Introduction to Aircraft Aeroelasticity and Loads

532 Pages·2007·8.41 MB·English

by  Jan R. Wright

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Introduction to Aircraft
Aeroelasticity and Loads
Jan R. Wright
UniversityofManchesterand
J2WConsultingLtd,UK
Jonathan E. Cooper
UniversityofLiverpool,UK
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Toourwives,JoyandSarah
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Contents
Preface xv
Introduction xix
Abbreviations xxv
PartI BackgroundMaterial 1
1 VibrationofSingleDegreeofFreedomSystems 3
1.1 SettingupequationsofmotionforsingleDoFsystems 3
1.2 FreevibrationofsingleDoFsystems 5
1.3 ForcedvibrationofsingleDoFsystems 7
1.4 Harmonicforcedvibration–frequencyresponsefunctions 7
1.5 Transient/randomforcedvibration–timedomainsolution 10
1.6 Transientforcedvibration–frequencydomainsolution 14
1.7 Randomforcedvibration–frequencydomainsolution 16
1.8 Examples 17
2 VibrationofMultipleDegreeofFreedomSystems 19
2.1 Settingupequationsofmotion 19
2.2 Undampedfreevibration 21
2.3 Dampedfreevibration 24
2.4 Transformationtomodalcoordinates 27
2.5 ‘Free–free’systems 31
2.6 Harmonicforcedvibration 31
2.7 Transient/randomforcedvibration–timedomainsolution 33
2.8 Transientforcedvibration–frequencydomainsolution 34
2.9 Randomforcedvibration–frequencydomainsolution 34
2.10 Examples 35
3 VibrationofContinuousSystems–AssumedShapesApproach 37
3.1 Rayleigh–Ritz‘assumedshapes’method 38
3.2 Generalizedequationsofmotion–basicapproach 39
3.3 Generalizedequationsofmotion–matrixapproach 44
3.4 Generatingaircraft‘free–free’modesfrom‘branch’modes 46
3.5 Wholeaircraft‘free–free’modes 49
3.6 Examples 50
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4 VibrationofContinuousSystems–DiscretizationApproach 53
4.1 Introductiontothefiniteelement(FE)approach 53
4.2 Formulationofthebeambendingelement 54
4.3 Assemblyandsolutionforastructurewithbeamelements 58
4.4 Torsionelement 63
4.5 Combinedbending/torsionelement 64
4.6 Commentsonmodelling 65
4.7 Examples 66
5 IntroductiontoSteadyAerodynamics 69
5.1 Thestandardatmosphere 69
5.2 Effectofairspeedonaerodynamiccharacteristics 71
5.3 Flowsandpressuresaroundasymmetricaerofoil 72
5.4 Forcesonanaerofoil 74
5.5 Variationofliftforanaerofoilatanangleofincidence 75
5.6 Pitchingmomentvariationandtheaerodynamiccentre 76
5.7 Liftonathree-dimensionalwing 77
5.8 Dragonathree-dimensionalwing 81
5.9 Controlsurfaces 82
5.10 Supersonicaerodynamics–pistontheory 83
5.11 Transonicflows 84
5.12 Examples 84
6 IntroductiontoLoads 87
6.1 Lawsofmotion 87
6.2 D’Alembert’sprinciple–inertiaforcesandcouples 90
6.3 Externallyapplied/reactiveloads 93
6.4 Freebodydiagrams 94
6.5 Internalloads 95
6.6 Internalloadsforcontinuousrepresentationofastructure 96
6.7 Internalloadsfordiscretizedrepresentationofastructure 100
6.8 Intercomponentloads 102
6.9 Obtainingstressesfrominternalloads–structuralmemberswith
simpleloadpaths 103
6.10 Examples 103
7 IntroductiontoControl 107
7.1 Openandclosedloopsystems 107
7.2 Laplacetransforms 108
7.3 ModellingofopenandclosedloopsystemsusingLaplaceand
frequencydomains 110
7.4 Stabilityofsystems 111
7.5 PIDcontrol 118
7.6 Examples 119
PartII IntroductiontoAeroelasticityandLoads 121
8 StaticAeroelasticity–EffectofWingFlexibilityonLiftDistribution
andDivergence 123
8.1 Staticaeroelasticbehaviourofatwo-dimensionalrigidaerofoilwith
springattachment 124
8.2 Staticaeroelasticbehaviourofafixedrootflexiblewing 127
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8.3 Effectoftrimonstaticaeroelasticbehaviour 129
8.4 Effectofwingsweeponstaticaeroelasticbehaviour 134
8.5 Examples 139
