Introduction to structural dynamics and aeroelasticity

271 Pages·2011·3.488 MB·English

by  Dewey H Hodges, G Alvin Pierce

INTRODUCTION TO STRUCTURAL DYNAMICS
AND AEROELASTICITY, SECOND EDITION
Thistextprovidesanintroductiontostructuraldynamicsandaeroelasticity,withanem-
phasisonconventionalaircraft.Theprimaryareasconsideredarestructuraldynamics,
static aeroelasticity, and dynamic aeroelasticity. The structural dynamics material em-
phasizes vibration, the modal representation, and dynamic response. Aeroelastic phe-
nomenadiscussedincludedivergence,aileronreversal,airloadredistribution,unsteady
aerodynamics,flutter,andelastictailoring.Morethanonehundredillustrationsandta-
bleshelpclarifythetext,andmorethanfiftyproblemsenhancestudentlearning.This
textmeetstheneedforanup-to-datetreatmentofstructuraldynamicsandaeroelasticity
foradvancedundergraduateorbeginninggraduateaerospaceengineeringstudents.
PraisefromtheFirstEdition
“Wonderfully written and full of vital information by two unequalled experts on the
subject,thistextmeetstheneedforanup-to-datetreatmentofstructuraldynamicsand
aeroelasticityforadvancedundergraduateorbeginninggraduateaerospaceengineering
students.”
–CurrentEngineeringPractice
“HodgesandPiercehavewrittenthissignificantpublicationtofillanimportantgapin
aeronauticalengineeringeducation.Highlyrecommended.”
–Choice
“...a welcome addition to the textbooks available to those with interest in aeroelas-
ticity....Asatextbook,itservesasanexcellentresourceforadvancedundergraduate
andentry-levelgraduatecoursesinaeroelasticity....Furthermore,practicingengineers
interestedinabackgroundinaeroelasticitywillfindthetexttobeafriendlyprimer.”
–AIAABulletin
DeweyH.HodgesisaProfessorintheSchoolofAerospaceEngineeringattheGeorgia
Institute of Technology. He is the author of more than 170 refereed journal papers
and three books, Nonlinear Composite Beam Theory (2006), Fundamentals of Struc-
tural Stability (2005, with G. J. Simitses), and Introduction to Structural Dynamics and
Aeroelasticity, First Edition (2002, with G. Alvin Pierce). His research spans the fields
ofaeroelasticity,dynamics,computationalstructuralmechanicsandstructuraldynamics,
perturbationmethods,computationaloptimalcontrol,andnumericalanalysis.
ThelateG.AlvinPiercewasProfessorEmeritusintheSchoolofAerospaceEngineering
attheGeorgiaInstituteofTechnology.HeisthecoauthorofIntroductiontoStructural
DynamicsandAeroelasticity,FirstEditionwithDeweyH.Hodges(2002).

