I3 1176 00140 2891

NASA Technical Memorandum 81789

NASA-TM-81789 19800011797

WING/STOREFLUTTERWITHNnNLINEARPYLONSTIFFNESS

ROBERTN,DESMARAIS AND WILMER H, REED, Ill

ItD_1"0Br-'IAI"_P_"

APRIL1980

[F_Ariy_,,_-,,?Y

it1,__.i980LAr'SLK: ,.:_.._=,K_;_CENTER

__I_A Lt3RP,RY,NASAHAMPTON,_dlRGINIDNationalAeronautics andSpace Administration

Langley ResearchCenterHampton,Virginia 23665

https://ntrs.nasa.gov/search.jsp?R=19800011797 2018-08-19T09:01:22+00:00Z

WING/STOREFLUTTERWITH NONLINEARPYLONSTIFFNESS

Robert N. Desmarais and Wilmer H. Reed IIINASA Langley Research Center

Hampton, Virginia 23665

Abstract The decouDler pylon uses a low frequency con-trol system to compensate for changes in static

Recent wind tunnel tests and analytical stud- deflections of the store that would otherwise existies show that a store mounted on a pylon with during maneuvers or airspeed changes. Depending on"soft" pitch stiffness provides substantial in- the time constant of the store alignment system andcrease in flutter speed of fighter aircraft and the rate of change of load, however, the store mayreduces dependency of flutter on mass and inertia deflect enough to exceed the linear range of theof the store. This concept, termed the decoupler soft pitch spring and "bottom" against a relativelypylon, utilizes a low-frequency control system to stiff back-up structure. Under such conditions,maintain pitch alignment of the store during maneu- pylon pitch stiffness varies in a nonlinear mannervers and changing flight conditions. Under rapidly which depends on both the static Dreload andchanging transient loads, however, the alignment oscillation amplitude of the store.control system may allow the store to momentarilybottom against a relatively stiff backup structurein which case the pylon stiffness acts as a hard- Symbolsening nonlinear spring. Such structural nonlinear-ities are known to affect not only the flutter K spring constant of linear soft springspeed but also the basic behavior of the Ke equivalent linear spring constant ofinstability. This paper examines the influence of nonlinear spring

: pylon stiffness nonlinearities on the flutter M elastic restoring moment about store Ditchcharacteristics of wing-mounted external stores, axis

M1 fundamental Fourier component of store pitchmoment

Introduction Mo static moment required to deflect storeagainst hard spring

Analytical investigations of aeroelastic sys- M static preload momenttems are usually based on linear theory which as- N ratio of hard spring constant to soft springsumes both the structural and aerodynamic proper- constantties to be independent of the amplitudes of V flutter speedoscillation. Aircraft structures typically exhibitnonlinearities, however, such as backlash or kine- Vnom flutter speed of linear system with nominal-matic deflection limits in moving control surfaces design, stiff pylon (sorinq constant = NK)and in the connecting structure between wing and t timeexternal stores. Studies of flutter of wings with t time at which store contacts hard springcontrol surfaces that contain structural nonlinear- _ describing function (5 = Ke/K)

ities (references I-5) have shown that nonlineari- 6" describing function when N/FIo = 1.0ties can affect not only the flutter speed of thesystem but also the characteristics of flutter 0 store pitch anglemotion. Similar studies in reference 6 investigate 01 amplitude of sinuso_dal store Ditchthe effects of control system nonlinearities, such oscillationas actuator force or deflection limits, on perform- Oo pitch angle at which store contacts hardance of an active flutter suppression system, springWhereas flutter of a linear system is characterized 0 static store pitch deflection due to preloadby an exponential growth of oscillation amplitude w circular frequencywith time, flutter of a nonlinear system may be

amplitude limited. On the other hand, a nonlinear Nonlinear Systemsystem which is stable with respect to small dis-

turbances may be unstable with respect to large An idealized representation of the nonlinearones. Interest in this particular problem stems pylon suspension system is shown in the upper partfrom studies in reference 7 of a passive wing/store of figure 2. The store is suspended from the winqflutter suppression concept known as the "decoupler by a pivot located near thewing elastic axis. Thepylon." These studies and others have shown that store pitch frequency is controlled by a soft lineara store mounted on a pylon with "soft" pitch stiff- spring. The spring stiffness K is chosen to makeness can provide substantial increase in flutter the uncoupled store pitch frequenc_ somewhat lowerspeed and reduce the dependency of flutter on the than the fundamental wing bending frequency when themass and inertia of stores relative to that of store is rigidly_mounted (see reference 7). A"hard-mounted" stores. By decoupling the influence static Dreload M is assumed to act on the store

