Introduction to Aircraft Aeroelasticity and Loads

605 Pages·2015·16.22 MB·English

by  Cooper

INTRODUCTION
TO AIRCRAFT
AEROELASTICITY
AND LOADS
Aerospace Series List
IntroductiontoAircraftAeroelasticityandLoads, WrightandCooper December2014
2ndEdition
AircraftAerodynamicDesign:GeometryandOptimization SóbesterandForrester October2014
TheoreticalandComputationalAerodynamics Sengupta September2014
AerospacePropulsion Lee October2013
AircraftFlightDynamicsandControl Durham August2013
CivilAvionicsSystems,2ndEdition Moir,SeabridgeandJukes August2013
ModellingandManagingAirportPerformance Zografos,Andreatta July2013
andOdoni
AdvancedAircraftDesign:ConceptualDesign,Analysis Torenbeek June2013
andOptimizationofSubsonicCivilAirplanes
DesignandAnalysisofCompositeStructures:With Kassapoglou April2013
ApplicationstoAerospaceStructures,2ndEdition
AircraftSystemsIntegrationofAir-LaunchedWeapons Rigby April2013
DesignandDevelopmentofAircraftSystems,2ndEdition MoirandSeabridge November2012
UnderstandingAerodynamics:ArguingfromtheReal McLean November2012
Physics
AircraftDesign:ASystemsEngineeringApproach Sadraey October2012
IntroductiontoUAVSystems4e FahlstromandGleason August2012
TheoryofLift:IntroductoryComputationalAerodynamics McBain August2012
withMATLABandOctave
SenseandAvoidinUAS:ResearchandApplications Angelov April2012
MorphingAerospaceVehiclesandStructures Valasek April2012
GasTurbinePropulsionSystems MacIsaacandLangton July2011
BasicHelicopterAerodynamics,3rdEdition SeddonandNewman July2011
AdvancedControlofAircraft,SpacecraftandRockets Tewari July2011
CooperativePathPlanningofUnmannedAerialVehicles Tsourdosetal November2010
PrinciplesofFlightforPilots Swatton October2010
AirTravelandHealth:ASystemsPerspective Seabridgeetal September2010
DesignandAnalysisofCompositeStructures:With Kassapoglou September2010
applicationstoaerospaceStructures
UnmannedAircraftSystems:UAVSDesign,Development Austin April2010
andDeployment
IntroductiontoAntennaPlacement&Installations Macnamara April2010
PrinciplesofFlightSimulation Allerton October2009
AircraftFuelSystems Langtonetal May2009
TheGlobalAirlineIndustry Belobaba April2009
ComputationalModellingandSimulationofAircraft Diston April2009
andtheEnvironment:Volume1–PlatformKinematics
andSyntheticEnvironment
HandbookofSpaceTechnology Ley,WittmannHallmann April2009
AircraftPerformanceTheoryandPracticeforPilots Swatton August2008
AircraftSystems,3rdEdition Moir&Seabridge March2008
IntroductiontoAircraftAeroelasticityandLoads Wright&Cooper December2007
StabilityandControlofAircraftSystems Langton September2006
MilitaryAvionicsSystems Moir&Seabridge February2006
DesignandDevelopmentofAircraftSystems Moir&Seabridge June2004
AircraftLoadingandStructuralLayout Howe May2004
AircraftDisplaySystems Jukes December2003
CivilAvionicsSystems Moir&Seabridge December2002
INTRODUCTION
TO AIRCRAFT
AEROELASTICITY
AND LOADS
Second Edition
Jan R. Wright
University of Manchester and
J2W Consulting, UK
Jonathan E. Cooper
University of Bristol, UK
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Wright,JanR.
Introductiontoaircraftaeroelasticityandloads/JanR.Wright,JonathanE.Cooper.–Secondedition.
pages cm
Includesbibliographicalreferencesandindex.
ISBN978-1-118-48801-0(cloth)
1. Aeroelasticity. I. Cooper,JonathanE. II. Title.
TL574.A37W752014
629.132'362–dc23
2014027710
AcataloguerecordforthisbookisavailablefromtheBritishLibrary
Setin10/12ptTimesbySPiPublisherServices,Pondicherry,India
1 2015
Toour children and grandchildren
Jodi, Peter, Laura, Rhys & Erin
&
William, Rory,Tyler & Ella

