INTEGRATED CONCEPTUAL DESIGN OF JOINED-WING

8/13/2019 INTEGRATED CONCEPTUAL DESIGN OF JOINED-WING

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APPLICATIONOFADAPTIVEMATERIALSIN FLUTTERSUPPRESSIONOFAIRCRAFTSTRUCTURESC O N T R A C TNo.SPC-98-4082

SubmittedbyProf.AfzalSuleman

InstituteSuperiorTecnico DepartamentodeEngenhariaMecnica

Av .RoviscoPais1096LisboaCodex

PORTUGAL Tel:351-1-8417324Fax:351-1-8474045

E-mail:suleman(a),ist.utl.pt

F I NALR E P O R TOctober1998-October1999

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October1999 3 .EPORT TYPEAN DDATESC O V E R E D

FinalReport4. ITLEAN DSUBTITLE

Applicationof AdaptiveMaterialsfo rFlutter SuppressioninAircraftStructures

6. U T H O R ( S )Dr.AfzalSuleman

7.ERFORMINGORGANIZATIONN A M E ( S )AN DA D D R E S S ( E S ) InstitutoSuper iorTecnico DepartmentodeEngenhar iaMecanica Av .RoviscoPais,Lisbon1096 Po rtugal

9.PONSORING/MONITORING A G E N C YN A M E ( S )AN D A D D R E S S ( E S ) EOARD P S C80 2BO X14FP O09499-0200

11 . S U P P L E M E N T A R YNOTES

5.UNDINGNUMBERS F61775-98-W E125

8.ERFORMINGORGANIZATIONR E P O R TNUMB ER N /A

10.S P O N S O R I N G / M O N I T O R I N GA G E N C YREPORTNUMB ER S PC 98-4082

12a.DISTRIBUTION/AVAILABILITY S T A T E M E N T Approved for publicrelease;distributionisunlimited.

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ThisreportresultsfromacontracttaskingInstitutoSuperiorTecnicoasfollows:h econtractorwil linvestigateth eapplicationofintegratedadaptiveactuatorsoth eproblemoffluttercontrolinaircraftstructures.h eresearchwil lfocusonelectro-mechanicalfiniteelementmodels (FEM) their application tosimulationsof flutter onairframecomponents.

14.S U B J E C T T E R M S EOARD,StructuralDynamics ,StructuralMaterials

17.S E C U R I T YC L A S S I F I C A T I O NOFREPORT U N C L A S S I F I E D

18. S E C U R I T YCLASSIFICATION OF T H I SPAGEU N C L A S S I F I E D19 ,S E C U R I T YC L A S S I F I C A T I O NOF A B S T R A C TU N C L A S S I F I E D 15 . NUMBER OFPAGES 6 116 .PRICECODEN /A 2 0.LIMITATIONOFA B S T R A C TUL

N S N7540-01-280-5500 S t a n da r dor m9 8Rev.-89) Prescribed by A N S IS t d .239-18298-102


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EXECUTIVESUMMAR Y

Inecentears,igorousesearchnmaterialscienceasesultednheevelopmentofmultifunctionalmaterials.Thesemechano-electro-magneto-thermo-rheologogicalmaterialswhenembeddedinadaptivecompositesystemshavepresentedanexceptionalpromiseinth efieldsofactiveibrationuppression,hapeontrolndoisettenuation.oreformationfhin structuralelements,themostwidelyusedmultifunctionalmaterialsar epiezoelectricactuators.Piezoelectricshavehigherbandwidthsthanarepossibleinshapememoryalloys,theyar emorecompactthanmagnetostrictivedevicesan dtheyarebidirectionalbynatureunlikeelectrostrictivematerials.esignroblemsnircrafttructuresequiringctiveolutionssingdaptivecompositestosuppressvibrationan dcontrolth eshapeofthestructurear epresented. Panelflutterisaself-excitedoscillatingphenomenonan dinvolvesinteractionsbetweenelastic, inertiaan daerodynamicforces.Whenaflightvehicletravelsathighsupersonicspeeds,tm ay experiencenonlinearlimitcycleoscillationsduetoth edynamicpressurean dhighaerodynamicheatingemperatureradients.nrderonvestigateheerformanceofactivematerialsnpanelfluttersuppression,coupledelectro-thermo-mechanicalnonlinearpanelflutterequationsofmotionreerivedsingheinitelementmethod.Modelsordaptiveompositehallowshellswithmbeddediezoelectricctuatorsndensorsreeveloped.assivendctiveflutteruppressionfdaptiveompositeircraftki nanelsreresented.oundary conditions,in-planeforcesan dshellcurvatureeffectsarestudied.Theresultsrevealthatactivefluttercontrolusingpiezoelectricbendingcontrolactionsisfeasible.Experimentalsubsonicaeroelasticflutteran d buffetingsuppressionusingpiezoceramicactuatorsan dsensorstoimpartchangesindampingan daerodynamiccharacteristicstoth ewinghavealsobeennvestigated.nppreciableuffetingeductionwasbtained,speciallywhensingairfoilshapecontrol,whichcombinedwithth erootactuatorswereabletodecreaseth eaverageamplitudenuffetingrom2%o7.5%.heirfoilhapeontrolls oecreasedhe frequencyfheibrationy4% .oesolveheiminishingontroluthorityfhe piezoceramicactuatorsasairspeedisincreased,th eairfoilshapecontrolha spresented afeasiblesolutionwhereth epiezoactuatorsareusedtocreateafavourablevariationinliftcharacteristics.


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ACKNOWLEDGEMENTS

TheEuropeanOfficeofAerospaceResearchan dDevelopment(EOARD)underContractNo .SPC-98-4082hasupportedth ecurrentinvestigation.Thisinvestigationwasaccompaniedan d monitoredbyDr .V.B.Venkayya,atth eAirForceResearchLaboratory,Wright-PattersonAFB an d MajorJerrySellersatEOARD.


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Chapter1 -AdaptiveStructuresTechnology Chapter2-NonlinearPanelFlutterChapter3 -AdaptiveCompositeModelling Chapter4-FlutterAnalysisan dControlChapter5-ExperimentalBuffetSuppression Chapter6-Conclusionsan d FurtherWork

References


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CHAPTER1

ADAPTIVESTRUCTURESTECHNOLOGYInthepastdecade,technologicaldevelopmentsinmaterialsan dcomputerscienceshaveevolved toheointwhereheirynergisticombinationav eulminatedn ewieldofmulti-disciplinaryesearchndaptation.hedvancesnaterialciencesav erovidedcomprehensivendheoreticalrameworkormplementingmultifunctionalityntomaterials,an dth edevelopmentofhighpeeddigitalomputersha spermittedth etransformationofthatframeworkintomethodologiesfo rpracticaldesignan dproduction.Theconceptiselementary:ahighlyintegratedsensorsystemprovidesdataonth estructuresenvironmenttoaprocessingan d controlsystemwhichinturnsignalsintegratedactuatorstomodifythestructuralpropertiesinan appropriatefashion.Th eultifunctionalechano-electro-magneto-thermo-rheologicalaterialsmbeddednadaptiveompositeystemsav eresentednxceptionalromisenngineeringesignproblemsrequiringsolutionsinactivevibrationsuppression,shapecontrolan dnoiseattenuation.Piezoelectricmaterials,hapememoryalloysan dmagnetostrictive materialsar eth ethreemostrecognizedtypes.hesematerialseveloptrainsrisplacementswhenxposedtolectric,thermalan dmagneticfields,respectively.

ActuationTechnologyWhentheshapem em o r yalloyisheatedabovecriticaltemperatureth ematerialrecoversitsoriginalpre-deformedshape.Th emostcommoncommerciallyavailableshapememoryalloyisNitinol.hi slloyser yuctilendaneeformedasily.nddition,tls oasoo d strengthan dstrainrate,itiscorrosionresistant,nditistableathightemperature.Alimited numberofeffortsaimedatusingshapememoryalloysasactuatorsincompositestructureshavebeenmade.ecenttudiesncludeheworkyBoydndagoudas1]herehe yav edevelopedamicromechanicalmodelorshapememorycomposites,nd Sullivan2] ,whoha sdevelopedamodeltopredictshapememorycompositebehaviour.Othersignificanttheoretical


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studiesonthemodelingofsystemscontainingshapememoryalloysincludeth eworksby Liangan dRogers3] ,en gndi4]ndGraesserndCozzarelli5] .esearchnsinghapememoryalloysinactivestructuralcontrolincludeth eworksbyBazetal6] ,Ikegamietal7]an dMacleanetal[8].