- of store pitch inertia on wing torsion modes, the as a result of loads such as a high-g pitch-uDfrequency separation between flutter-critical modes maneuver. When the Dreload exceeds a value No, theis increased and the flutter speed is increased associated static pitch disolacement causes theas indicated in figure I. pylon to contact mechanical stops at 0 = 0o. The

stiffness then increases by a factor N over thatof the soft spring. This situation results in the

*Aero-Space Engineer, Structures and Dynamics load displacement curve shown in the lower part of**Div. figure 2.

Head, Aeroelasticity Branch, Structures andDynamics Div.

In thisnaperthe preloadand resulting lessthan 8o, the equivalentspringconstantisdisplacementare suchthat the discontinuityin the loaddisplacementcurveat negative 0 the sameas thatof the linearsoftspring,valuesis neverreachedso onlythe positive ' i.e.,6 = l.O. With increasingoscillation

amplitude,the systembeginsto contactthe harddiscontinuity,00, is analyzed. The nonlineareffectsof dampingare innoredbecausestudies springwhen 8 = 8o and the equivalentspringin reference7 showedthatflutteris insensitive thenstiffensas the amplitudeincreases.Thisto pylondamping, transitionbetweena linearsoftspringand

a nonlinearhardeningspringoccursin figure4at the oscillationamplitudeswherethe curves

Describin9 FunctionAnalysisTechniQue for constantpreloadbreakawayfrom the 6 = l.Oline. Conversely,when preloadexceeds Mo, the

The analysistechniqueusedis the "describingfunction"or equivalentlinearizationmethod(see equivalentspringconstantis the sameas thereferences2 and 4). In particular,reference4 linearhardspring(6 = 20) for smallamplitudepresentscomparisonsof the resultsof the oscillations.However,as oscillationamplitudesdescribingfunctiontechniquewith resultsusing increaseand deflectionsenter the softspringrange the stiffnessis characterizedby thatofa completenonlinearsolutionof the sameproblemto illustratethe validityof the method, a nonlinearsofteningspring.

The basisof the describingfunctionmethod An interestingand significantfeatureof ais to assumea sinusoidaldisplacementand then bilinearspringis apparentin figure4. Whenthe preloadexactlymatchesthe "bottoming"load,

computethe loaddevelopedin the nonlinear _!/Mo = I O, the equivalentspringconstantissDrinq. The sorinqload is thenexpandedintoa Fourierseries. The fundamentalis retained, independentof oscillationamplitude. In otherand higherharmonics,whichare assumedto be woras,the systemnenavesas tnoughthe sprinQnegligible,are discarded.The springconstant were linearfor all oscillationamplitudes.Theof the equivalentlinearspringis thendetermined describingfunctioncorrespondingto this transi-by obtainingthe ratioof the coefficientof the tionregionbetweena hardenings_ringand a

softeningspringis designated_ , and itsloadfundamentalto the displacementamplitude, valuedependson N, the ratioof the two sprinqKe = MI/Ol, where constants. For the caseshownin figure4,

N = 20 and 6* = 2.412. The variationof 6*

= _+ _l sin _t with N is indicatedin figure5.

M = M+ Z M sin notn=l n FlutterCalculations

The describingfunctionmethodis incorporatedIn thistypeof analysis,for eachpreload intofluttercalculationsas follows. First,

and displacementamplitudethe problemis linear,consequentlya linearflutteranalysismay be the fluttervelocityis computedas a functionmade. The nonlinearityonlyappearsas d change of equivalentpylonpitchstiffnessusinganyin equivalentlinearspri1_constantwhen the standardlinearflutteranalysistechnique. Forpreloador displacementamplitudeis changed, convenience,thisflutterboundaryis expressed

in termsof nondimensionalratios V/Vnom and

With referenceto figure3, the describing 6 = Ke/K where Vnom is the flutterspeedoffunctionis computedas follows: The load M, a linearsystemwith nominalpylonpitchstiffnessdevelopedin the nonlinearspring,is expressed