9 StaticAeroelasticity–EffectofWingFlexibilityonControlEffectiveness 141
9.1 Rollingeffectivenessofaflexiblewing–thesteadyrollcase 141
9.2 Rollingeffectivenessofaflexiblewing–thefixedwingrootcase 146
9.3 Effectofspanwisepositionofthecontrolsurface 149
9.4 Fullaircraftmodel–controleffectiveness 149
9.5 Effectoftrimonreversalspeed 151
9.6 Examples 151
10 IntroductiontoUnsteadyAerodynamics 153
10.1 Quasi-steadyaerodynamics 153
10.2 Unsteadyaerodynamics 154
10.3 Aerodynamicliftandmomentforaharmonicallyoscillatingaerofoil 157
10.4 Oscillatoryaerodynamicderivatives 159
10.5 Aerodynamicdampingandstiffness 160
10.6 Unsteadyaerodynamicsrelatedtogusts 161
10.7 Examples 165
11 DynamicAeroelasticity–Flutter 167
11.1 Simplifiedunsteadyaerodynamicmodel 167
11.2 Binaryaeroelasticmodel 168
11.3 Generalformoftheaeroelasticequations 171
11.4 Eigenvaluesolutionofflutterequations 171
11.5 Aeroelasticbehaviourofthebinarymodel 172
11.6 Aeroelasticbehaviourofaflexiblewing 180
11.7 Aeroelasticbehaviourofamultiplemodesystem 182
11.8 Flutterspeedpredictionforbinarysystems 182
11.9 Flutterconic 184
11.10 Divergenceofaeroelasticsystems 186
11.11 Inclusionofunsteadyreducedfrequencyeffects 187
11.12 Controlsurfaceflutter 191
11.13 Wholeaircraftmodel–inclusionofrigidbodymodes 193
11.14 Flutterinthetransonicregime 194
11.15 Flutterinthesupersonicregime–wingandpanelflutter 194
11.16 Effectofnonlinearities–limitcycleoscillations 197
11.17 Examples 198
12 Aeroservoelasticity 201
12.1 Mathematicalmodellingofasimpleaeroelasticsystemwitha
controlsurface 202
12.2 Inclusionofgustterms 203
12.3 Implementationofacontrolsystem 204
12.4 Determinationofclosedloopsystemstability 204
12.5 Gustresponseoftheclosedloopsystem 205
12.6 Inclusionofcontrollawfrequencydependencyinstabilitycalculations 206
12.7 Responsedeterminationviathefrequencydomain 208
12.8 Statespacemodelling 208
12.9 Examples 209
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13 EquilibriumManoeuvres 211
13.1 Equilibriummanoeuvre–rigidaircraftundernormalacceleration 213
13.2 Manoeuvreenvelope 217
13.3 Equilibriummanoeuvre–rigidaircraftpitching 218
13.4 Equilibriummanoeuvre–flexibleaircraftpitching 225
13.5 Flexiblecorrectionstorigidaircraftpitchingderivatives 238
13.6 Equilibriummanoeuvres–aircraftrollingandyawing 239
13.7 Representationoftheflightcontrolsystem(FCS) 243
13.8 Examples 243
14 FlightMechanicsModelforDynamicManoeuvres 245
14.1 Aircraftaxes 246
14.2 Motionvariables 247
14.3 Axestransformations 248
14.4 Velocityandaccelerationcomponentsformovingaxes 250
14.5 Flightmechanicsequationsofmotionforarigidaircraft 252
14.6 Representationofdisturbingforcesandmoments 255
14.7 Equationsforflexibleaircraftinlongitudinalmotion 257
14.8 Solutionofflightmechanicsequations 262
14.9 Flightcontrolsystem(FCS) 263
15 DynamicManoeuvres 265
15.1 Dynamicmanoeuvre–rigidaircraftheave/pitchduetoelevatorinput 266
15.2 Dynamicmanoeuvre–flexibleaircraftheave/pitchduetoelevatorinput 271
15.3 Generalformoflongitudinalequations 278
15.4 Dynamicmanoeuvre–rigidaircraftrollduetoaileroninput 279
15.5 Dynamicmanoeuvre–flexibleaircraftrollduetoaileroninput 283
15.6 Flexiblecorrectionstoflightmechanicsequations 290
15.7 Representationoftheflightcontrolsystem(FCS) 290
15.8 Examples 290
16 GustandTurbulenceEncounters 293
16.1 Gustsandturbulence 294
16.2 Gustresponseinthetimedomain 295
16.3 Timedomaingustresponse–rigidaircraftinheave 297
16.4 Timedomaingustresponse–rigidaircraftinheave/pitch 303
16.5 Timedomaingustresponse–flexibleaircraft 306
16.6 Generalformofequationsinthetimedomain 312
16.7 Turbulenceresponseinthefrequencydomain 314
16.8 Frequencydomainturbulenceresponse–rigidaircraftinheave 317
