VAPEPS MANAGEMIiNT CENTER

Juan 1’. FerntindczJet Propulsion Laboratory

California institute of Technology

BIOGRAPHY

Juan P. Fern6ndez is the task manager of theVA1’E1’S Management Center at the Jet PropulsionLaboratory. For the past six years, Mr. Ferntindexhas been involved with the development, utilizationand maintenance of the VAPEPS program and hasprovided dynamics environments support to anumber of ]1’1, flight projects. He received his B.S.(1986) and M.S. (1988) in Aeronautics andAstronautics Engineering from the University ofIIlinois in Chan~paign-Urbana.

ABSTRACT

A VAPEI’S (VibroAcoustic Payload Environmentl’rediction System) Management Center isestablished and being maintained at the JetPropulsion Laboratory (JI’L). VAI’IWS is acomputer program that utilizes statistical energyanalysis (SEA) theory and SEA extrapolationmethods to predict the vibroacoustic environmentsof complex systems. The program is commonlyutilized to establish random vibration and acoustictest requirements for aerospace componentsexposed to launch environments. It can also beused in the payload or launch vehicle designprocess for control or mitigation of the launch oron-orbit vibration and acoustic environments, aswell as to calculate acoustically induced stresses instructures such as solar panels and reflectors. Thispaper briefly summarizes the VAPIWS programcapabilities am-l presents results of its application tothe prediction of the vibroacoustic response ofspacecraft solar panels.

KEYWORDS

SEA, VA1’E1’S, VMC, Vibroacoustics, Environment,l’ayload, Launch Vehicle, Solar Panel, Magellan,Mars Observer, TOPEX, Vibration, Acoustics

INTRODUCTION

Methods for developing aerospace vibroacousticdesign and test requirements have improvedsignificantly since the advent of computer programsbased on statistical energy analysis. In the past,vibroacoustic analysis tools were more limited intheir scope of application. For instance,conventional finite element analysis is generallylimited to the low frequency range due to practicalconsiderations such as complexity and computationcosts. Also, extrapolation techniques are valid onlyif test or flight data from a similar structure exist.Current SEA based analysis tools provide ameaningful approach for understanding andestimating the mid to high frequency vibration ofstructures. The VAPEPS program has been in theforefront of more consistent and reliable methodsfor the prediction of vibroacoustic environments.

~he VAPEPS Management Center (VMC) at JI’L,originally established by the National Aeronauticsand Space Administration (NASA) and the U.S. AirForce Space Llivision (USAF/SD), is currentlysponsored by the NASA L,ewis Research Center(1.eRC). The VMC maintains the VAPEPS computerprogram and a data base of flight and ground testvibroacoustic data. The VAI’13PS predictiontechniques can be used with or without a data baseto predict the mid and high frequency structuralresponse of payloads or other aerospace structures.~’hc program can also be used to predict the noisereduction through shrouds or panels, or to calculateacoustically induced stresses in structures such assolar panels and reflectors. The VMC also providesprogram inl}>lel~~el~tatio]~, improvement, andapplications support to the VAPEPS community.

Since its inception, the VMC has actively promotedthe use of VAPIWS in the aerospace community.The VMC has conducted numerous highlysuccessful workshops to train analysts in the use ofVAI’M%. The VMC publishes a VAPEPSNewsletter to keep users informed of new program

developments. The VMC also provides usersupport for the distribution, installation andutilization of the program. As a result of its efforts,VAPI?PS has bccomc the most widely used SEAprogram in the industry. VAPEPS is used by morethan forty organizations including six NASAcenters and several educational institutions. At ]1’1.,VAPEPS is used extensively for SEA modeling of allmajor projects such as TOI’EX/Poscidcm, Galileo,Magellan, and Cassini.

VAPEPS OVERVIEW

The VAPEPS computer program was developed byLockheed Missiles & Space Company and GoddardSpace Flight Center under the auspices of theUSAF/SL> and NASA [1]. ~’he VA I’H’S programwas initiated because of the need for an analyticaltool that incorporates the state-of-the-art intheoretical, empirical and data base generatedvibroacoustic predictions.