in termsof the storeoscillationamplitude01 typicalof currentfighterdesignnractice(inthiscase,20 timesthe softpylonpitchstiffness).and the time _ at whichthe storecontacts Then,the familyof curvesrelatinqthe describinqthe hardspring. This loadis integratedover functionto amplitudeand preload(figure4),one cycle to givean expressionfor the preIoad, is crossplottedagainstthe flutterboundarytoM (thezerothFouriercoefficient).For each eliminate 6. The resultis a familyof flutterspecifiedprelect;B, this expressionis then boundaries(velocityversusdisplacementamplitudesolvedfor T. This informationis-thenused curves),one for eachpreload. This procedureto computethe firstfew Fouriercoefficients, is illustratedgraphicallyin figure6. TheAll the Fouriercosinecoefficientsintegrate lineartheoryflutterboundaryis the upper leftto zerobecausethe loadfunctionis symmetric partof the figureand the describingfunctionabout the zerosof the cosinefunction. The (figure4) is plottedbelowit. FlutterboundariesfirstFouriersine coefficient,MI,is used for the nonlinearsystemare in the upperrightto computethe equivalentspringconstant, partand the dashedlineswith arrowsindicate

Ke = MI/@I, and the describing function, 6 = Ke/K. how they are related.The second Fourier sine coefficient, which has Several points can be made regarding thea very small magnitude, is used to assess the flutter boundaries shown in figure 6 for variousvalidity of the method. No other Fourier preloads and oscillation amplitudes. Considercoefficients were computed, first the case where static deflections due to

preload lies within the linear range of theFigure4 is a plotof describingfunction decouDlerpylon,i.e.,M/Mo < 1.0. If the system

= Ke/K versusamplitudefor variouspreload is initiallyat rest,the flutteronset speedmoments. Note thatwhen the preloadis lessthan is the sameas thatfor the linearsystem,i.e.,M and the staticplusdynamicdeflectioniso

2

i

•....._!: !/%¸•::!/'_-_::.i/

_....

aporoximatelyV : 2.8 Vnom. However,for speeds are mountedon decouplerpylonswhichgiveanuncoupledstorepitchfrequencyof 4.0 Hz (on

withinthe interval 2.3 < V/Vnom < 2.8,the the full-scaleairplane). Thisfrequency,systemcan experiencedivergentflutterosciila- selectedon the basisof a criterionoftionsif a sufficientlylargedisturbancecauses reference7, is approximately70% of the firstoscillationsintothe destabilizingstiff-spring antisymmetricwing bendingfrequencywith therange. For example,in figure6 witha oreload storerigidlyattached. The pitchstiffness

I, when the systembottomsagainstmechanicalstopsof ',/Mo = 0.6,it can be seenthatthe degradinqeffectsof stiffnessnonlinearityon flutter is takento be the stiffnessof the nominalbeginto appearwhen the disturbanceamplitude F-16pylondesignwhich is 20 (N = 20) times

becomesgreaterthan el/Oo = 0.4 For greaterthan thatassumedfor the decouplerpylon. A linearflutteranalysisfor F-16V > 2.8 Vnom, divergentoscillationsoccurfor any configuration32 was performedby Generaldisturbance.The lineseparatinginitialdisturb- Dynamics,FortWorth,withvaryingpylonpitchanceswhichcauseflutterfromthosewhichdo not stiffnesses.Resultsof the analysisforis showndashed. Notealsothatwhen M/Mo = l.O, antisymmetricalflutter(themost criticalmode)the fluttervelocityis independentof the at Machnumber0.9 are presentedon the leftmagnitudeof the disturbance,the sameas for a sideof figure7. The companioncurvesplottedlinearsystem. This interestingfeatureis, of on the rightsideof figure7 is a familyofcourse,a consequenceof the describingfunction flutterboundarieswhich accountfor pylonbeingindependentof amplitudeat _/Mo : l.O stiffnessnonlinearities.Theseflutterfor a bilinearspring,as was discussedearlier, boundariesare for the sameconfigurationas

thosepreviouslypresented,in abbreviatedform,Considernext,the rangeof preloadswhich in figure6 to illustratethe analysisprocedure.

causestaticdeflectionsgreaterthanthe limits Thus,earliercommentson figure6 regardingof the softspring,i.e.,H/Mo > l.O. Flutter divergentflutterand limitedamplitudeflutter

: onsetundertheseconditionsoccursat Vnom, are applicableto figure7 as well.