16.9 Frequencydomainturbulenceresponse–rigidaircraftinheave/pitch 320
16.10 Frequencydomainturbulenceresponse–flexibleaircraft 323
16.11 Generalformofequationsinthefrequencydomain 325
16.12 Representationoftheflightcontrolsystem(FCS) 326
16.13 Examples 326
17 GroundManoeuvres 329
17.1 Landinggear 329
17.2 Taxi,take-offandlandingroll 333
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17.3 Landing 340
17.4 Braking 345
17.5 ‘Spin-up’and‘spring-back’condition 348
17.6 Turning 350
17.7 Shimmy 350
17.8 Representationoftheflightcontrolsystem(FCS) 353
17.9 Examples 353
18 AircraftInternalLoads 355
18.1 Limitandultimateloads 356
18.2 Internalloadsforanaircraft 356
18.3 Generalinternalloadsexpressions–continuouswing 358
18.4 Effectofwing-mountedengines/landinggear 360
18.5 Internalloads–continuousflexiblewing 361
18.6 Generalinternalloadsexpressions–discretizedwing 366
18.7 Internalloads–discretizedfuselage 370
18.8 Internalloads–continuousturbulenceencounter 373
18.9 Loadsgenerationandsortingtoyieldcriticalcases 374
18.10 Aircraftdimensioningcases 376
18.11 Stressesfrominternalloads–complexloadpaths 377
18.12 Examples 377
19 PotentialFlowAerodynamics 381
19.1 Elementsofinviscid,incompressibleflowanalysis 381
19.2 Inclusionofvorticity 386
19.3 Numericalsteadyaerodynamicmodellingofthintwo-dimensionalaerofoils 388
19.4 Steadyaerodynamicmodellingofthree-dimensionalwingsusinga
panelmethod 391
19.5 Unsteadyaerodynamicmodellingofwingsundergoingharmonicmotion 394
19.6 AICsinmodalspace 397
19.7 Examples 400
20 CouplingofStructuralandAerodynamicComputationalModels 401
20.1 Mathematicalmodelling–staticaeroelasticcase 401
20.2 Two-dimensionalcoupledstaticaeroelasticmodel–pitch 403
20.3 Two-dimensionalcoupledstaticaeroelasticmodel–heave/pitch 404
20.4 Three-dimensionalcoupledstaticaeroelasticmodel 405
20.5 Mathematicalmodelling–dynamicaeroelasticresponse 409
20.6 Two-dimensionalcoupleddynamicaeroelasticmodel–bending
andtorsion 410
20.7 Three-dimensionalflutteranalysis 411
20.8 Inclusionoffrequency-dependentaerodynamicsforstatespace
modelling–rationalfractionapproximation 412
PartIII IntroductiontoIndustrialPractice 417
21 AircraftDesignandCertification 419
21.1 Aeroelasticsandloadsintheaircraftdesignprocess 419
21.2 Aircraftcertificationprocess 421
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22 AeroelasticityandLoadsModels 427
22.1 Structuralmodel 427
22.2 Aerodynamicmodel 432
22.3 Flightcontrolsystem 435
22.4 Othermodelissues 435
22.5 Loadstransformations 436
23 StaticAeroelasticityandFlutter 437
23.1 Staticaeroelasticity 437
23.2 Flutter 439
24 FlightManoeuvreandGust/TurbulenceLoads 443
24.1 Evaluationofinternalloads 443
24.2 Equilibrium/balancedflightmanoeuvres 443
24.3 Dynamicflightmanoeuvres 446
24.4 Gustsandturbulence 449
25 GroundManoeuvreLoads 455
25.1 Aircraft/landinggearmodelsforgroundmanoeuvres 455
25.2 Landinggear/airframeinterface 456
25.3 Groundmanoeuvres–landing 456
25.4 Groundmanoeuvres–groundhandling 457
25.5 Loadsprocessing 458
26 TestingRelevanttoAeroelasticityandLoads 461
26.1 Introduction 461
26.2 Windtunneltests 461
26.3 Groundvibrationtest 462
26.4 Structuralcouplingtest 463
26.5 Flightsimulatortest 464
26.6 Structuraltests 464
26.7 Flightfluttertest 465
26.8 Flightloadsvalidation 466
Appendices 467
A AircraftRigidBodyModes 469
A.1 Rigidbodytranslationmodes 469
A.2 Rigidbodyrotationmodes 469
B TableofLongitudinalAerodynamicDerivatives 471
C AircraftSymmetricFlexibleModes 473
C.1 Aircraftmodel 473
C.2 Symmetricfree–freeflexiblemode 474
D ModelCondensation 481
D.1 Introduction 481
D.2 Staticcondensation 481
D.3 Dynamiccondensation–Guyanreduction 482