Contents
Series Preface xxi
Preface to the Second Edition xxiii
Preface to the First Edition xxv
Abbreviations xxix
Introduction 1
PART I BACKGROUND MATERIAL 7
1 Vibration of Single Degree of Freedom Systems 9
1.1 Settingup Equations of Motionfor SDoF Systems 9
1.1.1 Example: Classical SDoF System 10
1.1.2 Example: Aircraft Control Surface 11
1.2 Free Vibration of SDoF Systems 11
1.2.1 Example: Aircraft Control Surface 13
1.3 ForcedVibration of SDoF Systems 13
1.4 Harmonic ForcedVibration –Frequency Response Functions 14
1.4.1 Response to Harmonic Excitation 14
1.4.2 Frequency Response Functions 15
1.4.3 Hysteretic (or Structural) Damping 16
1.5 Transient/Random ForcedVibration –Time Domain Solution 17
1.5.1 Analytical Approach 17
1.5.2 Principle of Superposition 18
1.5.3 Example: Single Cycle of Square Wave Excitation –Response
Determined by Superposition 18
1.5.4 Convolution Approach 19
1.5.5 Direct Solution of Ordinary Differential Equations 21
1.5.6 Example: Single Cycle of Square Wave Excitation –Response
Determined by Numerical Integration 21
1.6 Transient Forced Vibration –Frequency Domain Solution 21
1.6.1 Analytical Fourier Transform 21
1.6.2 Frequency Domain Response– Excitation Relationship 22
viii Contents
1.6.3 Example: Single Cycle of Square Wave Excitation –Response
Determined via Fourier Transform 22
1.7 RandomForcedVibration –Frequency Domain Solution 23
1.8 Examples 24
2 Vibration of Multiple Degree of Freedom Systems 27
2.1 Settingup Equations of Motion 27
2.2 Undamped Free Vibration 29
2.2.1 Direct Approach 29
2.2.2 Eigenvalue Approach 30
2.2.3 Example: ‘Chain-like’2DoFSystem 30
2.3 DampedFree Vibration 31
2.3.1 Example: 2DoF ‘Chain-Like’ System with Proportional Damping 32
2.3.2 Example: 2DoF ‘Chain-Like’ System with Non-proportional Damping 33
2.4 Transformation to ModalCoordinates 34
2.4.1 ModalCoordinates 34
2.4.2 Example: 2DoF ‘Chain-like’System with Proportional Damping 35
2.4.3 Example: 2DoF ‘Chain-like’System with Non-proportional Damping 36
2.4.4 Mode Shape Normalization 36
2.4.5 Meaning of Modal Coordinates 37
2.4.6 Dimensions of Modal Coordinates 37
2.4.7 Model Order Reduction 38
2.5 Two-DoFRigid Aircraft in Heave andPitch 38
2.6 ‘Free–Free’ Systems 40
2.7 Harmonic ForcedVibration 41
2.7.1 Equations in Physical Coordinates 41
2.7.2 Equations in Modal Coordinates 42
2.8 Transient/Random ForcedVibration –Time Domain Solution 43
2.8.1 Analytical Approach 43
2.8.2 Convolution Approach 44
2.8.3 Solution of Ordinary Differential Equations 44
2.9 Transient Forced Vibration –Frequency Domain Solution 44
2.10 RandomForcedVibration –Frequency Domain Solution 44
2.11 Examples 45
3 VibrationofContinuousSystems–AssumedShapesApproach 49
3.1 Continuous Systems 49
3.2 Modelling Continuous Systems 49
3.3 Elastic and Flexural Axes 51
3.4 Rayleigh–Ritz ‘Assumed Shapes’ Method 52
3.4.1 One-dimensional Systems 52
3.4.2 Two-dimensional Systems 53
3.4.3 Choice of Assumed Shapes 53
3.4.4 Normal Modes for aContinuous System 53
3.5 Generalized Equations of Motion –Basic Approach 53
3.5.1 Clamped–Free Member in Bending–SingleAssumed Shape 54
3.5.2 Clamped–Free Member in Bending–TwoAssumed Shapes 55
3.5.3 Clamped–Free Member in Torsion –One Assumed Shape 57