Magnetostrictivematerialsxhibit hangenimensionwhenlacednmagneticield.Terfenol-Dsheos topularommerciallyvailableagnetostrictiveaterial.ecentresearchonmagnetostrictivematerialsshowsthattheyprovidestrokessignificantlylargerthantheirelectromechanicalcounterpartshowevertheytendtobedifficulttoimplementinstructural systems9] .orknompositesncorporatingagnetostrictiveaterialsncludehe unimorphsbyHondaetal[10]an dthemicro-compositesystemsby Bian dAnjanappa[11] .Piezoelectricaterialsresentwoistinctharacteristics:hedirect'iezoelectricffectoccurshen iezoelectricaterialecomeslectricallyhargedhenubjectedomechanicalstress.Thus,thesedevicesca nbeusedtodetectstrain,movement,force,pressureor vibrationyevelopingppropriatelectricalesponses.heconverse'iezoelectricffectoccurswhenth epiezoelectricmaterialbecomestrainedwhenplacedinnelectricield.he abilitytoinducestrainca nbeusedtogenerateamovement,force,pressure,orvibrationthroughtheapplicationofasuitableelectricfield.Th emostpopularcommercialpiezoelectricmaterialsareleadzirconatetitanate(PZT)an dpolyvinylidenefluoride(PVDF).Th epotentialofapplying piezoelectricmaterialssistributedctuatorsnompositetructuresasesultedneveralsignificanttudies.ulemanndenkayya12]av eodelled impleompositelatestructurewithpiezoelectriclayersusingclassicallaminationtheory,however,th efirstreported studiesonadaptivecompositesincludeth eworksby Baileyan dHubbard[13],Crawleyan ddeLuis[14],Leibowitzan dVinson[15]an d Wangan dRogers[16].Theelectrostrictivephenomenonisanonlinearpropertywhichexistsinal ldielectricmaterials.Whennlectricieldisppliedcrossnelectrostrictivematerial,heositivendnegativeionsaredisplacedan dastrainisinducedinthatmaterial.Theresultingstrainisproportionaltothequareofth eppliedelectricieldan dindependentoftheppliedelectricield'spolarity.Sincehetrainsroportionalohequareofthelectricield,hetrainwilllwayse


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positive.hi ssnalogousithheagnetostrictiveehaviorescribedarlier.heos tpopularelectrostrictivematerialisleadmagnesiumniobate(PMN);however,thismaterialisstillno tidelyvailablenheommercialarket.heseaterialsenerallyfferigherelectricallynducedtrainithowerysteresisha nheiezoelectricaterials,oweverconstitutivemodelsorelectristrictorsareno tasmatureasmodelsfo rpiezoelectricsduetothenonlinearities.Hornan dhankar17]av eormulatedullyoupledconstitutivemodelor electrostrictiveceramicmaterials.Electrostrictivematerialsusedasdistributed actuatorelementsinadaptivecompositeshaveno tbeenreportedinth eliterature.Magneto-an delectro-rheologicalfluidsaremultiphasematerialsconsistingofadispersionofpolarizableparticlesinacarrieroil,an dtheyexhibitpropertiesofatypicalviscoelasticmaterial.Th etilizationofelectro-rheologicalmaterialsorvibrationampingasee nth eubjectofconsiderableesearchincethesematerialsxhibitfast,eversiblendcontrollablehangesnbehaviour.owever,npiteofadvancesnensingndontrols,undamentalheologicalresearchasappliedtovibrationdampingha slagged behind.Specifically,essentialinformationintermsofmaterialasedtructureeliabilityndontrollabilitystilleededouccessfullyimplementsuchsystems.Typically,th eperformanceofanactuatorisevaluatedintermsofth efollowingcharacteristics: displacement(theabilityoftheactuatortodisplaceanobject;orcegeneration(theamountofforcehectuatoranroduce);ysteresistheegreefeproducibilitynositioningoperations);responsetime(howquicklyanactuatorca nstarttheactuationprocess);bandwidth(rangefrequenciesnwhichhectuatoranperateffectively;emperatureangefoperation;repeatabilityan dprecisionoftheactuator;powerrequiredtodriveth eactuator;massofactuatormaterialrequiredfo ragivenisplacement;ndcost.ableresentstheeneralcharacteristicsofcommerciallyavailableactuators[18].ThepiezoelectricPZ Tprovidesthepotentialfo rth egreatestforcehandlingcapability.PZ Talsooperateswithth ehighestbandwidthofthemicroactuatorsan damongth ehighestdisplacements. ElectrostrictivePM Npossessesth elowesthysteresisofan yof th eactuatormaterials.


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SensingTechnology

Opticalibersmakexcellenttrainensorsecausehe yremmuneolectromagnetic interference.Opticalfibersca nbebondedtoth esurfaceofastructureorembeddeddirectlyintoth etructure.Therearemanytypesofopticalibersensors.Th emoreusefulfiberopticbasedstrainsensorsusesth eintrinsicpropertiesoftheopticalfiber.Inanintrinsicfibermeasurement,on eormoreoftheopticalfieldparameters,whichincludefrequency,wavelength,phase,modeindex,olarization,ndexfefractionndttenuationoefficient,reffectedyhe environment.

Piezoelectricsensorsen dtoperatees tnynamicituationsecausehenducedhargeimbalancesreatedytrainingheaterialissipatewithime.owuicklyhi sccursdependsnth ematerialsapacitance,esistivityndutputoading.orceransducerstilizepiezoelectricelementstoproduceanelectricaloutputwhichisproportionaltotheappliedforce.Th eorcetransducerismountedinserieswiththeorcetransmissionpathinordertoirectly exposethepiezoelectricelementtoth eforceswhicharetobemeasured.inceth epiezoelectricispreloaded,th eforcesensorca nmeasurebothtensilean dcompressiveforces.Ahighstiffness ensuresahighresonantfrequencyan ditwillhaveaminimumeffectonthestructuralintegrity. Inth ecaseofsensors,th etechnologiesconsidered fo rth eadaptivecompositesmustbeabletowithstandth eompositemanufacturerocess.mbeddingssuesmakeNitinol uestionablechoice.Iftheshapememoryalloyhad tobeelectricallyinsulatedfromtheconductivecomposite itwouldcomplicatethecompositemanufacturingprocessan dincreaseth ecostsignificantly.Th eperformanceofan ysensorca nbeevaluatedintermsofsensitivity(amountofsignalwhichasensorwillproducefo ragivenchangeinthevariable);thelengthoverwhichth emeasurementismade;bandwidth(thefrequencyrangeoverwhichth esensorremainseffective);responsetime(thepeedatwhichth eensorca nrespondtoachangeinth evariable);thetemperaturerangeoverwhichthesensorca noperate;repeatabilityan dprecisionofth eactuator;weightan dcost.Table2presentsarelativeassessmentofthesensortypesconsideredsuitablefo rembeddinginadaptivecompositesystems.


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Table2-SensorTechnologyAssessmentFffiEROPTICS PZT

Sensitivity moderate moderate GageLength moderate high Bandwidth high moderate Resolution high moderate TemperatureRange high high

Th etemperaturerangeiscriticaltoth eadaptivecompositesystembecauseitisanticipatedthattheensorsm ayembeddedndwouldhereforendergoheompositeuringrocess.Embeddingwould befeasibleinthecaseoffiberopticsensors,bu tno tasdesirablein thecaseofPZTstrainsensors.Fromanassemblyan dhandlingpointofview,straingaugesorevenPZ Tarefavoredbecauseoftheavailability ofknowledgean dexperiencewiththesetechniques.

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CHAPTER2

NONLINEARPANELFLUTTERPanelflutterisaself-excitedoscillatingphenomenonan dinvolvesinteractionsbetweenelastic,inertianderodynamicorces.tsupersonic/hypersoniceroelastichenomenonha tsoftenencounteredinth eoperationofaircraftan dmissiles.Th eairflowsonon esideof thepanel.Becauseofthelargedeflectiongeometricaltructuralnonlinearity,imitcyclescillationswilloccurbeyondth eriticalynamicressure.When lightvehicleravelsthighupersonicspeeds,itwillexperienceflutterduetoth edynamicpressurean dhightemperatureowingtotheaerodynamicheating.Th epresenceofhightemperatureloadresultsinafluttermotionatlowerdynamicpressures.naddition,thetemperaturerisem ayalsocauselargeaerodynamic-thermaldeflectionsoftheskinpanels,whichaffectflutterresponsean dca nleadtochaoticmotion.Th emodeoffailurefo rpanelflutterisfatigueduetolimit-cycleoscillations.Toincreaseth ecriticaldynamicressurerouppressheimit-cyclescillationss,herefore,nefthean yimportantfactorsthatanaircraftdesignershouldconsider.

Althoughtherehasbeenavoluminoustheoreticalliteratureonth epanelflutterproblemoverthepast0ears,mostnalysisal lntoneofth eou rategoriesasednhetructuralnd aerodynamictheoriesemployed:

inearstructuraltheory;quasi-steadyaerodynamictheory inearstructuraltheory;fulllinearized(inviscid,potential)aerodynamictheory onlinearstructuraltheory;quasi-steady aerodynamictheory on-linearstructuraltheory;fulllinearized(inviscid,potential)aerodynamictheory

Ofheseourolutionethods,heineartructural/quasi-steadyerodynamicpproach comprisesthegreatbulkofth eliteratureduetoitssimplicity.Unfortunately,thisapproachdoesno taccountfo rstructuralnonlinearities,thereforeitca nonlydetermineth eflutterboundaryan d givenoinformationaboutth eflutteroscillationitself.urthermore,th eus eofthequasi-steady

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aerodynamicsneglectsth ethree-dimensionality an dunsteadinessofth eflow;henceitcannotbe usedinthetransonicflightregime.Anonlinearstructural/inviscidpotentialtheoriesrepresentthestateof th eartin panelflutteranalysis.Anumberofclassicalanalyticmethodsexistfo rth einvestigationoflimitcycleoscillationsofpanelsinsupersonicflow.Ingeneral,Galerkin'smethodisusedinth espatialdomain,wherethepaneldeflectionisexpressedintermsoftw otosixormorelinearmodes;an dvarioustechniquesinthetemporalomainuc hastheumericalntegration,armonicbalance,nd perturbationmethods,tociteafew,areemployed.Al loftheanalyticalinvestigationshavebeenlimitedto2- to3-dimensionalrectangularplateswithallfouredgessimplysupportedorclamped.Th eclassicapproachesalsoindicatethatatleastsixlinearlinearnormalmodesarerequiredfo raconvergedlimit-cycleamplitude.Earlyworksnanellutterwereoncernedmainlywithonventionalsotropicanels.he researchprogressndom eoftheeferencesanbeound,orxample,ntheextbooksbyFung[19] ,Bisplinghoffan dAshley[20],an dDowell21].Olson[22],anderetal23],Yangan dSung[24],an dM ei[25],amongothers,havestudiedtheflutterofisotropicflatpanelsusingthefiniteelementmethod.Somestudieswerealsodevotedtoth eflutterofcompositepanels.Fo rexample,Pidapartian dYang[26]considered th eeffectsofboundaryconditionsan dfiberangleofpanelsonth eflutterboundaries.Rosettosan dTong[27]appliedahybridstressfiniteelementmethodan dusedlinearizedpistontheorytoanalyzeth eflutterofanisotropiccantileverplates.Theirresultsndicatehatfluttercharacteristicsretronglydependentonth eompositeiberanglean danisotropy.rinivasanan dBabu[28]tudiedthepanelflutterofcross-plylaminatedcompositesbyusingtheintegralequationsmethod.Linetal[29]usedan8dofhighprecisiontriangularinitelementoerformlutternalysisofsymmetricallyaminatedompositepanels.Theirtudiesncludedtheffectsofcompositeiberangle,rthotropicmodulusratio,flowirection,nd,erodynamicampingnhelutteroundaries.awyer30 ]se dhe Galerkinmethodtostudyboththeflutteran d bucklingproblemsofgenerallaminatedplateswithsimplyupportedoundaryonditions.yibo31 ]resentednnalyticalpproachy combininglassicallateheoryndAckeret'serodynamictripheoryotudyhelutterbehaviourofanorthotropicpanel.Leean dCho32 ]an dLiaw[33]haveinvestigated theus eof

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compositeanelsnlutterroblems.eendee34 ]av eerformedupersoniclutteranalysisofanisotropicpanelstakingintoconsiderationth eeffectsofpanelgeometry,boundary conditions,laminationscheme,flowdirectionsan d thermaleffects.