The VAPEPS program consists of an extensivelibrary of routines that can be subdivided into threemajor categories: theoretical and empirical predic-tion routines, general computational and analysisroutines, and data base creation, search and retriev-al routines. Each subset is described here briefly.1 ‘he program is documented in Reference 1.

Theoretical and Empirical l’redicticm kXlthleS

I’hc basis for the VAPEPS prediction methodologyis SEA [2]. This technique is statistical in nature andassumes that the excitation is random. The processunder analysis is also assumed to be steady state sothat energy balance equations can be applied. Theprediction schemes take structural, acoustic spaceand excitation parameters of a dynamical systemand provide an energy balance from which themean-squared value of response can be calculatedin one-third octave frequency bands. The mostimportant SEA parameters for response predictionarc modal density, damping and coupling lossfactors.

The modeling approach is to divide the payloadstructure into simplified SEA elements consisting offlat plates, cylinders, cones, beams or trusses andacoustic spaces. The inputs to the program includephysical dimensions, material properties anddamping loss factors for each SEA element. Next,the connect ions, or energy transfer paths, between

elements are specified and an excitation level isinput. The VAPEPS program calculates, in one-third octave frequency bands, the spatial and timeaveraged response of each element in the model tothe given dynamic environment.

VA1’EPS can yield purely theoretical or empiricalpredictions, or a combination of both. There aretwo extrapolation routines in VAPFTS, namely,FXTRAP I and EXTRA1’ 11. FXTRAP I uses boththe theoretical and scaling methods, whereasEXTRAP 11 uses only the scaling methodstraditionally used in the aerospace industry. Eachextrapolation procedure takes structural/excitationdata sets of a baseline system, corrects forparametric differences between the baseline systemand the new system configuration, and thenestablishes one-third octave power spectral densityresponse values or decibel levels for the newsystem. Both extrapolation routines require adynamically similar configuration to be used as abaseline model. The VAI’EI’S prediction routinesare useful in establishing random vibration andacoustic environments for developing design andtest requirements for new payload components.

General Computational and Analysis Routines

This category encompasses a wide variety ofgeneral mathematical and statistical routines fordata manipulation and presentation. Also includedare a set of vibroacoustic routines for calculatingFast Fourier Transforms (FFTs), Shock ResponseSpectra (S1{S), overall grins levels, and performingother types of data analysis. These generalprocedures can be used alone or with a data base toobtain averaged or maximum levels, standarddeviations and other data ana]yscs.

2’WO notable vibroacoustic analysis routines inVAPEI’S are the STRESS and TBL1’ commands. TheSTRESS command calculates a theoretical spatialaverage mean-square stress for a flat plate, curvedplate, or cylinder based on an input mean-squareacceleration response. The acceleration responseinput k assumed to be known either empirically orfrom a VA I’IWS SEA prediction. Stress predictionresults provide an estimate of the magnitude of thein-plane stresses in a structure. The estimate canserve as a guide for determining whether a designproblem might exist and whether a more detailedstress analysis is in order. The TBI.P commandprovides the capability to perform statistical energyanalysis of simple structures uncler turbulent

boundary layer excitation. The unsteady pressurefield in a turbulent boundary layer is modeled as aprogressive wave in the TBLP code. ‘I’he commandcalculates the j>ower input from a progressive wavefield into a flat plate or cylinder.

I lata Base Crest ion, Search and Retrieval

The VAPEPS program gives the user the flexibilityto create a local data base using VAPEPS or toimport data from a data base external to theprogram. Data base creation commands allow forspectra] accelerometer and microphone data,payload structural parameters and generalbookkeeping information to be added to a database. l~ata maybe entered in almost any form,however, VAI’13’S automatically converts it tostandard one-third octave band frequencies. Searchand retrieval routines permit interrogation of thedata base information. Retrieval commands canthcm be used to recover any required informationfrom the data base, once a specific event of interesthas been identified.