CambridgeAerospaceSeries
Editors:WeiShyyandMichaelJ.Rycroft
1. J.M.RolfeandK.J.Staples(eds.):FlightSimulation
2. P.Berlin:TheGeostationaryApplicationsSatellite
3. M.J.T.Smith:AircraftNoise
4. N.X.Vinh:FlightMechanicsofHigh-PerformanceAircraft
5. W.A.MairandD.L.Birdsall:AircraftPerformance
6. M.J.AbzugandE.E.Larrabee:AirplaneStabilityandControl
7. M.J.Sidi:SpacecraftDynamicsandControl
8. J.D.Anderson:AHistoryofAerodynamics
9. A.M.Cruise,J.A.Bowles,C.V.Goodall,andT.J.Patrick:PrinciplesofSpace
InstrumentDesign
10. G.A.KhouryandJ.D.Gillett(eds.):AirshipTechnology
11. J.P.Fielding:IntroductiontoAircraftDesign
12. J.G.Leishman:PrinciplesofHelicopterAerodynamics,2ndEdition
13. J.KatzandA.Plotkin:Low-SpeedAerodynamics,2ndEdition
14. M.J.AbzugandE.E.Larrabee:AirplaneStabilityandControl:AHistoryof
theTechnologiesthatmadeAviationPossible,2ndEdition
15. D.H.HodgesandG.A.Pierce:IntroductiontoStructuralDynamicsand
Aeroelasticity,2ndEdition
16. W.Fehse:AutomaticRendezvousandDockingofSpacecraft
17. R.D.Flack:FundamentalsofJetPropulsionwithApplications
18. E.A.Baskharone:PrinciplesofTurbomachineryinAir-BreathingEngines
19. D.D.Knight:NumericalMethodsforHigh-SpeedFlows
20. C.A.Wagner,T.Hu¨ttl,andP.Sagaut(eds.):Large-EddySimulationfor
Acoustics
21. D.D.Joseph,T.Funada,andJ.Wang:PotentialFlowsofViscousand
ViscoelasticFluids
22. W.Shyy,Y.Lian,H.Liu,J.Tang,D.Viieru:AerodynamicsofLowReynolds
NumberFlyers
23. J.H.Saleh:AnalysesforDurabilityandSystemDesignLifetime
24. B.K.Donaldson:AnalysisofAircraftStructures,2ndEdition
25. C.Segal:TheScramjetEngine:ProcessesandCharacteristics
26. J.F.Doyle:GuidedExplorationsoftheMechanicsofSolidsandStructures
27. A.K.Kundu:AircraftDesign
28. M.I.Friswell,J.E.T.Penny,S.D.Garvey,A.W.Lees:DynamicsofRotating
Machines
29. B.A.Conway(ed):SpacecraftTrajectoryOptimization
30. R.J.AdrianandJ.Westerweel:ParticleImageVelocimetry
31. G.A.Flandro,H.M.McMahon,andR.L.Roach:BasicAerodynamics
32. H.BabinskyandJ.K.Harvey:ShockWave–Boundary-LayerInteractions