Extensionofth einitelementmethodsotudyonlinearupersonic/hypersonicimitycleoscillationoftwo-dimensionalisotropicpanelsweregiven by Zhouetal[35],Ra oan dRa o[36],Sarmaan dVaradan[37],an dGrayan dM ei[38];threedimensionalisotropicpanelsby M eian d Weidman[39],M eian dYang[40],an dHanan dYang[41];an dlaminatedcompositepanelsby Dixonan dM ei[42]an dLiawan d Yang[43].

Inmostofth eclassicndfinitelementnonlinearpanellutterstudies,th eeffectsofuniform temperaturehangearetreatedbyanequivalentsystemofmechanicaloads.ewlinearpanelfluttertudiesav eealtwithtemperatureistributionsirectly.Reportedtudiesncludehe paperby Liaw[44]an dX uean dM ei[45]haveextended th efiniteelementmethodtoinvestigatetheonlinearlutteresponsesoftwo-dimensionalanelswithemperatureistribution.he thermalnvironmentanffectanelotionsyntroducinghermaln-planeorcesnd bendingmoments.Inanellutteruppressionesignroblems,heonventionalesignpproachasee noincreaseheaneltiffnessesultingndditionalweightWithhedventofmultifunctionalmaterialsnd adaptivetructuresechnology,heresbeenonsiderableffortreportednth eliteratureinvestigatingtheapplicationofadaptivematerialsan dstructurestechnologyfo rpassivean dctiveontrolofflexibletructures.elativelyewnvestigationsav eoncentratednactivepanelluttercontrol.cottan dWeishaar46 ]ndHajelaand Glowasky47 ]roposed linearanellutterontrolsingiezoelectricctuatorsndensors.houtl48]av eextendedtheus eofpiezoelectricactuatorsan dsensorstoincludeth enonlinearpanelflutter.Xue an dM ei49 ]av eecentlytudiedtheeasibilityofapplyinghapememorylloysninearpanelsuppression.

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ProposedDesi g nMethodologyThistudypresentsnoptimalcontrolmethodtouppressth epanellimit-cyclescillationsatdynamicpressuresgreaterthanth ecriticalvalueusingpiezoelectricactuatorsan dsensors.Th enonlinearinitelementquationsofmotionreevelopedbasednth eonlineargeometriclargeeflectionheory. initelementmodelorndaptiveompositehallowhellsdevelopedsubjecttoaerodynamican d thermalloads.

Tw oontroltrategiesremployedtossessth eerformanceofth eiezoelectricctuators.First,hen-planepassivectuationcapabilityofth epiezoelectricpatchessmeasuredan ditseffectnheerodynamicarametersuantified.hispproacheliesntiffeninghe structurebyapplyingin-planeloadstoth estructureduetodenticalelectricalfieldstothetopan dbottomlayersofpiezoelectricsnthetructure.heecondapproachconsistsofactivelycontrollingthestructurebyallowingthepiezoelectricpatchestoactuateinbending.Byapplying th eoptimalontroltheory,endingcontrolctionsanbeeterminedbasedontheinearizedequationsofmotion.Numericalsimulationsbasedon th enonlinearequationsofmotionareperformedtodemonstrate theeffectivenessofth epiezoelectricactuators.Th eperformanceoftheactuatordesignsan dthemaximumflutter-freedynamicpressureareinvestigatedan d presented.

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CHAPTER3

ADAPTIVECOMPOSITEMODELFo rheas twoecades,hereasee nnncreasedesearchctivitynhere aoffiniteelementmodellingofadaptiveomposites.herimarynterestasee nnhenalysisofpiezoelectricallyactuatedcompositesan dearlyinvestigationsweredevotedtothree-dimensionalelectromechanicallements.mongheeportedtudies,zo undseng50 ]av esed variationalmethodsomodelinitelementiezoelectricolids.Hatl51 ]evelopedneight-nodethree-dimensionalcompositebrickfiniteelementfo rmodelingth edynamican dstaticresponseflaminatedompositesontainingistributediezoelectriceramicsubjectedomechanicalan delectricalloading.Th eelectricalpotentialistakenasanodaldegreeoffreedom,leadingonlementwithou regreesfreedomerode.heseodelssinghree-dimensionalinitelementsaniv eccurateesultsyettingomputationallyxpensive refined mesheswithacceptableaspectratios.Classicalplatetheorieshavebeenproposedfo rth enalysisofrectangularpiezoelectricplates(LeendMoon52],CrawleyndLazarus53],Wangan dRogers54 ]ndLam etal55]).Otherplateformulationsincludeth eworkreportedbyChandrashekharaan dAgarwal56],who usedafiniteelementformulationbasedonfirst-ordersheardeformationtheoryfo rmodelingthebehavioroflaminatedcompositeplateswithintegratedpiezoelectricsensorsan dactuators.Th edevelopedmodeldoesno tintroduceth evoltageasanadditionaldegreeoffreedom.Tzouan dYe [57]resentedaminateduadraticCiezoelasticriangularhellinitelementsinghe layerwiseonstanthearngleheorywhichccountsor onstantpproximationofthenonlinearross-sectionalarpingppliedoiezoelectricaminatedystems. odelcontaininganactuatorelement,nadhesiventerfaceelementan daneight-nodeisoparametric plateelementwasdeveloped by Linetal[58].Ananalyticsolutionisalsoderivedan d resultsarecomparedwithth efiniteelementmodel.Chattopadhyayan dSeeley59 ]se dafinitelementmodelbasedonarefinedhigherordertheorytoanalyzepiezoelectricmaterialssurfacebounded ormbeddednompositeaminates.heisplacementieldccountsorransversehearstressesthroughthethicknessan dsatisfiesth eboundaryconditionsat th efreesurfaces.hrough

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numericalexamplestheyshownthattherefinedtheorycapturesimportanthigherordereffectsthatreotmodeledyhelassicalaminateheory.ecently,odelssingigher-ordertheoriesfo rpiezoelectriclaminatesca nbefoundinReddyan d Mitchell[60]an dJonnalagaddaet al[61],amongothers.Veryfe wcompositeshellelementswithelectromechanicalpropertieshavebeenreportedinth eliterature.A-nodedhelllementxtendinghehallowhellheareformationtheoryas beenproposed,usinganequivalentsinglelayermodelfo rathreelayershell62].An8-noded quadrilateralshellelement[63]withnoelectricaldegreesoffreedomusingth e3D-degeneratedshelltheoryha salsobeenproposed,whereth epiezoelectriceffectwastreatedasaninitialstrainproblem.Anxisymmetric-noderiangularhelllementaslsoee nevelopedtotudymooneytransducers64].A2-nodeddegenerated3Dshellelementwithalayer-wiseconstantshearngleasee normulated65].However,moreesearchsequiredtonderstandnd quantifyth einfluenceofthecurvatureonth epiezoelectricactuatorsan dsensors.ulemanan d Venkayya[12]av ereportedanefficientfinitelementormulationorvibrationontrolofalaminatedcompositeplatewithpiezoelectricsensorsan dactuators:Bymodellingtheplatean d theensor/actuatorystemwithheou rodedilinearMindlinlatelement,heroblemsassociatedwiththesolidelementareeliminatedan dmodellingth eplatean dth esensor/actuatorsystemwithheou rnodedbilinearMindlinplatelementonsiderablyeducesheroblem size.Inthepresentinvestigation,heimpleuadrilateralplateinitelementha sbeenextendedto includeth eeffectofcurvaturefo rtheanalysisofadaptivelaminatedcompositeshallowshells.Theinitelementsuadrilateralnhapendasightodalointswith0egreesoffreedom.Theobjectiveistoactivelycontrolflutterusingadaptiveshapean dvibrationcontrolofaircraftskinompositepanelswithmbeddedpiezoelectricctuatorsndsensors.igurehowstheadaptivecompositeconfigurationan dthedirectionofpolarizationofthepiezoelectriclaminatesthatm ay compriseatypicalwingorfuselageskinpanel.