PREDICTION EXAMPLE

The following example illustrates the application ofthe VAPEI’S vibroacoustic capabilities to theprediction of the acoustically-induced randomvibration of large solar panels. Solar panels are ofparticular interest since they are commonly used inmodern spacecraft to power electrical systems.l’hese large surface area lightweight structures areeasily excited by sound and often experience highacceleration responses during spacecraft acoustictests. To demonstrate the capabilities of VAPE1’S,vibration prediction results for models of theMagcllan, Mars Observer [MO] and TOI%X space-craft solar panels are evaluated and compared toacoustic test data.

VA1’EPS Analysis

SEA I’heory

SEA basically results in a procedure for analyzingthe flow, storage and dissipation of energy in asystem. An SEA model is developed by dividingthe system into elements (i.e. plates, acoustic spaces,etc. ) with groups of similar modes. The. modes ofthe system represent the energy storage elements.Energy is input into the storage elements by anexternal acoustic or vibration source. That energy is

then dissipated by mechanical damping in thesystem and transferred between storage elements.Element responses arc then calculated from anenergy balance in the system, The principal SRAparameters involved in this storage, dissipation andtransfer of energy are modal density, damping andcouj>ling loss factors [2].

Since SEA assumes that energy is stored in themodes of a structure. The fewer modes availablefor energy storage, the higher the variance in theresponse magnitudes and the more conservative theprediction. Normally, at least three modes per one-third octave band of analysis are required to allowfor predictions with an acceptable degree ofcertainty.

Damping also plays a major role in the response ofdynamical systems. Similarly, SEA responsepredictions are sensitive to the value of dampingassumed for a model. Unfortunately, damping isonc of most difficult parameters to determineaccurately.

Description of Panels

Solar panels lend themselves to SEA due to theirsimple geometry and large surface area. All threesolar panels are of lightweight, honeycombconstruction with very large surface areas. Asimplified model of each spacecraft’s solar pane]was developed from drawings and data of materialproperties [3-5]. The structural dimensions of thepanels for the three spacecraft are listed in Table 1.

Modeling Approach

An analyst needs to be aware of the assumptionsimplicit in using a SEA approach as implemented inVAPEPS. The following are two importantassumptions. First, SEA assumes that the resonantresponsd of a structure is to be modeled therefore itsuse below the fundamental frequency of the solarpanels is inappropriate, Second, it is assumed that aplate to be modeled is located in an infinite bafflesuch that sound cannot wrap around the edges.According to theory, this results in more efficientacoustic excitation of the plate and consequentlyhigher panel response accelerations at lowfrequencies, below the plate’s critical frequency.

Also, the VAPEPS vibroacoustic prediction routine,SEMOD, is applicable only to homogeneousisotropic tnodel elements. Therefore, a multilayered

.

Width (in.) I 98.2 I 72.0 I 75.8

Facesheet Thickness (in.) 0.015 0.01

+

0.012

Core Thickness (in.) 0.50 1.00 1.35 —

Faceshect Material I Aluminum I Kcvlar \ A l u m i n u m

Core Material I Aluminum I A l u m i n u m \ A l u m i n u m

Table 1. Structural Properties and Dimensions for the Magellan,Mars Observer and TOPI?X Spacecraft Solar Panels

stiffened panel needs to be converted into a hcmm- each plate was coupled to its acoustic space usinggeneous flat plate with equivalent properties. Path 49. Finally, each panel model was analyticallyEquivalent structural properties were calculated subjected to acoustic excitation levels correspondingusing the KUN=EQPL ro;tine. The processorcomputes an equivalent Young’s Modulus, massdensity and thickness for multilayered, stiffenedplates.

