled on athin rectangular aluminum plate with the help of adhesive tip �Fig.6�. The detonating cord length can vary from 0 to 1 m dependingon the desired excitation level. A zero detonating cord length cor-responds to the single detonator. Figure 7 illustrates the arrange-ment of the explosive device for different lengths of the cord.NONEL detonators are used for safety issues but also becausethey generate less electromagnetic pulse than electrical detonators.This is especially important when operating electronic units aretested.

4.3 Reference Experimental Data. The test fixture is asquare steel plate �110.015 m3�, which is vertically sus-pended to a tubular structure with steel cables �Fig. 8�. The explo-sive charge is fixed on the center of the plate by means of adhe-sive tip. We have considered lengths of the detonating cordvarying from 0 cm to 50 cm. The accelerations are measured withpiezoelectric sensors, which are directly screwed on the steelplate. Their location is given in Fig. 9. The signals of the accel-erometers are finally filtered by a low pass electronic filter with acutoff frequency of 10 kHz.

Figure 10 gives a summary of the main experimental observa-tions.

• The energy of a pyroshock is mainly injected perpendicu-larly to the plate �Fig. 10�a��.

• The maximum amplitude of the SRS increases with thelength of the detonating cord �Fig. 10�b��.

• Acceleration levels weakly vary with the location of thesensor �Fig. 10�c��.

• The repeatability between two pyroshocks, which are real-ized in the same conditions, is satisfactory; the mean differ-ence between the two SRS is below 2 dB �Fig. 10�d��.

Fig. 8 Experimental setup and location of the explosive device

different lengths of the detonating cord



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Finite Element Model

5.1 Description. The model of the test facility has been builtnder a classical FE software �ANSYS 8.1� and has been validatednd updated from an experimental modal analysis. 3D structuralolid elements �SOLID45� have been used for the plate. The ele-ent size is a significant parameter in the simulation and is cho-

en according to the analyzed frequency range. As the SRS speci-cations are generally defined in the range �0–10 kHz�, the FEMhould be able to describe the dynamic behavior of the plate in

ig. 9 Location of the explosive device and piezoelectric sen-ors „circles…

Fig. 10 Main experim



this same range.It is recommended to define an element size that is lower than

the smallest bending wavelength. In an infinite uniform plate, thewavelength � of the bending waves is given by �22�

� =�2�

f� D

Ms�1/4

�3�

D =Eh3

12�1 − �2��4�

where Ms is the surface mass density, E Young’s modulus, � Pois-son’s coefficient, h the plate thickness, and f the frequency of thebending wave. Table 2 gives the geometric and physical charac-teristics of the studied plate. The bending wavelength � corre-sponding to a frequency of 10 kHz is equal to 0.121 m.

In the plane of the plate, a 5656 element grid has been de-

Table 2 Physical characteristics of the plate

Steel plate

E 2.02E11 N /m2

� 7800 kg /m3

M 117 kg� 0.3h 0.015 mf 10 kHz� 0.121 m

ental observations

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ned in order to respect a number of six elements per wavelengthp to a bending wave of 10 kHz. We have defined three elementsn the direction of the thickness of the plate.

5.2 Model Validation. A model validation has been realizedy comparing the modal properties of the test facility deducedrom the model and those experimentally identified from mea-ured frequency response functions. The frequency response func-ions Hij�� have been measured in the direction perpendicular tohe plate, with the help of an impact hammer, and in the frequencyange �0–1000 Hz� with a frequency resolution of 0.625 Hz. Theodal characteristics have been identified with EasyMod, which

s a MATLAB toolbox of modal analysis developed by the Depart-ent of Theoretical Mechanics of the Facult Polytechnique deons �23�. The Least Square Complex Exponential �LSCE� �24�ethod has been used to identify the resonant frequencies fk,

amping factors �k, and modal vectors �k.The finite element model was updated from the experimental

esults by minimizing the relative difference between natural fre-uencies calculated as follows �24�:

k =�fk

E − fkS�

fkS �5�

here the superscripts E and S are used for experimental andodel data, respectively.The experimental and numerical mode shapes are matched from

he modal assurance criterion �MAC� defined by �24�

MACk =��k

ET�kS�2

��kET�k

E��kST�k

S��6�

here �E and �S denote the experimental and simulatedodal vectors, respectively.Table 3 summarizes the first 15 experimental and analyticalodes, correlated with a MAC value greater than 0.6 and a rela-

ive frequency gap lower than 10%. These results allow to validatehe FE model up to 1000 Hz. Mode shapes at higher frequenciesre much more difficult to identify due to the high modal density.evertheless, we have assumed that it can be extrapolated atigher frequencies �until 10 kHz�.