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i

pt^rdirection

' A O A f f l v f f ,coMrosrrK^LAn

Figure1-Adaptivecompositeconfigurationandth edirectionofpolarizationofth epiezoelectriclaminatesTh eformulationan dimplementationofastructuralanalysisprogramtostudyfluttersuppressionofcurvedpanelsusingadaptivecompositeshallowpanelsispresentednext.hallowshellsaresurfaceswithnegligibleurvatureomparedtoitspan.hemediansurfaceisefinedbytheradiusofcurvatureRxand Ry nd thetwistradiusRxy,al lassumedconstant.EquationsofMotion Toeriveth equationsofmotionfo rth eaminatedcompositeplate,nanaerodynamicield withiezoelectricallyoupledlectromechanicalroperties,w eseheeneralizedor mofHamilton'sprinciple

5' 2[T-Tl+ W +W]dt= 0 1 (1 )whereTisth ekineticenergy,Isth epotentialenergy,Wm isth eworkdoneby th emagneticfield,W e isth eworkdonebyth eelectricalfieldan dWaistheworkdonebyth eaerodynamicforces.hekinetican d potentialenergiesca nbewrittenintheform

T= \-puTV ;= j-STTd1 7


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wherecndTcreth egeneralizedelastictrainan dstressectors.heworkdonebytheelectricalforcesca nbewrittenas

1 W e=j-STTedVp 2

whereSesavectorofelectricalfield(volts/meter)nthepiezoelectricmaterial,ndTesavectorofelectricalisplacementscharge/area).nheontextofth eresentnalysis,tsassumed thattheworkdomeby th eelectromagneticforcesisnegligible.

ElectromechanicalConstitutiveRelationsFo riezoelectricsheropertiesreefinedelativeoheocalolingirection.Availablepiezoelectricmaterialshavethedirectionofpolingassociatedwithth etransversedirectionan d thematerialisapproximatelyisotropicinth eothertw odirections.nmatrixformtheequationsgoverningthesematerialpropertiesca nbewrittenas

T =eTS+eSTc=cScS

whereTesth eelectricdisplacementvector;sth edielectricpermittivitymatrix;cstheelastictrainvector;isth edielectricmatrixatconstantmechanicaltrain;estheelectric fieldvector;Tcstheelasticstressvectoran d sthematrixofelasticcoefficientsatconstantelectricfieldstrength.

Stress-StrainRelationsTh ecompositelaminateshellispresumedtoconsistofperfectlybondedlaminae.Moreover,thebondsarepresumedtobeinfinitesimallythin.Thus,ollowingth eclassicallaminationtheory,thestateofstressintheelementisgivenby

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S={T rp Spe IrpmpbpbpbptSptS\* xyyz yzEighteneralizedtrainsndnelectricalieldarametereraminaescribehetateof

deformationorMindlinhellithlectromechanicalroperties.hus,heugmentedgeneralizedstrainvectortakestheform

s = {sr= \s : s s

e]sm sb xyS* -E,z-E n]

Th estress-strainrelationshiptakesth eform

\Tec c 0 e" ~ S m~ m~ c c 0 e sb 00 0 gS1 0

er eT 0 e se 0AT

wheresth etransformedmodulimatrixfo reachlaminaincludingth epiezoelectriclayers.Th etransverseshearstiffnessmatrixsdefinedintermsofth etransversestrainenergythroughthethickness.Tsth etemperatureradientacrosstheaminatendc mretheoefficientsofthermalexpansionfo reachlamina.

Strain-DisplacementRelationsTh elargedeformationstraindisplacementrelationfo rageneralshellelementundergoingbothextensionan dbendingatan ypointthroughth ethicknessisthesu mofmembranean dchangeofcurvaturestraincomponents:

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sb= K l ,* 1 2 w2 w xx k .= < v,y w2y + z- W,yyMj-V 2ww ,x ,y 2wxy Th eshapefunctionsusedfo rthe8-nodedshallowshellelementare:A7=(l+^J(ll+7j77j(


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V

dNdx 00

dN* By

dN* dN*B y00

dx00

0 0 0 0 0 0

N [_ Ry yN*

0 0

dN* dxdN * dx

0 0 00dN * z-

0-N*

0 0 0dN* dx 0 dydN * dN *

:Zdxx N* 0

for i=l,---,nel

Th elementtiffnessndmassmatricesreirstvaluatedbyxpressingth entegralsnthelocalnaturalcoordinates an d 7 ]oftheelementan d then performingnumericalintegrationusingtheaussianuadrature.helementatricesrehenssembledobtainhelobalKssandMMatricesafterappropriatetransformationtoccountfo rth eurvednatureoftheshellsurface.Substitutingfo rthegeneralizedstressan dstrainexpressionsintoEquation(1),weobtainthemass,elasticstiffnessand piezoelectricstiffnessmatrices:

M =pKTNdV,Ki^ly eb dVj,KJm=jh *h dTj, for j=l>---,nel

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GeometrieStiffness

Inth epassivecontrolmethodologyadoptedinthistudy,theinplaneorcesgeneratedbythepiezoelectricactuatorsareccountedfo rthroughth enonlineargeometrictiffnessmatrix.he termsinth egeometricstiffnessmatrixfo ranelementar elinearfunctionsofth ecomponentsofstressnth element.orplatendhelllementstissualtoonsideronlythemembranestresses.helementsoftheeometrictiffnessmatrixKganbeerivedro m otentialenergyfunctionlggivenby theexpression

a 2n,K = JLg dxdywhereng= j\(xTGaX+X2 TGbX) TdS,

an d

du dy dw dv

dx Xi= dx dw G0=du dv dy dx dy

= 0

2 1 L 2

2 mm

2nfflxy

Th eembranetressomponentsrenitiallyeterminedyrescribing oltageohe piezoelectricpatchesndubsequentlythealculatedstressesreusedtoetupth eeometricstiffnessmatrix.

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AerodynamicLoads

Th eerodynamnicheorymployedthemostorflutteratsupersoniclo wM > v2jshe quasi-steady,firstorderpistontheory.Th eaerodynamicpressureca nbeexpressedas

Pa- 2 qJMI-I M > Ml-2.,

W eca nre-writethisequationinthefollowingform:

Pa\,DaDDao Q rp

where= paV 2/sth edynamicpressure;pasth eai rdensity; sth eairflowspeed,Msth eMachnumber, sth epanelength,D= Ehz/l2 l-v2)sth ebendingrigidity, stheradiusfurvaturend G ) 0=\D/phaA) is onvenienteference frequency.Th eon -dimensionaldynamicpressurean daerodynamicdampinggacoefficientsaregiven by :

X = 2 qaalDyJMl-l s\AM ~-ywhere = Ml-1,ndj ,=paa/m0istheir-panelmassrationdm 0stheveragemassdensityper unitareaofthepanel.Fo rhighsupersonicflowsi.e.(M l),ga~^X\ijM.Thus,theworkdonebytheexternalaerodynamicforcesisgivenby :

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w =-\ .Ddw ga w X D w a3x ( O 0 4t 2ra3/ w dA Substitutingntoquation1),webtainheollowingerodynamicampingndtiffnessmatricesforeachelement:

GJ= 8a X D2ra3JA KJ=X\NTNd

\TNdA, for j= l,-,nel

Theerodynamictiffnessmatrixisnon-symmetric,uetoth enon-conservativenatureoftheaerodynamicloading. Fo rtheentirestructure,usingth estandard assemblytechniquefo rth efiniteelementmethodan d applyingtheappropriateboundaryconditions,weobtainth ecompleteequationsofmotionfo rathermo-piezoelectrically coupledelectromechanicalcompositepanelinaflowfield

x 0" 0 0thermal stiffness KAT 0"

0 0\ u <

+ aeroamping

G 0" 0 0aerostiffnessIX 0"

0 0

l inear stiffness piezot iffness

where

Mccsth emassmatrix;Gsth eaerodynamicdampingmatrix;Kccsth elinearelasticstiffnessmatrix Ksth eelectromechanicalcouplingmatrix;

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Kee isthepiezodielectricmatrix;KAT isth einitialthermalstressstiffnessmatrix Kg isth enonlinearstiffnessmatrix Th eequationsofmotionfo ralaminatedadaptivecompositepanelwithpiezoelectricactuatorsan dsensorssubjected toaerodynamican d thermalloadshavebeenpresented.

SolutionProcedureToolveth eonlineareigenvalueroblem,nterativeroceduresused.oragivenetofaerodynamicarameter A,n-planeorce,od eumber,ndaximummplitude,he iterationstartsfromacorrespondinginitialmodeshapeobtainedfromlinearflutteranalysis,withamplitudescaledupbyasmallfactor.Basedonthisinitialmodeshape,thetangentialstiffnessmatrixKrisormed,ndnigenvaluendtsorrespondingigenvectorreound.hi seigenvectoristhencaledupgain,nd th eiterationcontinuesuntilth eonvergencecriterion| < p |orksachieved:

whereM, .sthechangeineigenvalueduringth ehterativecycle.When=0,th eproblemisreducedtoha toffindinghen-vacuorequenciesorheonlinearibrationofplates.Asdynamicpressure sincreasedfromzero,tw ooftheseeigenvalueswillusuallyapproacheach otheran dcoalescetocr t= X cr nd becomeacomplexconjugatepairfo r> X cr.Herecrisconsidered tobethatvalueofX twhichthefirstcoalescenceoccursfo raspecificamplitudeofthelimitcycleoscillation.


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CHAPTER4

FLUTTERANALYSISANDCONTROLToevaluateth epresentfiniteelementformulationan dsolutionprocedurean d tostudyth eeffectsofcertaindesignparametersonth enonlinearsupersonicflutterbehaviourofadaptivecomposite panels,aseriesofsimulationsfo rth enonlinearsupersonicflutteranalysisofadaptivecomposite panelswereperformed withtheresultspresented,discussed,an d physicallyinterpreted.

A25x25x0.025msotropicquareplate6061-T6luminum)w asusedinal limulationsan da10x10elementmeshwasused toobtaintheelementlinearstiffness,initialstress,nonlinearstiffness,mass,an daerodynamicmatrices.Thisgridwasshowntonumericallytobesufficiently finean daccuratefo ral lth epresentsimulationcases.Apreliminarylinearflutteranalysiswasperformedtoprovideinformationregardingth eairflowspeedatwhichthepanelbecomesdynamicallyunstablean dtheamplitudeofoscillationgrowswithtime.Asth eamplitudeincreasestoacertainlevel,th enonlineareffectsbecomedominantand theamplitudereachesaboundedvaluedefined by thelimitcycleoscillation.Typicaleigenvaluecoalescenceresultsobtainedby usingth efiniteelementmethodfo rasimplysupported plateareshowninFigure2.Theresultswerecompared withdatareported byM ei[25]an ditisobservedthatth epresentfiniteelementformulationgivesaccurateresults.