the fluttervelocityof the linearsystemwithstiffpylon. However,unlikea linearsystem, To put in betterpersoectivethe magnitudewhereoscillationamplitudegrowsindefinitely of staticdeflectionsa decouplerpylonwithand exponentiallywithtime,the flutterampli- softDitchstiffnessmightexperiencein pitch-uotudefor thisnonlinearsystemis selflimiting maneuvers,somecalculationshave beenmadebecauseas amplitudeincreasesthe resultant for the F-16configurationconsideredin figure7.softeningeffectof the nonlinearspring(see In thesecalculationsthe benefitsof an aliqn-figure4) tendsto stabilizethe system. This mentcontrolsystemwere neglectedand thecan be illustrated,for example,by the flutter mostcriticalcombinationsof designmaneuvers

pointshownin figure6 where,for MI/Mo = 1.5, specifiedin Mil SpecMILA-8591E(ref.8) wereassumed,i.e.,pitchacceleration,4-4radiansthe flutteramplitudeis limitedto about O.l 00• per second;normalacceleration,+6 g's;and

The solidcurveshowsthe magnitudeof the longitudinaloffsetof storecenterof gravity,3.5 inchesforward. The staticpitchdeflection

limitedamDlitudeflutter, of the GBU-SBstorepredictedfor thisextreme

By physicalreasoningit can be deducedthat pitch-upmaneuverwas only0.9 degrees.the signof the slopeof the velocityversus Therefore,even thoughthe decouplerpylonhasdeflectionamplitudecurves,dV/dBl, determines a pitchstiffnessthat"islow relativeto thewhetherflutteroscillationswill be divergent nominalpylondesignstiffness,staticdeflectionor of limitedamplitude: a curvewithpositive of the storeduringmaneuversis small. Theslopeindicateslimitedamplitudeflutter;a boundson storepitchdeflectionfor othertypescurvewith negativeslopeindicatesthe distur- of transientloads,suchas gusts,are alsobanceamplitudethatmust be exceededto cause beinganalyzedin a separatestudy. It appears,

however,the main requirementfor a storealign-divergentflutter, ment controlsystemis to comgensatefor the

quasi-steadyvariationin drag loadsdue to

Applications changingflightconditions.

In thissectionof the papersomeanalytically DecouplerPylonResearchModelpredictedeffectsof pylonstiffnessnonlinear-itieson wing/sotreflutterare presentedfor The secondconfigurationanalyzedis thetwo configurations:the F-16and a flutter decouplerpylonresearchmodel usedin studiesresearchmodel. Wind tunneltestsof both reportedin reference7. The modelis aconfigurationswith lineardecouplerpylonshave cantileveredrectangularwing witha storebeenconductedin the LangleyTransonicDynamics mountedat the 80-percentsemisDanstation. TheTunnel. Additionaltestswithnonlinearpylon linear-systemflutter(velocity)boundaryfor

• stiffnessare beingplannedfor the research themodelas a functionof pylonpitchstiffnessshownin figure8 was derivedfrom figure6 of

model, reference7. As in the previousexample,pylonstiffnessis expressedin termsof the describinq

F-16FlutterModel functionfor a bilinearspringwith N = 20.

The F-16storeconfigurationconsideredin Note thatin contrastwith the F-16 flutterthisexampleis designatedconfiguration32 in boundary(figures6 and 7) whichdecreasesmono-reference6. It consistsof a GBU-8Bstore tonicallywith increasingpylonpitchstiffness,carriedat wing stations120,and an'AIM-9 the linear-systemflutterboundaryin figure8 ismissileat eachwing tip. The GBU-8Bstores characterizedby a peaknear _ : 5.0. This peak

3

falls in the region of pylon stiffness where (4) Some sample calculations for an F-16there is frequency coincidence between the fighter performing a design-limited pitch-upuncoupled pylon pitch mode and the wing funda- maneuver were made to determine the static pitchmental bending mode. Because of t_is peak in deflections of a decoupler-pylon mounted store.the linear-system flutter boundary, the effects The maximum predicted deflection (without anof stiffness nonlinearities on flutter are some- alignment control system) was less than 1°what different from, and more complicated than, Thus, the requirement for an active aliqnmentthe case shown previously. Again solid lines are control system to avoid excessive staticused to show the magnitude of limited amplitude deflection of the store appears to be governedflutter and dashed lines lines to separate dis- more by drag loads than by maneuver loads.turbance regions which lead to either stablemotion, or catastrophic divergent flutteroscillations. For this nonlinear system, Referenceslimited amplitude flutter can occur for anypreload condition; in the previous example, it IWoolston, Donald S.; Runyan, Harry L.; andoccurred only when M/Mo > 1.0. Andrews, Robert E., "An Investigation of Effects

of Certain Types of Structural NonlinearitiesConclusions on Wing and Control Surface Flutter. Journal of

the Aeronautical Sciences, January 1957,This paper investigates the effects of pylon pp. 57-63.