Equivalent Mechanical Shock

6.1 Definition. The computations of the pyroshock responseequire a dynamic model of the test facility and a mathematicalescription of the excitation sources. The latter is the main diffi-ulty in the modeling because it cannot be properly measured.

able 3 Correspondence between experimental and numericalodal characteristics

fE �Hz� fS �Hz� k �%� MAC

47 49 3.4 0.9892 89 3.7 0.85124 127 2.5 0.69231 224 2.4 0.88282 282 0.6 0.98457 445 2.6 0.83488 477 2.2 0.77493 498 1.2 0.84564 560 0.73 0.98622 635 2.1 0.80738 730 1.0 0.64790 771 2.5 0.85796 803 0.9 0.73897 919 2.4 0.68898 899 0.1 0.66

oreover, a lot of complex physical phenomena can appear dur-

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ing the pyroshock as, for example, the interaction between theshock wave, generated by the explosion, and the geometry of theroom, which controls the numerous reflection waves.

The EMS corresponds to the mechanical force that has to beapplied to the FE model to obtain equivalent acceleration levels.In our case, the force is applied on the node corresponding to thecenter of the explosive charge. Although the pyroshock is a three-dimensional excitation source, we have considered an EMS actingonly in the direction perpendicular to the plate because the energyis mainly injected in this direction �Fig. 10�a��. Different impactprofiles can be used to describe the shock �rectangular, half sine,versed sine, etc.�. For a given impact duration �, the shape of theexcitation does not influence the SRS calculations as far as theintegral �0

�Fdt, which represents the energy injected in the system,is constant �Fig. 12�. In our work, we will consider only triangularsymmetrical profiles equivalent to those observed during a ham-mer impact. Consequently, the EMS is completely defined by twoparameters �Fig. 11�:

• the intensity Fmax of the impact• the duration � of the impact

The parameters Fmax and � of the EMS are deduced by anoptimization process that minimizes the difference between ex-perimental and simulated SRS:

� = minFmax,�

f=1000 Hz

10 kHz

j=1

NSRS

�SRSjmeasured − SRSj

simulated�Fmax,��2 �7�

where SRSjmeasured and SRSj

simulated represent the shock responsespectrum at node j of the measured and simulated accelerations,respectively. NSRS is the number of measurement points on theplate �Fig. 9� and f the frequency.

Such a procedure is laborious because of the calculation time:for each couple �Fmax,��, it is necessary to evaluate the accelera-tion fields with the FE model. To simplify the optimization pro-cedure, we have considered durations varying from20 �s to 200 �s by discrete steps of 20 �s. For each duration �, areference SRS corresponding to a shock with a unitary intensityhas been calculated and the optimal intensity Fmax minimizing thedifference between the experimental and simulated SRS has beendetermined by optimization:

�� = minFmax

f=1000 Hz

10 kHz

j=1

NSRS

�SRSjmeasured − FmaxSRSj

ref�2 �8�

The parameters of the EMS correspond to the couple �Fmax,��for which the function error � is minimal.

Let us mention that in low frequencies, the pyroshock measure-ments are generally perturbed by zero-shift problems: A decreas-ing exponential, originating from electric effects, adds to the real

Fig. 11 Definition of the EMS

acceleration. An error of some percent in the time domain gives



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ore than one order of magnitude of error in the SRS at lowrequencies. In the literature, several authors, such as Smallwoodnd Cap �25�, suggest different curve fitting techniques to correcthe original data. Neverthless, it is important to underline thathese methods must be employed carefully because they can leado unphysical corrections if they are applied without sufficientngineering judgment. That is why, although we have applied aero-shift corrections, the frequency range begins at 1 kHz in Eqs.7� and �8�.