Bo u n d a r ysupporteffectInFigure,hepanelmplitudeofthelimitcyclescillationisivenasfunctionofAor simplyupportedndlampedboundaryonditions.heimityclescillationsreifferentsincetheclampedplateisamuchstifferstructurecomparedtoth esimplysupportedboundary conditions.

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2000

1500

1000

5 00

-500

-1000

6 00

A e r o d y n a m i cP a r a m e t e r

LFigure2-Typicalvariationof eigenvalueswithdynamicpressureforasimplysupported panel

1000

l_ Figure3-Limitcycleamplitudevs.dynamicpressurefo rsimplysupportedpanelfo rtwodifferentsupportconditions

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Effectofin-planeloadingFigure howsheanelmplitudes.erodynamicarameterorifferentn-planeorcesactingn implyupportedanel.helassicalulerucklingoadorimplyupported panelsisNcr=-7t2D/a2.Th etotalmembraneforceiscomposedoftheappliedin-planeload A^andthemembraneforceNxnduced by th elargedeflectionsofth epanel.Itisobservedthattheppliedcompressivein-planeorcereducesth eriticalynamicpressure.However,sthedynamicressuresncreased,heanelmplitudencreases,whichnducesensilen-planeforceshatounteractheppliedompressiveorces.hisrocessontinuesntil lutterdynamicpressureisreachedwhichcorrespondstoagivenlimitcycleamplitude.

2 000000 AerodynamicParameter 80 0L _

Figure4-Limitcyclemplitudevsynamicpressurefo rsimplysupportedpanelunderdifferentin-planeforces

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CurvedPanelsTh epplicationofth epresentshallowhelliniteelementformulationinfluttersimulationofsimply-supportedcylindricalan dspericalskinpanelsisshown.Th ecurvedpanelswereassumedtohaveradiusofcurvaturex=Ry=50 0cm.Theoalescenceofmodesorth eylindricalan dsphericalpanelsareshowninFigures5(aan db) ,respectively.Itca nbeobservedthator thecylindricalpanel,th efluttermodeiscausedby th ecoalescenceofmodesnd3,whilefo rthephericalshells,thecriticalflutteriscausedbyth ecoalescenceofmodesnd2orbothcases.Summarizing,thecurvatureha saneffectonthecoalescenceofmodesan dflutterdoesno tnecessarilyoccurby th ecoalescenceofthetw olowestmodes.

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w oo - K

30 0 0 -D ;3T 00 0D

mS i

1000 K 1

111i1i 111 i i i i2 3 4 0 0 5 B O O 7 6AerodynamicParameter

4000

3 0 0 0

C D 00 0CD raLJ

1000

:4:3 ; 2 ' K1

L 000 20 0 30 0 40 0 50 0 60 0 70 0 60 0AerodynamicParameterFigure5-Coalescenceofmodesforcylindricallyandsphericallycurvedpanelswithallsimplysupported edges.

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NONLINE R FLUTTER ONTROLPassiveControlBeforeattemptingtous epiezoelectricmaterialsinpanelfluttercontrolproblems,aknowledgeoftheegreefontroluthorityxhibitedy ypicaliezoelectricctuatoreedsoequantified.

Relationshipsetweenheppliedorcesndheesultantesponsesependponhe piezoelectricpropertiesofth ematerial,th esizean dshapeofth epatchan dth edirectionoftheelectricalndmechanicalxcitation.orexample,onsideratypicalpiezoceramicatchwithdimensionsx x .0 5m .Thetressreeengthhangenhen-planeirectionaneexpressedasDL=d3]Ea=6.6mm,whereE,th eelectricalfield,isth eappliedvoltageperunitlength.Th estrainfreeforceinthein-planedirectionduetoanappliedvoltageof40 0V isF= YduEbh=2 0 0 N. Th eeffectofin-planestressesisparticularlyimportantsincepassivecontrolca nbeimplementedby thein-planetressesgeneratedbythepiezoelectriclayersinthecompositepanel.twillbe assumedthatth epanelasreachedastateofequilibriumduetoth epresenceofth en-planestresses,an dth estabilityofth esystemwillbeexaminedatthatposition.Itisalsoassumedthatthepanelha sno treachedabuckledstate.heffectofthenitialpre-stressivesiseothegeometricstiffnessmatrixKgTh euestionthateedsoeaisedowsheiezoceramicatchapableofgeneratingsignificantforceoutputinordertoaffectthestiffnessofth epanel,an dthuspushbackth eflutterboundaryenvelope.Tensileloading,whichca nbegeneratedbypiezoelectricctuators,ausesthelutteroundaryohiftonsiderably.orxample,or imply-supportedanelwithdimensions30 x30 x0 .1cm ,therangeofin-planeforcethataffectsth ecoalescenceofthefirstmodeliesnthe2 0 0 to2 ,000 N range.tca nbeinferredthatanarrangementofpiezoelectric

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patcheswhereeachexertsanin-planeforceofapproximately2 0 0 N ,duetoanappliedvoltageof40 0V,couldconsiderablyaffectth epanelfluttercharacteristics.

First,le tusexamineth edevelopmentofflutterinth epanel,intheabsenceofan ypiezolectricactuation.Thealuminiumpanelissimplysupportedalongal lfourofitssides.Asth edynamicpressurencreases,heaturalrequenciesoftheirstan dsecondmodesge tcloser,untiltheycoalesce,nd theynamicpressure tthispointiscalledthecriticaldynamicpressure.or thisparticularpanel,neglectingth eaerodynamicdampingeffect,th ecriticaldynamicpressureparameters8 .8 si.fteroalescenceofth eirstwomodes,hemaginaryartsoftheeigenvaluesbecomesplit,on etowardsthenegativeside,an dtheothertowardsth epositiveside.When assesheriticaloint,heystembecomesnherentlyunstable,uc hha tmalldisturbancemakeshemplitudeofth eaneleflectioniverge.As ncreasesurther,he thirdan dfourthmodescoalesceaswell.Usingth eassiveontrolmethodology,heluttervelocityofpanels,rimilarlyth eriticaldynamicressure,anbencreasedbymakingiezoelectricctuatorsnducen-planeensileforcesthatalterth eeffectivetiffnessofthepanel.Theam evoltageisappliedtothetopan d bottompiezoelectriclayers,resultinginuniformcompressionortensionintheplate.Thisstaticloadingonditionntheanelnducesn-planetressesNx,yan dNxy.Thesetressesresubsequentlyusedtoalculateth egeometrictiffnessoftheplate,whichcouplesthen-planean dtransversemotionsofth epanel.Subsequently,thegeometricstiffnessmatrixisaddedtoth elinearstiffnessmatrix,an d th eeigenvalueproblemissolved.Th evaluefo rXatwhichacomplexsolutionexistsisconsideredtobetheonsetofflutter.Whenth epiezoelectricpatchescreateastateoftensioninth epanel,theynamicpressureincreases.fth epiezoelectricpatchesxertcompressiveforcesonth epanel,thedynamicpressuredecreases.

Now,le tusexamineapassiveactuationconfigurationinwhichth epiezoelectricpatchescoverthecenteroftheplate(Figure6).First,consideracasewhereth epatchescoveronly6 oftheplatearea.Here,th emassincreasesby17 duetoth eadditionofth epiezopatchestothebasestructure.bviously,heffectivetiffnesslsoncreases.tw asbservedhatheriticaldynamicpressureincreasedfrom36.8to46.9,animprovementof2 7 .Notethatthisincreaseis

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solelyduetoth ebondingofth epiezopatchestoth etopan dbottomsurfacesofth ealuminumpanel.ubsequently,heiezoatcheswerectuatedwith oltageof40 0and,nhisinstance,urtherncreaseof42 w asttained,elativeoheas ewhereooltagewas applied.ummarizing,betterperformancewasindeedattainedbyth epiezoelectricactuation.Theeffectivestiffnesswasincreasedbymerelyattachingth epiezopatchesinthefirstinstance,an dafurtherincreasewasobtained byactuatingthepiezopatcheswithanappliedvoltage. Next,heperformanceofapatchwhichovered2 5 oftheplatereawasssessed.Here,substantialincreaseinmasswasobserved(69 ).Theadditionofpiezopatcheswithnovoltageappliedresultedinanincreaseof9 2 > indynamicpressure.Furtherapplicationof40 0 acrosseachayeresultedn mallerurthermprovementnynamicressureo3.5, r2relativetoth e case.hus,tisnotedthatanncreasenizeofth epiezoatchesnd/oractuationower,oe sotecessarilyesultnettererformance.nact,he5 atchconfigurationerformedworsehanhe atchase.pparently,heargeriezoatchconfigurationresultedinarelativelymuchlargermassincreasethusoffsettingth ebenefitsofan increasedactuationcapability.Threemoreatchonfigurationsav eee nnalyzedtourtherprobehi smatter.etusal ltheseconfigurations2an d3,asshowninFigure6.Inconfiguration1,fivepiezopatchesareplacedinastarshapedform,resultinginamassincreaseof86 .Th eflutterdynamicpressure,inthepresenceofanappliedvoltageof40 0 , xhibitspoorperformancewithmereincreasenalueelativeoheoppliedoltagease.ntherwords, argerctuationcapability,ollowedbyamuchlargermassncreaseresultedinanegligiblemprovement.orconfiguration2,with4piezoelectricpatchesarrangedinacrossshape,th emassincreasedby69

.Th eresultantcriticaldynamicpressureincreasedby 8 to99.2 duetoanappliedvoltageof40 0V .Finally,configuration3 withthepiezopatchesarranged alongth eperimeterofasquareat thecentreofth eplate,xhibitedanincreaseof2 0 indynamicpressure,withanincreaseof52 inmass.Thus,nconfiguration3,betterperformancewasattainedinth epresenceofarelativelysmallerincreaseinmass,whileinconfiguration,apoorperformancewasexhibited withanincreaseinmass.

