Introduction to Aircraft Aeroelasticity and Loads (Aerospace Series (PEP))

559 Pages·2008·8.7 MB·English

by  Jan Robert 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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Introduction to Aircraft
Aeroelasticity and Loads
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JWBK209-FM-I JWBK209-Wright November14,2007 2:58 CharCount=0
Introduction to Aircraft
Aeroelasticity and Loads
Jan R. Wright
UniversityofManchesterand
J2WConsultingLtd,UK
Jonathan E. Cooper
UniversityofLiverpool,UK
iii
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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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viii CONTENTS
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