Fig. 12 Influence of the sha

ig. 13 Evolution of the product Fmax� in relation to the lengthf the explosive cord

Table 4 Characteristi

Length Fmax �N� � ��s�

0 83,518 604 cm 129,830 6010 cm 203,980 6020 cm 199,260 8030 cm 191,210 10050 cm 240,870 100



7 Model Validation

7.1 Agreement Between Experimental and NumericalShock Response Spectrum. In order to verify and quantify thecorrespondence between experimental and simulated SRS, wehave used some statistical indicators:

• i�f�, which represents the difference at frequency f be-tween experimental and simulated SRS in terms of fre-quency for node number i:

i�f� = �SRSisimulated�f� − SRSi

measured�f�� 9�

• �� i� and �� i�, which correspond to the mean and thestandard deviation, respectively, of the indicator i�f� alongthe frequency range:

�� i� = f� i�f��

N�10�

�� i� =� 1

N f

� i�f� − �� i��2 �11�

where N represents the number of samples of the frequencyvector.

• �G and �G relate to the mean and the standard deviation,respectively, of the frequency difference between experi-mental and simulated SRS considered on the whole set ofmeasured nodes:

�G = i

�� i�NSRS

�12�

of the excitation on the SRS

of the reference EMS

Fmax � �N s� �G �dB� �G �dB�

5.01 0.82 0.647.79 0.76 0.57

12.24 0.88 0.6815.94 0.84 0.6719.12 1.32 1.8324.09 1.27 1.16

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For the whole set of experimental data that we have previouslyescribed, we have identified the EMS for each length of theetonating cord.

Table 4 summarizes the characteristics of the EMS for the con-idered excitation levels and gives the values of statistical indica-ors �G and �G. Whatever the length of the explosive cord, theMS reproduces in a satisfactory way, in terms of SRS, the dy-amic behavior of the plate; the mean frequency difference �G isidely below the tolerances that are generally admitted by the

quipment manufacturers. The mean frequency difference �� i�nd the standard deviation �� i� calculated at seven measuredodes are given in Table 5 for detonating cord lengths of 0 cm and0 cm. Figures 14�a� and 14�b� show some comparisons betweenxperimental and simulated SRS. The evolution of the productmax� in relation to the length of the explosive cord is given inig. 13.Although the SRS is the most frequently used tool to quantify a

ibratory environment, the comparison between experimental andimulated SRS is not a sufficient criterion to validate the EMSodel because different acceleration profiles can lead to the sameRS �15�. Consequently, it is essential to make sure that the modelllows to reproduce also the experimental acceleration fields.

Figures 15�a� and 15�b� represent at Nodes 1 and 6 the timeistory and the 1 /3 octave band spectrum of the experimental andimulated acceleration fields, respectively. The modal superposi-ion method has been used to predict the transient response of thetructure. We have introduced in our FE model a constant damp-

Table 5 Accuracy between experimental and simulated SRS

Length cord

0 cm 30 cm

�� i� �� i� �� i� �� i�

Node 1 1.30 0.89 3.13 4.02Node 14 0.70 0.52 0.86 0.61Node 11 0.67 0.44 0.83 0.54Node 6 0.76 0.48 1.15 0.94Node 15 0.67 0.53 0.88 0.65Node 12 0.70 0.66 0.83 0.63Node 5 0.91 0.65 1.58 0.98

Fig. 14 Comparison between exp

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ing ratio of 0.1%, which corresponds to the mean value measuredexperimentally in the frequency range �0–1000 Hz�. The rmsvalue of the acceleration in each 1 /3 octave band is relatively wellreproduced.

7.2 Application to Other Configurations. We have studiedin detail three other configurations of the test facility.

Configuration 1. Steel plate �110.015 m3� on which analuminum block of 15 kg is screwed, simulating an electronicdevice �Fig. 16�a��.

Configuration 2. Double plate facility composed by a squaresteel plate �110.015 m3� and by a rectangular aluminumplate �0.80.60.006 m3�, the two plates are linked by screwbolts �Fig. 16�b��.

Configuration 3. Same configuration as the previous item butwhere a dummy of electronic equipment ��4 kg� has been addedat the center of the aluminum plate �Fig. 16�c��.

For each of the three configurations, we have developed a FEmodel, which has been validated and updated from a modal analy-sis in the frequency range �0–1000 Hz�. The plates have beenmodeled by 3D structural solid elements �SOLID45� and thescrew bolts by beam elements �BEAM4� with equivalent geomet-ric properties.