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Anotheraspectthatdrawsattentionisth efactthatth e2 5 centralpatchconfigurationan dthenumber2configurationprovideasimilarmassincrease69 ).However,th e2 5 centralpatchconfigurationesultedn 2 mprovementnynamicressure,hilehectuationnconfiguration2xhibitedapoor8 mprovement.Onpreliminarynalysisasis,tanbe inferredthatno tonlyistheaddedmasstotiffnessratioimportant,butalsoth econfigurationan dplacementofth epatchesnthetructurehouldbetakenintoccounturingtheesignprocess.

Summarizing,thereisanoptimumpatchsize,an dthereinanoptimalpatchconfigurationwhichdeliverth ebestperformance.Aompromiseneedstobeoundbetweenth edvantagesofan increasedactuationcapabilityan d th edisadvantagesofanincreased weightduetoth eadditionofpiezoelectricmaterial.Thesequestionsneedtobeaddressedthroughformaloptimizationdesign procedures.

# 1 2 3 4

X # 5

CriticalAerodynamicParameterhcritical = 36 .8

Configuration#1 # 2 #3 # 4 # 5ov 46.9 70.5 88.5 91.8 63.9400V 66.7 93.5 92.5 99.2 76.5

^critical +42% +32% +5% +8% +20% Mass +17% +69% +86% +69% +52%

Figure6-Passivecontrolperformancefo r5differentpiezoelectricpatchconfigurations.

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ActivecontrolTh eendingmomentinducedbyth epiezoelectricsotffectiveoontrolheinearpanelfluttersincethereisnobendingbehaviourinthelinearcase.Onth eotherhand,th einducedin-planeforceisno tsufficientinlinearpanelfluttercontrolbecauseofthelo wmodulusan dlimited abilityof th epiezoelectricstocreatelargein-planeforces.Fo rsuppressionofpanelflutterlimit-cyclemotions,noptimalcontrolapproachbasedonthelinearoptimalontrolheorysproposed.heinearpanellutterisunstablewhen X^whereasthenonlinearpanelflutterisastablelimit-cycleoscillation.inceth eflutteriscaused by theinstabilityofth elinearmodel,th egoalofth econtroldesignistokeepth esystemstable.Th eactivecontrolmethodologyselectedisbasedonth estate-spacedomainsincethesystemisamulti-input-multi-outputwithalargenumberofpiezoelectricactuatorsand sensors.Th egenericstatespaceequationfo radynamicsystemisgivenin th eform

3 c =A3c+Bw+FvyCx+H+w

whereisthesystemstatevector,istheactuatorinputvector,yisth esensoroutputvector,isthestatesperturbationvector,wsthesensornoisevector,Asth esystemdynamicsmatrix,Bsactuatorinputmatrix, Can d D areoutputmodellingmatricesan dFsth estateperturbationmatrix.Aommonor mofcontroleliesneedingbacktheensedoutputvariablesmultipliedbyaconstantmatricialfactor(gainmatrixG).Thisformofcontrolisknownasthelinearfeedbackcontrol,i.e.

U= -Gy

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ThelinearQuadraticRegulator(LQR)ha sbeenselected todetermineth evaluesofth ematrixG.TheLQ Rmethodisbasedonthessumptionthatal lthetatesofth eystemaremeasurable.Whenitisno tpossibletomeasureal lth estatesofthesystem,thereisaneedtoimplementan observer.heobserveroutputisanestimateofthestatesofth esystemx.Thus,th econtrolleriscomposedoftw omainblocks:theestimator,whichreceivesth einputan doutputofthesystem an dprocessesth estatesofth esystem;an dthefeedbackgain,whichreceivesth estateestimatesan d processesth esystemcontrolactuation.

Theclosedloopdynamicsofth esystemca nberepresentedasfollows:PlateStructuralModel:

x= Afxf+Bfea+Ffv e=Cfxf+w

Observerdynamics : xr=Arx+Brea+K(esrx)

Feedbackla w

es=-Gxwhereheubscript refersoheul ltatemodelndreferstoheeducedrdermodel. Combiningth eaboveequations,th edynamicsofth eclosedloopsystemca nbewritteninmatrixformas:

KC/BG

A-BG-KCFf 00 F lvIw l

Th enumericalsimulationwascarriedou tusingth eMATLABsoftwaretool.Th eblockdiagramsforth ecompletemodelwithfeedbackispresentedinFigure7.Th eKaimanobserverisastate-spaceblockwithmatricesA &Be,C ean dDe.Th einputsfo rth edynamicmodelaretheactuation

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voltagese a .Therearetw ooutputsfromthedynamicmodelblock:th estatesofth esysteman d thesensedvoltagesfromth esensorpiezopatchese u.Th estatevectorisusedtocomparewiththeestimatedstatesand th esensedvoltagesarefe dtoth eobserverblock.Thereslsonrroralculationlock.heurposeofthislocksoalculateherrorgenerated by theobserverand thisisgivenby

error=(x-x) (x -x)

ThepenaltyfunctionweightmatricesQan dRweredefinedasdiagonalwithavalueof10000 an dxlO" 5,espectively.heoiseovarianceorhetateswasett0%ofthenitialdeflection.Fo rth esensornoise,th enon-correlated covariancematrixw assetwithanoisepowerof2V 2.hesevalueswereusedtodesignthecontrollerinal lsimulations.Th efullordermodelaccountsorllheegreesoffreedomncludednth elatemodelwhileheeducedrdermodelincludesonlytheirst6modesofvibration.Thefirst6naturalfrequencyvaluesfo ran isotropicsquareplatewithfourpairsofactuatorsan d2pairsofsensorsareshownbelow:

Mode ( O nrad/s)1 57.30 2 365.473 1057.714 1133.86 5 1193.716 2178.08

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DynamicModelofPlatew f t h PiezoelectricSensors andActuators

Eh >r n_1 J %

x sA x + B uy=C x + D u

StateNoiseSourceSum Outport

clisp |

Figure7-Blockdiagramforthecompletemodelwithfeedback,stateobserverand errorestimation.

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Th etablebelowdepictsth efirstsixmodescontrolled by areducedordercontroller.

M o d e OpenL o o p ClosedLoop c o n(rad/s) c orad/s) D a m p i n g Co m m en t s

1 57.30249 57.30438561 0.009520978 Structure2 365.4731 70.25461695 0.927711305 Controller3 1057.714 365.4493213 0.007791086 Structure4 1133.858 567.3243875 0.52316159 Controller5 1193.705 1056.67806 0.000688374 Structure6 2178.078 1133.858129 0 Structure

Th eommentsolumnefersoheriginofth emodehatseterminedbyomparingthenaturalfrequenciesofthesysteminopenan dclosedlooparchitecture.Asca nbeobserved,thecontrollerinthelosedloopystemintroducestw odditionalmodes,whicharequivalentto fouradditionaltates.ro mthetable,tca nalsobebservedthatthereretw oWellbehavedmodes(2ndan d4th)whichareassociatedwiththecontroller.Alsoitwasobservedthatthemodesestimatedbyth econtroller(1stan d3 rd)presentlo wdampingwhileth eremainingmodespresentzeroamping,whichmeansthattheontrollerdoesno taffectthesemodes.Thisindicatesthepossibilityofaspill-overeffect.Figure8showstimehistory plotsof th e1 stand 2ndmodes.

PtpMXtOiOi*..:


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Thepassivecontrolincreasescriticaldynamicpressureby approximately20%whensettingtheappliedelectricfieldtoth emaximumvalue(400V).Theeffectofth epiezoelectricallyinduced in-planeorcessmallndtsoncludedhatassiveontroloe sotuppresslutterefficiently.hectiveontrolpproachisttemptednext,whereth epiezoelectricpatchesreassumed toimpartonlybendingmomentstothestructure. Thus,heptimalontrolheorywasmplementedoctivelyuppresslutterysinghe piezoelectricpatchestoinducebendingmomentsonly.Thepaneldeflectionwasrepresentedby theirstixodes.onlinearquationsfmotionav eee nsedorllheumericalsimulations.hemaximumlutterfreeynamicressure maxisefinedasth emaximumunderwhichth eflutterca nbecompletelysuppressed withpiezoelectricactuation.Th enumericalsimulationhowedhathelutteraneuppressedompletelyelowmaxbysinghe constantgaincontrolfeedbackdesignedatth emaximumdynamicpressure.Th erationofXmax to raselectedasnndicatorfo rth eperformancereffectivenessofth epiezoelectricactuatordesign.Th eiv eonfigurationstudiednheassiveontrolmethodologywereonsideredorhe activeontrolmethodologystudy.heresultsrepresentedbelow.twasbservedthatmorepiezoelectricactuatorsdono tnecessarilyimplyabetterperformanceinactivecontrolapproachaswell.However,nthectiveontrolmethodology,th eperformaceslsoependentonthecontrolleresign.hectiveontrolmethodonsistentlyerformedetterha theassive controlethodologyith77 %nerodynamicressurearametersomparedo2% improvementnassivemodeoronfiguration1.heam erendwasbservedortherconfigurations.heesultsemonstratethatth ebendingctuationtechniqueut-performsth epassivecontrolapproachbyanorderofmagnitudean dthatfurthersimulationsar enecessaryto studytheeffectof th econtrollerdesignon thesolution.