A uniform modeling approach was used for allthree solar panels to reduce the number of factorsaffecting the predictions. Each panel model consistsof two basic elements: an equivalent homogeneousplate, 1’1 ,AT, and an external reverberant acousticexcitation space, EXTA. The model parameters foreach spacecraft solar panel, listed in Table 2, wereinput into the theoretical prediction routine. Then,

to i~s spacecraft’s protof]ight test levels. -

The following modeling assumptions were alsomade for each of the solar panels. A scale factor ofone (scalefac=l ) is used for all solar pane] modelpredictions. This assumption implies that analyti-cally the model is acoustically excited on one sideand that it radiates from only one side. An analystcan elect to use a scale factor between one and twobased on the particular configuration of the systembeing modeled. Also, a damping loss factor (dIf)value of .05, equal to twice the critical dampingratio, was used for all three models. The damping

Model Parameters Parameter (Units) Magellan Mars Observer TOPEX

‘1’hickness H (in.) 0,701 1.738 1.7

Mass Density RHO (lbs s2/in4) 2.45E-05 7.88E-06 1 .17E-05.—— ——%rface Mass Density RllOS (lbs s2/in3) 1.7213-05 1.3713-05 2.00E-05—.. — —.youll~’S Modulus E (lbs/in2) 6.18~+05 2.15E+05 2.87E+05

Longitudinal Wavespeed Clj (in/seC) _~.ol~+05 1 . 6 5 E + 0 5 — 2.20E+05

Surface Area AF’ (in2) 9741 6 4 2 6 — 9808— .——Typical Sub-dimension AI,X ( i n ) 98.2 8 9 . 3 — 77.6

~’ypical Sub-dimension A L Y (in) 49,6 7 2 . 0 — 45.5.—.Damping I,oss Factor LXJ 0.05 - 0.05 0.05

Non-Structural Mass—

ASMS (lbs s2/in) _ 0.0 0.0 040Pivot Frequency Pivotlkeq (H7,) 250 2 5 0 — 250

Table 2. VAPIH% Model Parameters for the Magellan, Mars Observer and TOPEX Spacecraft Solar Panels

+7,

A

+7,

.

5A113X 11OX(5A121X)*

1

+ x

5A] 17X (5 A123X)* * Mcasurcnlcnt on +X Array

Figure 1. Magellan Spacecraft Solar Panels - Accelerometer Locations

function selected for the solar panel model ischaracterized as follows: a constant damping lossfactor value of .05 below 250 Hz, and a value above250117, that varies linearly with frequency by thefollowing equation:

Dll= 0.05 ‘ 250 Hz / f f >250 Hz

(pivotfreq=250 H7,)

A consistent approach was also used to model thenon- structural mass of the solar panels. Nonstructural mass is defined as component mass thatis attached to the panel but does not act to stiffen it.‘1’here are two approaches to incorporating this typeof mass into a model. The first and most commonapproach is to use the ASMS parameter. ASMSreduces the response of the panel model by a factor,M= Structural Mass/ ( ASMS + Structural Mass ).The second approach involves incorporating themass into the model by modifying the densityparameter, I{HO. The latter approach was used tomodel the mass of the solar cells for all three panels.It has the distinct advantage of reducing the re-sponse prediction at the low frequencies, whereexperience shows that VAPEPS tends to be conser-vative, much more than at the high frequencies.‘1’he ASMS approach reduces the prediction by aconstant factor (M) across the frequency spectrum.

l’redicticms versus Acoustic Test Data

Magellan

The Magellan spacecraft system acoustic test wasconducted at Martin Marrieta cm March 1988 [6].During this test, a dynamic mass model (DMM) ofthe Magellan solar panel was exposed to pmtoflightsound pressure levels (SPLS), 146.0 dB overall (OA).Figure 1 shows the panel instrumentation andconfiguration during the test. Data representativeof the spatial average response of the panel wereselected for comparison with the model responseprediction. The data and the actual average soundpressure levels during the test are plotted inFigure 2.