stiffness nonlinearities on the flutter charac-teristics of wings with externally mountedstores. In particular, the focus of the paper 2Shen, S. F., "An Approximate Analysis ofis on a passive wing/store flutter suppression Nonlinear Flutter Problems," Journal of theconcept known as the decoupler pylon. This Aero/Space Sciences, January 1959, pp. 25-32, 45.concept uses a soft pylon pitch spring todecouple the store pitch mode from wing torsion 3Breitbach, E., "Effects of Structural Non-modes assisted by a low frequency active control linearities on Aircraft Vibration and Flutter,"system to reduce static deflections of the store AGARD-R-665, January 1978.due to maneuvers and changing flight conditions. 4The structural nonlinearity under consideration Laurenson, Robert M.; and Trn, Robert M.,is associated with bottoming of the system "Flutter Analysis of Missile Control Surfacesagainst a relative stiff backup structure as a Containing Structural Nonlinearities," AIAAresult of excessive static and/or dynamic PreDrint 79--796, presented at the AIA#/AS_IE/ASCE/

deflections of the store in pitch. By use of an I AHS 20th Structures, Structural Dynamics andapproximate analysis technique (describing Materials Conference, St. Louis, MO, April 4-6,function technique), the nonlinear flutter 1979.behavior of two wing configurations with externalstores is studied. On the basis of these studies 5Breitbach, Elmar J., "Flutter Analysis of anthe following conclusions may be drawn: Airplane with MultiDle Structural Nonlinearities

in the Control System," NASA TP-1620, January(I) If the store static pitch deflection due 1980.

to preload falls within the linear stiffness

range of the decoupler pylon (M/Mo < 1.0), the 6peloubet, R. P., Jr.; Haller, R. L.; andBalding, R. M., "F-16 Flutter Suppression System

flutter speed is substantially greater than (more Investigation," presented at the AIAA/ASME 21stthan twice) the flutter speed with a nominal SDMConference held in Seattle, Washington,stiff-pylon design. When store pitch oscilla- May 12-14, 1980.tions are superimposed on this static deflection,

causing the system to bottom against a stiff 7Reed, W. H., III; Foughner, J. T., Jr.; andbackup structure, the flutter speed is changed Runyan, H. L., "Decoupler Pylon: A Simple,but remains well above the flutter speed of the Effective Wing/Store SuDpressor," AIAA Journalnominal stiff pylon, of Aircraft, Vol. 17, No. 3, March 1980,

(2) If the st_r_ static pitch deflection pp. 206-211.

due to preload exceeds the linear range of the 8Anon., "Military Specification MIL-A-8591Esoft pitch spring (M/M > 1.0), flutter onset Airborne Stores, Associated Suspension Lugs,occurs at the same spe_d as for the linear and Aircraft-Store Interface (Carriage Phase);system with stiff pylon; however, the flutter General Design Criteria," January 12, 1976.amplitude is limited due to the stabilizingeffect of the softening pitch spring withincreasing deflection amplitude.

(3) If the static preload exactly equalsthe load required to bottom the system(M/Mo = I), the flutter speed becomes independent

of amplitude, as in a linear system, but is afunction of N, the ratio of hard springstiffness to soft spring stiffness.

NONLINEARSPRING LOAD EQUIVALENTLOAD

K M(t)

..... MIT--_FREQUENCY M(]_- _'---_-------_ _- -_._7=---- -t- _t- ---- "%_F t

BENDINGMODES-A_ I 80 e..... _ _ , t' l/'--_ l /'-SINUSOIDAL

_=_--_ _DECOUPLERPYLON ! I D,SP_CEMENTEQUIVALENTSPRINGCONSTANT:

_WITH OFFSET M1

RIGID PYLONFLUTTER FLUTTER

,._ .qm Ke "_']AIRSPEED - 6K

Fig. 1 Effect of decoupler pylon on tfl utter speed,

Fig, 3 Representation of nonlinear springby an equiv.alent linear spring.