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CriticalAerodynamicParameterXr=36.8no piezoelectricpatches)

# 1 # 2 # 3 # 4 # 5cr 46.9 70.5 88.5 91.8 63.9 ma x 128.6 163.4 152.5 175.5 115.8ax 2.7 2.3 1.7 1. 9 1.8

ConcludingRem a r ksAnonlinearsupersoniclutteranalysisoflaminatedcompositeplatesnd shellssarriedou tusing oublyurveduadrilateralhinhellinitelement,evelopednheasisoftheMindlinhinhellheory,lassicalaminationheoryndinearistonerodynamicheory. Numericalresultsar eobtainedfo rlaminatedcompositeplatesand curvedshells.Th efirst-orderpistontheoryusedtomodelth eaerodynamicpressure,providesareasonableestimateofflutter,deflectionshapes,ndfrequenciesorthinplate/shellpanelstapproximateMachnumbersofgreaterthan2 Goodgreementoftheom eofth ebtainedolutionswithexistingresultsservedostablishhealidityoftheresentormulationorupersoniclutternalysisofadaptivecompositeplatesan dshells.Th eerformanceflutteruppressionsingiezoelectricctuationsemonstratedy increasinghemaximumlutter-freeynamicressure maxorheatioofthe maxohe criticalynamicpressure r.Th eptimalontroldesignisbasedonth einearequationsofmotionwhereasthesimulationsarebasedonthenonlinearequationsofmotion.Th enumerical simulationsho whatth en-planeorcesnducedbyth eiezoelectricctuatorsreotverysignificantenoughinordertoconsiderablyaffectth eflutterenvelope.tw asobservedthattheperformaceoftheiezoelectricctuatorsnynamicendingctuationmodesonsiderably superiorcomparedtoth epassiveactuationmode(177%improvementcomparedto42%inthepassivemodefo rconfiguration#1).

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CHAPTER5

EXPERIMENTALBUFFETSUPPRESSION

Experimentalbuffetingan dgustalleviationresponseresultsarepresentedfo rasweptbackflatwingmodelusingpiezoelectricactuatorstocontrolbendingan dwingtipcambershape.Modelresponsewasensedbytraingages,ccelerometersnd piezoelectricensors.hepen-loop an dclosed-loopresultsofthisexperimentalstudyshowthatpiezoelectricactuationiseffectiveinattenuatingibrationndheake-induceduffetesponsev erheangefarametersinvestigated.Th eairfoilcambershapecontrolincreasesremarkablytheefficiencyofth esystem,byusingacontrolledchangeofliftinordertoproducetherequired bendingmoments.

Introduction Th eprimarypassivesolutionstodynamicaeroelasticproblemsconsistofincreasingth estiffnessan dblancingth emassan dthesehavebeenusedasearlyas922.Theystillcompriseth ebasicpassivemeansofimprovingth eresponsean dstabilityofanaircraft.Increasedstiffnessca nalsobechievedysingdvancedompositeailoringhichanreatlylterhetability characteristicsofagivenwing.Activeontrolonceptstomprovetheaeroelasticperformanceofwingshaveincemerged.Theactiveaeroelasticcontrolsolutionsconsistofusingaerodynamiccontrolsurfacesastheyarereadilyavailableonconventionalaircraft.On eofthefirstactiveaeroelasticcontrolexperimentsbegantestingn972nNASALangleyResearchCenter'sTransonicDynamicsTunnel.he modelwasaclippeddeltawingwithaleadingedgean datrailingedgeactuator.Sincethattime,controlexperimentsusingflapactuatorshavestudiedavarietyofcontroldesigntechniquesan d objectives.TheActiveFlexibleWingprojectusedth eflexibilityofthewinginconjunctionwithactivecontrolstoprovidegreatermaneuverability. Inthelastcoupleofdecades,activeaeroelasticcontrolhasevolvedand ane wactuationconcept

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ha semergedfo rstructuralcontrol.Thisisthedirectstrainactuationusingadaptivematerialsan d structures.heselectro-magneto-thermo-mechanicalmaterialsav eresentednxceptionalpromisewhencomparedtoconventionalones.ordeformationofthinstructuralelements,themostidelyse dultifunctionalaterialsreiezoelectricctuators.iezoelectricsav eseveraladvantagesoverhydraulicactuatorsbecausetheyhaveahigherfrequencybandwidthofoperationan dbecausetheyac tdirectlyinthestructurebystrainingit.Piezoelectricshavehigherbandwidthshanreossiblenhapeemorylloys,he yreoreompactha nmagnetostrictivedevicesan d theyarebidirectionalbynatureunlikeelectrostrictivematerials.Thereasee nonsiderablenalyticalndomputationalworkerformedoeterminehe feasibilityofapplyingpiezoelectricactuatorstocontrolwingflutteran dbuffeting.However,theexperimentalverificationeffortha sbeenratherlimitedtoafe wstudiesreported intheliterature. TheDARPA/USAFWrightaboratoryrogramwasoesign,uildndes twindunnelmodelstouantifyerformancemprovementsthatouldbechievedbyncorporatingmartmaterialssuchha sPZT'sfo ractuationan dsensingsystemsinaircraftwings.Th emartWingprogramerformedwindtunneleststheNASALangley'sransonicDynamicunnelodemonstratehesefmartctuatorystemsn ealisticodeledircraftperationalenvironment.Thewindtunneltestquantifiedaerodynamicimprovementsoftw ooncepts:he us eofembeddedSM Awiresinthetrailingedgetoprovideasmoothvariablecontouredcontrolsurface,an dSM Atorquetubesbuiltintoth ewingstructurewhichenabled th ewingtobetwisted or torqued.Severalactivevibrationssuppressionconceptshavealsobeeninvestigated byaprogramshared betweenDaimler-BenzAerospaceMilitaryAircraftDASA),Daimler-BenzorschungDBF)an dDeutscheorchungsantalturuftundRaumfahrtDLR).ere, hinurfaceofpiezoactuatorsissetouttoflattenth edynamicportionofthecombinedstatican ddynamicmaximum bendingmomentloadingcasedirectlyintheshellstructure. Crawleyndeuis66 ]onductedneoftheirsttudiesnheseofpiezoelectricsnvibrationontrolofflexibletructures.nhereaofactiveuffetoa dlleviation,heirstexperimentemonstratingth eeasibilityofusingpiezoelectricctuatorsneroelasticontrol

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wasconductedby Heegetal[67].Shapeontrolofalexiblewingtructureas reatpotentialomproveheerodynamiclifting-surfaceperformance.Significantreductionsinth eshock-induceddragca nbeachievedbysmalladaptivemodificationstoth ewingcross-sectionalprofile.Th eresultspresentedherearethexperimentalwindtunnelresultsobtainedtoctivelysuppressbuffetingbycontrollingtheshapeofth ewingcamberusingpiezoelectricactuators.Tw omethodologiesrepresentedan d compared.Oneusesth epiezoelectricactuatorsinth etraditionalway,placingthematth erootto generatebendingmomentstocompensatethemechanicalvibrationalongth espanofthewing.Th ethermethodonsistsofusingheiezoelectricsochievectiveirfoilamberhapecontrol,inordertocontrollift,sothatthechangeof liftca nbeusedtogeneratethesametypeofmomentsan dhopefullyresultintheus eoffewerpiezoactuatorsan dlessexpendedenergy.

ExperimentalM o d elTh eplatewingmotionwascontrolledby six piezoceramicactuatorsbondedtothesurfaceatth ewingmountrootportionndtw ohapeontrolctuatorsea rth ewingtip.heiezowafersensorswerelocatedatth ewingmountrootan dth esignalwassenttodigitalsignalprocessorthroughilters.heontrolignalwasen toowermplifiers.Amplifiedignalrovehe piezoceramicctuatorsan dattenuatedvibrationtth ewingmount.Thisignalalsorovetheshapecontrolactuators.Acontrolla wwasdesigned basedonadiscretesystemmodel.

Aphotographan dasketchofthetestmodelareshowninFigures9,0an d11 .Th edimensionsweredeterminedbasedonthewindtunnelsize,blowingairvelocityan dth elimitationsofthepiezoceramicctuators.tructurally,twasimedtavingairlylexiblewingwithow bendingan dtorsionmodefrequencies.Sixpiezoceramicsensorpatches38x25x0.2m m readheredtoth etopan dbottomofth eplateneartheroot.Th ectuators(ACX-QPN40N)ar edividedintw ogroups,th eonesthatproducebendingmomentsalongth espanofth ewing,tw opairsnearth eleadingedgean don enearthetrailingedge,al lneartherootinordertomaximiseth ebendingmoment.Th eothergroup,which

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B

9 J f t

SH PE ONTROLTU TORS

IIENSOHS1 "flips'

*m

VASI r ; . -

Figure9.Wingwithpiezoactuators Figure10 .Wingwithpiezoactuatorsan dsensors

Figure11 .Windtunneltestsetup

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isesponsibleortheamberhapeontrol,socatednearth ewingtipnrdertoroducechangesinth ebendingmomentproducedbyth echangesinlift.TheoutputsignalofthePZ Tsensorswasmadeproportionaltoth everticaldisplacementof th emodel.Afiniteelementmodalanalysiswasperformedtogeneratenaturalfrequenciesan dmodeshapesneededtodetermineth eappropriateplacementofthepiezoelectricactuatingplatesfo rmaximumcontroluthorityan dtoesigntheontroller.heibrationmodehapesndfrequenciesreshowninFigure12.

f2=19.5Hz f3=54.8Hz

ps

V

Figure12 .W i n gFiniteelementmodelm o d a lfrequenciesand m o d eshapesusedinth econtrollerdesign.

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ControllerDesi g nAblockdiagramofth econtrollerfeedbacksystemispresentedinFigure3.Theoutputanalog signalro mheZTensormountednheupportootwasoutedonnalog-to-digital converter whichhad asamplerateof10"4seconds.Th ePZ Tsensorsignalisproportionaltoan d inphasewiththedisplacementofthemodel.Th edigitizedsignalwasthensenttothecontrollawwhichwasimplementedonaMATLABan dSIMULINKenvironmentrunningunderarealtimeoperatingenvironment.Theanalog-to-digitalconvertswere32bi tunits.