Also, the VAPEPS average response prediction iscompared to the spatial average response of the testdata, Figure 3. The prediction agrees well with thedata between 80-200 Hz and at frequencies above800 Hz. However, it overpredicts the data by 3-5 dBbetween 200-800 Hz and is very conservative below80 H7,. ~’he significant overprediction below 80 H7,

results from the panel having few modes at the lowfrequencies and from the panel being unbaffled,allowing the larger, low frequency acoustic wavesto wrap around.

. .

I 00

10

1

0.1

0.01

0.001

I I 1

-1

/

~’/

/4/

— Data Ave—— -5al 10x— . -5al 13x--------- 5al17x— -Sa120x—— -sa121x- - - - - Sa123x

‘,“,, , t I , , I , 1 40

100 1 0 0 0

One-Third Octave Band IJrcqmncy (11?)

Figure 2. Magellan DMM Solar Panel Acoustic Test Data and Measured Average Sound l’ressure Levels

I 00

10

1

0.1

0.01

0.001

10

— Data Ave— — - Prediction I

\

J

, , , , , , I , , , , , * , , I , , , ,

100 1000 ,04

Onc-’lhird Octave Iland Frequency (Hz)

Figure 3. Magellan DMM Solar Panel Data Average Con~pared to VAPEPS Panel Model I’rediction

+7.

1SP6-4Y

4 +y

SP6-2Y

Figure 4. Mars Observer Spacecraft Solar Array - Accelerometer Locations

Mars Observerlocation of the accelcrorncrs on panel 6, and the

The Mars Observer spacecraft system acoustic test configuration of the panel array during the test.was conducted at GE Astro Space cm April 1992 [7]. Response data from the outer panel and the actualThe MO flight solar array was exposed to proto- average sound pressure levels during the test areflight S1’1,s, 145.8 dB OA, during this test. The solar plotted in Figure 5.array consists of six stacked solar panels hinged atthe edges and held in the launch configuration by 7 ‘he VAI’EI’S average response prediction is com-spring loaded attachments. Figure 4 shows the pared to the spatial average response of the test

100

10

1

0.01

O.(M)]

100 1O(KI

One-Third Octave Band Frequency (Hz)

Figure 5. Mars Observer Solar Panel Acoustic Test Data and Measured Average Sound Pressure Levels

0.01

0.001

F , , m , , , I r , , , I 3L J

EiEl://

, $ , , , I I t , , , , , t

10 100 1000 ,04

Onc-’l’hird Octave Band lh-cquency (Ilz)

Figure 6. Mars Observer Solar Panel Data Average Compared to VAPEI’S I’anel Model Prediction

data in Figure 6. The prediction is conservativeacross the frequency spectrum. It is about 1-5 dBhigher than the data above 100 Hz and much higherbelow 100 Hz.

TOI’IIX/l’oseidon

The Topex/Poseidon solar array was tested toprotoflight ]WCIS, 146.0 dB OA, during the satellitesystem acoustic test conducted at Goddard SpaceFlight Center on February 1992 [8]. The location ofth;”accelercnneters cm pa;ml 4 of the solar array is

shown in Figure 7. The solar array was tested in thelaunch configuration which consisted of the fourhinged panels stacked and held together by fourbolts. Response data from the outer panel and theactual average sound pressure levels during the testarc plotted in Figure 8.

In Figure 9, the VAPEPS average response predic-tion is compared to the spatial average response ofthe test data. The prediction is 2-4 dB higher thanthe data below 300 Hz, intersects the data at 400 Hz,and underpredicts the data above 500 I Iz by 1-3 dB.

[

+-x

Lb i-z

4A092;

4A099Y

4A094YI

Panel 4

1

4A;OOY

4AI02Y

4A090Y

4A101Y

4A096Y

Figure 7. TOPEX/Poseidon Spacecraft Solar Array - Accelerometer Locati ons

100 k I I I

4----

0.001 L____lIll

—. - 4a092— - - - - 4 a 0 9 4- - - - - 4a096— - -4a099- - - - - 4aloo. . . . - 4a101--------- 4a

100 Iwo

Frequency (}Iz)

Figure 8. TOPEX Solar Panel Acoustic Test Data and Measured Average Sound Pressure Levels

t / \ 1\

Onc-’lhird Octave Band Frequency (Ilz)

Figure 9. TOI’EX Solar Panel Data Average Compared to VAPEPS Panel Model I’rediction

,,,4

.’