The same pyroshock excitation �length of detonating cord of0 cm� has been applied on all configurations and the EMS hasbeen identified. Table 6 gives the characteristics of the identifiedEMS from the different studied configurations and the statisticalindicators �G and �G. On average, the duration of the impact is ofabout 80 �s, which is coherent with the typical values found inRefs. �4,26�. Although the intensity of the impact varies from oneconfiguration to another one, the product Fmax�, which representsan image of the energy injected in the system, is close to 5 N swhatever the EMS. In order to compare the different EMS, wehave applied the reference EMS ��=60 �s and Fmax=83,518 N�to the three configurations. Table 7 gives the global deviationbetween simulated and measured SRS for each configuration.

The agreement between experience and simulation is less sig-nificant for the double plate Configurations �Configurations 2 and3�; the mean difference �G is higher than 3 dB. Nevertheless, thevibration levels of the steel plate, on which the excitation source isapplied, are very well reproduced �Fig. 17�a��. The model hassome difficulties to reproduce the acceleration levels of the alu-minum plate, particularly at high frequencies �Fig. 17�b��. Thisobservation can be explained by the filter effect of beam elements

erimental and simulated SRS



Fig. 16 The other analyzed configurations

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Table 6 Characteristics of the EMS for more complex configurations

Fmax �N� � ��s� Fmax� �N s� �G �dB� �G �dB�

Configuration 1 58,580 80 4.69 2.43 1.62Configuration 2 89,092 60 5.34 3.36 2.35Configuration 3 65,500 80 5.24 3.35 2.88

Fig. 15 Comparison between experimental and simulated acceleration fields

ournal of Vibration and Acoustics AUGUST 2008, Vol. 130 / 041012-9

ded 23 Mar 2011 to 210.117.158.180. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm

Tc

CCC

Fig. 18 Influence of some

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Downloaded 23 Mar 2011 to 210.117.158.180. Redistribution subject to ASM

used to describe the dynamic behavior of the screw bolts. In theframework of this work, we have not verified this assumption.

8 Parametric AnalysisThe model can be exploited to estimate the influence of some

parameters such as the localization of the explosive device, thegeometric and physical characteristics of the plate, or the additionof localized masses.

ulated SRS-double plate in vertical configuration

able 7 Application of the reference EMS to otheronfigurations

�G �dB� �G �dB�

onfiguration 1 2.74 2.19onfiguration 2 3.47 2.40onfiguration 3 4.09 3.07

Fig. 17 Comparison between experimental and sim

operating parameters



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The acceleration levels vary significantly with the thicknessFig. 18�a�� and the material properties of the plate �Fig. 18�b��;n increase of about 10 dB is obtained when the thickness is re-uced by half or when the steel plate is replaced by an aluminumlate. It also turns out that the vibrations are slightly influenced byhe location of the EMS �Fig. 18�c��.

As illustrated in Fig. 18�d�, the addition of a judiciously local-zed mass �10 kg� allows to lessen the influence of some reso-ance peaks. In this example, the SRS are calculated from theime history of the acceleration simulated at Node 6.

ConclusionsThis paper has presented some pyroshock test facilities that are

ommonly used by Thales Alenia Space ETCA to check the py-oshock resistance of electronic units dedicated to space applica-ions. Different configurations of the test facility have been stud-ed and modeled by the FE method. The FE model has beenpdated and validated at low frequencies from an experimentalodal analysis.An approach by EMS has been used to identify the excitation

ources generated by pyrotechnic explosions. This approach con-ists in replacing the actual excitation by a localized force appliedn the FE model at the center of the explosive device.

From a simplified configuration of the pyroshock test facilitysimple plate suspended vertically�, the EMS has been identifiedor several excitation levels. This identification procedure pro-ides accurate results; the average differences between experi-ental and simulated SRS are below the tolerances that are gen-

rally admitted by the equipment manufacturers.Our pyroshock model allows to predict the influence of several

perating parameters of the test facility and in this way it canrientate the experimental procedure of the pyroshock testing.

We have applied our methodology to more complex test facili-ies. This analysis has shown that, for a given amount of explosiveharge, similar EMSs have been identified when different configu-ations are used. Consequently, the approach by EMS is promisingo estimate the acceleration levels undergone by the electronicquipment during a pyroshock and, in this way, to predict someventual electrical malfunctions, such as the chatter of electro-agnetic relays �27�.

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Prediction of the Vibration Levels Generated by Pyrotechnic Shocks Using an Approach by Equivalent Mechanical Shock