Th econtrolla wwasbasedonasimplefeedbackgainloop,i.e.th edigitalsignalwasmultiplied byaconstantvalue.Thegainedsignalwasnextsenttoaon eteptimeelay.Th etimedelayprovidesameansfo rchangingth ephaseofth efeedbacksignal.Th egained-an dphased-shiftedsignalwasconvertedbacktoananalogsignalby azero-order-holddigital-to-analogconverter.Th eonvertedignalwasoutedowoperationalmplifiers.heutputignalsromhe amplifierswereusedtodriveth epiezoelectricactuators.Th emaximumoutputvoltagefromth eamplifiersw as+/-00volts.Fo rth epresentstudyasamplingrateof1000samplespe rsecond wasused.Thisrelativelyhighratewaschosentoensurethatth ebuffetingwaveformwaswelldefined.

Filtroacelerometro

I onstantFigure13 .chematicofth econtrollerdesignM A T LA B / SI M U LI N K

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TestResultsTh eexperimentalset-upisbasedonaDSPstateofth ear tlaboratoryfacilitycreatedfo rtestingan dalidatingheheoreticalmodelsndpplicationofctiveontrolmethodologies.he objectiveofthistestistomproveth eampingcharacteristicsofthetructurendverifythemethodofanalysis.Th egaincontrolmethodisusedfo rthevibrationcontrolinth etestbeingthefollowingcontrolla wapplied:=Kga(nGfilterac c

WereU istheLaplacetransformofinputu,Kgai nisthemultiplicativegainvalue,GfiUerisatransferfunctionfo rlow-passfilter,Yaccisth eLaplacetransformationoftheoutputyaCcofthesensor.hedditionoftheirst-orderow-passiltersnabledtomproveheualityofthesensorsignal.Varioussensortypeswereconsideredfo rapplicationinthephysicalmodel.Th esensorstested includeastraingagebridge,appliednearthewingrootwhereth estructuralloadsarelarge;an d anaccelerometer,placednearthewingtipwherethedisplacementsar elarge.Agoodlinearityin theesponsesequirednditlsomportantthatthehaserelationshipetweenth earioussensorsisofgoodquality.Inordertofilterth elo wan dhighfrequencycontentsofth eresponsesignals,theyweresubjected,atalaterstage,toalo wpassfilteringwithacu tofffrequencyof50 Hz .nFigure4,itca nbeee nacomparisonofthesignalcomingfromth edifferentsensors,withan d withoutfilteringbeingapplied,duringforcedvibrationtests.

During th efreevibrationtestsusingth ecentralrootpiezoelectricsensor,th etimeforth ewingtostoposcillatingafterbeingforcedtoa2Hzregimewasreducedfrom40 secondsinopenloopto 2econdswhenheoo pwaslosed.nheam eonditions,utsingowhewingip accelerometerasasensor,th etimefo rthewingtostoposcillatingwasreducedfrom40 secondsinopenloopto4secondswhentheloopwasclosed.

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Opticaldisplacement ||1

StrainGage+chargeamplifierMicro-Measurements

DytranPowerUnit+Endevco IsotronAccelerometer

SensorTec.Piezoelectric

I0.00

SSft*K**W #S5

-' .' . T 1 V ^

Figure14. ^s ri'i^'SensorIdentification

-i( i i

,7

controlauthorityLE>T E 4 pwardverticalgust t

Trailing InducedAngleof Attach 'T y

Figure15 .Wingreactiontoanupwardverticalgust

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Thisimplees tav e oo dndicationofth eypeofsensortose ,hemountofpowerrequiredtoachieveacceptabledampingan dth emaximumamountofdampingproduced bytheactuatorsndtheontrolystem.tca nbenferredthatthepiezoelectricensorpresentedth ebestqualityinthemeasuredsignal.Th eschematicsfo rth ebuffetcontroltestareth esameasfo rth efreevibrationcontroltest,th eonlydifference,isthatthewingpanelwasplacedinsideawindtunnel.Thesystemhasasingleoutputan dadoubleinput,on efo rth egroupofactuatorsthatperformbendingand anotherfo rth eshapecontrol(Figure15).Fo rheresenttudyhewindunnelwasmodifiedoha tigidlatew aslacedthe upstreamndofthees tection.hewakero mthisbstaclewasusedtoeneratebuffetingflow.heositionofthisbjectouldeasilydjustedohatheesultingwakewouldimpingeonth emodelmounteddownstream.Th econfigurationfinallyselectedwasth eon ethatproducedth eargestbuffetesponseofth emodel.herefore,llofth euffetresponseatapresentedhereinwereobtainedfo rth eobstacleinthesamelocationan dorientation.Testswerecarriedutwithnl yheluminiumlatensidehewindunnel,nrderoeterminehe speedsatwhichth ebuffetwouldoccur(aspeedof5.5m /swasconsideredoptimal). Withthecontrolla wgainset tothedesiredvalueth etunnelspeed wasincreasedtoan d thenheld constantatapr eelectedvalue.Buffetresponsemeasurementsweremadeatavelocityof5.5m/s.Theoutputsignalfromth ePZTsensorwaschannelledtoatransferfunctionanalyserthatwasusedtocalculateth eauto-correlationfunctionoftheresponsesignal.Whenth econtrollawsareapplied,th eaverageamplitudeduetobuffetingdecreasedha sitca nbeseeninTable1 .

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Tablel-Experimentalresults

Piezodamping Piezodamping& shapecontrolAmplitude Frequency Amplitude FrequencyControlla woff 58 5mm 1H z 620mm 1HzControlla won 39 5mm 0.9Hz 32 5mm 0.66HzImprovement 32% 10 % 47.5% 34%

Anppreciableuffetingeductionasee nbtained,speciallywhensingirfoilhapecontrol,whichombinedwithth eoo tctuatorswerebleoecreaseheverageuffetingamplituderom2%to7.5%.heirfoilhapeontrollsoecreasedth erequencyofthevibrationby 34%.Th eairfoilshapecontrolhaspresentedafeasibleengineeringdesignsolutionwhereheiezoelectrichapeontrolctuatorsrese doreateavorablehangesnift characteristics.

PreliminaryConcluding RemarksTh eonceptan dmethodofexperimentaleroelasticibrationuppressionusingpiezoceramic actuatorsan dsensorstoimpartchangesindampingan daerodynamiccharacteristicstoth ewinghavebeenpresented.Anppreciablebuffetingreductionwasbtained,speciallywhenusingirfoilhapeontrol,whichcombinedwithth erootactuatorswereabletodecreaseth eaverageamplitudeinbuffetingfrom32 %to47.5%.Theairfoilshapecontrolalsodecreasedth efrequencyofthevibrationby

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34%.Futurewind-tunneltestplanswillfocusonusingacompositewingmodelasatestbedfo ractivePZTsensing,actuationan dshapecontrol.Toesolveheiminishingontroluthorityoftheiezoceramicctuatorssirpeedsincreased,theairfoilshapecontrolha spresentedafeasiblesolutionwhereth epiezoactuatorsareused tocreateafavourablevariationinliftcharacteristics.

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H P TER 6

ON LUSIONS ND FURTHER WORKTh edaptivetructuresesignonceptsroposedresentngineeringeasibleolutionsoproblemsequiringctiveibrationuppressionndhapeontrolnircrafttructures.he objectiveinadaptivecompositestructuresistohaveastructurethatiscapableofrespondingto th environmentviacontrollgorithms.uc hstructureswouldno tonlyperformth eunctionsprogrammedintoitbutalsoaimtomaintainstructuralintegrityan dself-preservation.

Theerformanceflutteruppressionsingiezoelectricctuationsemonstratedyincreasingth eratiooftheAmaxoth ecriticaldynamicpressureAcr.Th eoptimalcontroldesignisbasedonthelinearequationsofmotionwhereastheimulationsar ebasedonth enonlinearequationsofmotion.heumericalimulationsho wthatthen-planeorcesnducedbythepiezoelectricactuatorsareno tverysignificantenoughinordertoconsiderablyaffecttheflutterenvelope.Itwasobservedthattheperformanceofth epiezoelectricactuatorsindynamicbendingactuationod esonsiderablyuperioromparedoheassivectuationod e177% improvementcomparedto42% inth epassivemode).Th eonceptan dmethodofexperimentalaeroelasticvibrationuppressionusingpiezoceramicactuatorsan dsensorstoimpartchangesindampingan daerodynamiccharacteristicstoth ewinghavebeenpresented.Anppreciablebuffetingreductionwasbtained,speciallywhenusingairfoilshapecontrol,whichcombinedwiththerootactuatorswereabletodecreaseth eaverageamplitudenuffetingrom2%o7.5%.heirfoilhapeontrollsoecreasedhe frequencyof th evibrationby 34%.Futurewind-tunneltestplanswillfocusonusingacomposite wingmodelstestbedoractiveZTensing,ctuationndhapeontrol.oesolvehe diminishingcontrolauthorityofthepiezoceramicactuatorsasairspeedisincreased,theairfoilshapeontrolaspresentedafeasibleolutionwhereth epiezoctuatorsreusedtoreatefavourablevariationinliftcharacteristics.

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Furtherworkisunderwayntw oronts:heirstistonhanceth eMARTTRUCTURES simulationprogramtoarryuttimeomainimulationsofth epanellutterphenomenand nonlinearcontrolstrategiesuc hasfeedbacklinearizationtechniquear ebeingincorporatedfo rth eactivepanelfluttercontrolproblem.Onthexperimentalide,moreomplexan dthree-dimensionalmodelseinguilttotudyheerformanceofth eiezoelectricctuatorsnd sensorsinthewind-tunnel.

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