Results

The MC), TOI’EX and Magellan panel model prcdic-ticms compared reasonably well with the acousticdata. Discrepancies in the comparison of thepredictions to data are due in part to the modeling “assumptions made. For example, it is debatable.whether a scale factor of one for one-sided acousticexcitation was an appropriate assumption for thesolar array models since one side of the outer panelis only partia]ly shielded from the acoustic field.Also, the values of damping used in the modelsrepresent only an estimate of the true damping inthe solar panels. Furthermore, the predictionsmprcse.nt the response of a homogeneous, isotropicplate simply supported in an infinite baffle; theseconditions are seldom achieved in real structures.

Additionally, other non modeling factors can helpexplain the discrepancies between the modelpredictions and the acoustic data, For instance,each solar pane] was tested in a different launchconfiguration. The MO solar array consisted of sixstacked panels, the TOPEX solar array consisted offour stacked panels and the Magellan solar arrayconsisted of two panels, one on each side of thespacecraft. Each spacecraft test configurationimposes different boundary conditions on itsrespective solar panel array, which affects thecharacteristic response of the panels, particularly atlow frequencies. Also, another factor to consider iswhether the data used in the comparisons trulyrepresents the spatial average for each solar panel.

Conclusions

It has bcwn shown that SEA provides a meaningfulapproach for understanding and estimating the midto high frequency multi modal vibration of largesolar panels. The VAPEPS program gave usefulestimates of the vibration response of the Magellan,Mars Observer and TOI’EX solar panels. Neverthe-lCSS, several points are made clear from the abovepresentation.

First, it is essential that the analyst have a goodunderstanding of SEA principles to obtain rationalpredictions. l’here are many factors to beconsidered that can affect the accuracy of SEApredictions, It is therefore advisable to alwaysperform an extrapolation prediction for a newmodel using available acoustic data from adynamically similar structure. The data for thethree spacecraft solar panels presented in this article

can be used in that regard when modeling largepanels. The best prediction is always that whichcan be validated with data.

ACKNOWLEDGEMENTS

The work described in this paper was carried out atthe Jet l’repulsion I,aboratory, California Institute ofTechnology, under a contract with the NationalAeronautics and Space Administration. The workwas sponsored by the NASA Lewis ResearchCenter.

[1]

[2]

[3]

[4]

[5]

[6]

[7

[8

REFERENCES

Park, L), M., VAPEI’S Users Reference Manual,Version 5.1, NASA Contractor Report 180781,May 1990.

Lyon, 1<. H., “Statistical Energy Analysis ofl~ynamical Systems: Theory and Applications,”MIT Press, 1975.

Fern6ndcz, J.I’., Vibroacoustic Response of SolarPanels: Case Study, J]% D-11341, June 15,1993.

Badilla, G., “Mars Observer Solar Array Vibro-acoustic Response I’redaction,” JPL IOM 5216-92-034, April 13,1992.

Scharton, T., “TOPEX/Poseiclon SpacecraftAcoustic Test Results,” JPL IOM 5216-92-058,April 23, 1992.

Paw]owski, S. W., “Magellan SFS Acoustic andPyro Shock Test Report,” MCR-t38-l 390, June,1988.

O’Connell, M. R., “Mars Observer Sine Vibra-tion, Acoustic Noise and Pyrofiring Results,”JPL IOM 5216-92-081, May 27,1992.

Boatman, D.J., “Summary Report of theTOI’EX/Poseidon System Sine Vibration andAcoustics Tests,” JPL IOM 5216-92-036, March18,1992.