20

FPIVOT_NK_NK _K

o@( , , r6

/__ SOFTENING

5 SPRING

NK 6"

M 0 l f f HARDENING0 .2 .4 .6 ,8 ].0 SPRING

e ed°o

O0 Fig.4 Describingfunctionfor bilinear

spring (N = 20).

Fig, 2 Decoupler pylon with nonlinearpitch stiffness.

3.0- _M ool.Ov/v

nora

2.5" 4LINEARSYSTEM ' NONLINEARSYSTEM(N"20)

6 M -- i_ .0

1.5 _ 1.l

NK FLUT - 3

l.O / FLUTTER " 6........ I- I0

0 _-STIFFPYLON

.5 l I I I I I I I I20 15 i0 5 0 .2 .4 .6 .8 1.0

l l I l I 5 01/00

0 4 8 12 16 20 Fig.7 CalculatedflutterboundariesforN I/4-scaleF-16modelwith nonlinear

Fig.5 Describingfunctionfor transition pylonstiffness(config.32, ref. 7).between hardening spring andsoftening spring that occurs when.= M .

o

4 /--DIVERGENTLINEARSTIFFNESSVIVnom NONLINEAR /_ FLUTTER

3 STIFFNESS /_/M0 V/Vnom.--I._.6

__D_I'O1 A _LINEARSYSTEM 4 /_ f--''L'>----'----- ._ ''--3NONLINEARSYSTEM(N-201/.... --2fVl/MOFIUTTER

- IPIITUDE 3 _\\.../ / -"_ 11

NOELU,TERI __+ FLUT,ER /__! • , --_--_--oI7------4..... Z_pZ-___-_---:_I:o5 _I_ "-DECOUPLERPYLON"

III /_ -U

6 i r I I I t I I I' .s _o l_ lo _ o .2 .4 .6 .8 1.o' ' I 6 8118001513

-( I.o°1100 Fig. 8 Calculated flutter boundaries forflutter research model with nonlinear

Fig. 6 lllust-ation of method for determining stiffness (config. l, ref. 6).wing/score flutter boundaries withnonlinearpylonstiffness. N : 20.

6

• .. • . .._..;.....:..;;]:._ ....

1. Report No.

NASA TM-8l7892. Government Accession No. 3. Recipient's Catalog No.

4. Title and Subtitle

WING/STORE FLUTTER WITH NONLINEAR PYLON STIFFNESS

7. Author(sl

Robert N. Desmarais and Wilmer H. Reed, III

5. Report Date

April 19806. Performing Organization Code

8. Performing Organization Report No.

9. Performing Organization Name and Address1----------------------------; 10. Work Unit No.

505-33-53-01NASA Langley Research CenterHampton, VA 23665

11. Contract or Grant No.

12. Sponsoring Agency Name and Address1----------------------------; 13. Type of Report and Period Covered

Technical MemorandumNational Aeronautics and Space AdministrationWashington, DC 20546

14. Sponsoring Agency Code

15. Supplementary Notes

This paper will be presented at the AIAA/ASME/ASCE/AHS 21st Structures,Structural Dynamics and Materials Conference, May 12-14, 1980, Seattle, Washington.

16. Abstract

Recent wind tunnel tests and analytical studies show that a store mounted on apylon with II soft ll pitch stiffness provides substantial increase in flutter speedof fighter aircraft and reduces dependency of flutter on mass and inertia of thestore. This concept, termed the decoupler pylon, utilizes a low-frequency controlsystem to maintain pitch alignment of the store during maneuvers and changingflight conditions. Under rapidly changing transient loads, however, the alignmentcontrol system may allow the store to momentarily bottom against a relatively stiffbackup structure in which case the pylon stiffness acts as a hardeninq nonlinearspring. Such structural nonlinearities are known to affect not only the flutterspeed but also the basic behavior of the instability. This paper examines theinfluence of pylon stiffness nonlinearities on the flutter characteristics of \1ing­mounted external stores.

17. Key Words (Suggested by Authorlsll

Nonlinear systemsFl utterStoresDescribing functionAeroel asticity

18. Distribution Statement

Unclassified - Unlimited

Subject Category 08

19. Security Classif. (of this report)

Unclassified20. Security Classif. (of this pagel

Unclassified21. No. of Pages

622. Price"

$4.00

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