Introduction to Structural Dynamics
and Aeroelasticity
Second Edition
Dewey H. Hodges
GeorgiaInstituteofTechnology
G. Alvin Pierce
GeorgiaInstituteofTechnology
cambridgeuniversitypress
Cambridge,NewYork,Melbourne,Madrid,CapeTown,
Singapore,Sa˜oPaulo,Delhi,Tokyo,MexicoCity
CambridgeUniversityPress
32AvenueoftheAmericas,NewYork,NY10013-2473,USA
www.cambridge.org
Informationonthistitle:www.cambridge.org/9780521195904
Firstedition(cid:2)c DeweyH.HodgesandG.AlvinPierce2002
Secondedition(cid:2)c DeweyH.HodgesandG.AlvinPierce2011
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithoutthewritten
permissionofCambridgeUniversityPress.
Firstpublished2002
Secondeditionpublished2011
PrintedintheUnitedStatesofAmerica
AcatalogrecordforthispublicationisavailablefromtheBritishLibrary.
LibraryofCongressCataloginginPublicationdata
Hodges,DeweyH.
Introductiontostructuraldynamicsandaeroelasticity/DeweyH.Hodges,G.AlvinPierce.–2nded.
p.cm.–(Cambridgeaerospaceseries;15)
Includesbibliographicalreferencesandindex.
ISBN978-0-521-19590-4(hardback)
1.Spacevehicles–Dynamics. 2.Aeroelasticity. I.Pierce,G.Alvin. II.Title.
TL671.6.H565 2011
629.134(cid:2)31–dc22 2011001984
ISBN978-0-521-19590-4Hardback
CambridgeUniversityPresshasnoresponsibilityforthepersistenceoraccuracyofURLsforexternalor
third-partyInternetWebsitesreferredtointhispublicationanddoesnotguaranteethatanycontenton
suchWebsitesis,orwillremain,accurateorappropriate.
Contents
Figures pagexi
Tables xvii
Foreword xix
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2 MechanicsFundamentals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6
2.1 ParticlesandRigidBodies 7
2.1.1 Newton’sLaws 7
2.1.2 Euler’sLawsandRigidBodies 8
2.1.3 KineticEnergy 8
2.1.4 Work 9
2.1.5 Lagrange’sEquations 9
2.2 ModelingtheDynamicsofStrings 10
2.2.1 EquationsofMotion 10
2.2.2 StrainEnergy 13
2.2.3 KineticEnergy 14
2.2.4 VirtualWorkofApplied,DistributedForce 15
2.3 ElementaryBeamTheory 15
2.3.1 Torsion 15
2.3.2 Bending 18
2.4 CompositeBeams 20
2.4.1 ConstitutiveLawandStrainEnergyforCoupledBending
andTorsion 21
2.4.2 InertiaForcesandKineticEnergyforCoupledBending
andTorsion 21
2.4.3 EquationsofMotionforCoupledBendingandTorsion 22
2.5 TheNotionofStability 23
2.6 SystemswithOneDegreeofFreedom 24
2.6.1 UnforcedMotion 24
2.6.2 HarmonicallyForcedMotion 26
vii
viii Contents
2.7 Epilogue 28
Problems 29
3 StructuralDynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.1 UniformStringDynamics 31
3.1.1 StandingWave(Modal)Solution 31
3.1.2 OrthogonalityofModeShapes 36
3.1.3 UsingOrthogonality 38
3.1.4 TravelingWaveSolution 41
3.1.5 GeneralizedEquationsofMotion 44
3.1.6 GeneralizedForce 48
3.1.7 ExampleCalculationsofForcedResponse 50
3.2 UniformBeamTorsionalDynamics 55
3.2.1 EquationsofMotion 56
3.2.2 BoundaryConditions 57
3.2.3 ExampleSolutionsforModeShapesandFrequencies 62
3.2.4 CalculationofForcedResponse 69
3.3 UniformBeamBendingDynamics 70
3.3.1 EquationofMotion 70
3.3.2 GeneralSolutions 71
3.3.3 BoundaryConditions 72
3.3.4 ExampleSolutionsforModeShapesandFrequencies 80
3.3.5 CalculationofForcedResponse 92
3.4 FreeVibrationofBeamsinCoupledBendingandTorsion 92
3.4.1 EquationsofMotion 92
3.4.2 BoundaryConditions 93
3.5 ApproximateSolutionTechniques 94
3.5.1 TheRitzMethod 94
3.5.2 Galerkin’sMethod 101
3.5.3 TheFiniteElementMethod 106
3.6 Epilogue 115
Problems 116
4 StaticAeroelasticity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .127
4.1 Wind-TunnelModels 128
4.1.1 Wall-MountedModel 128
4.1.2 Sting-MountedModel 131
4.1.3 Strut-MountedModel 134
4.1.4 Wall-MountedModelforApplicationtoAileronReversal 135
4.2 UniformLiftingSurface 139
4.2.1 Steady-FlowStripTheory 140
4.2.2 EquilibriumEquation 141
4.2.3 TorsionalDivergence 142
4.2.4 AirloadDistribution 145
Contents ix
4.2.5 AileronReversal 148
4.2.6 SweepEffects 153
4.2.7 CompositeWingsandAeroelasticTailoring 163
4.3 Epilogue 167
Problems 168
5 AeroelasticFlutter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
5.1 StabilityCharacteristicsfromEigenvalueAnalysis 176
5.2 AeroelasticAnalysisofaTypicalSection 182
5.3 ClassicalFlutterAnalysis 188
5.3.1 One-Degree-of-FreedomFlutter 189
5.3.2 Two-Degree-of-FreedomFlutter 192
5.4 EngineeringSolutionsforFlutter 194
5.4.1 ThekMethod 195
5.4.2 The p-kMethod 196
5.5 UnsteadyAerodynamics 201
5.5.1 Theodorsen’sUnsteadyThin-AirfoilTheory 203
5.5.2 Finite-StateUnsteadyThin-AirfoilTheoryofPetersetal. 206
5.6 FlutterPredictionviaAssumedModes 211
5.7 FlutterBoundaryCharacteristics 217
5.8 StructuralDynamics,Aeroelasticity,andCertification 220
5.8.1 Ground-VibrationTests 221
5.8.2 WindTunnelFlutterExperiments 222
5.8.3 GroundRoll(Taxi)andFlightTests 222
5.8.4 FlutterFlightTests 224
5.9 Epilogue 225
Problems 225
AppendixA:Lagrange’sEquations . . . . . . . . . . . . . . . . . . . . . . . 231
A.1 Introduction 231
A.2 DegreesofFreedom 231
A.3 GeneralizedCoordinates 231
A.4 Lagrange’sEquations 232
A.5 Lagrange’sEquationsforConservativeSystems 236
A.6 Lagrange’sEquationsforNonconservativeSystems 239
References 241
Index 243