Introduction to aircraft aeroelasticity and loads /
Jan R. Wright, Jonathan E. Cooper.
- Second edition.
- 1 online resource.
- Aerospace series. .
- Aerospace series (Chichester, England) .
Includes bibliographical references and index.
Table of 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 Setting up Equations of Motion for SDoF Systems 9
1.2 Free Vibration of SDoF Systems 11
1.3 Forced Vibration of SDoF Systems 13
1.4 Harmonic Forced Vibration – Frequency Response Functions 14
1.5 Transient/Random Forced Vibration – Time Domain Solution 17
1.6 Transient Forced Vibration – Frequency Domain Solution 21
1.7 Random Forced Vibration – Frequency Domain Solution 23
1.8 Examples 24
2 Vibration of Multiple Degree of Freedom Systems 27
2.1 Setting up Equations of Motion 27
2.2 Undamped Free Vibration 29
2.3 Damped Free Vibration 31
2.4 Transformation to Modal Coordinates 34
2.5 Two-DoF Rigid Aircraft in Heave and Pitch 38
2.6 ‘Free–Free’ Systems 40
2.7 Harmonic Forced Vibration 41
2.8 Transient/Random Forced Vibration – Time Domain Solution 43
2.9 Transient Forced Vibration – Frequency Domain Solution 44
2.10 Random Forced Vibration – Frequency Domain Solution 44
2.11 Examples 45
3 Vibration of Continuous Systems – Assumed Shapes Approach 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
3.5 Generalized Equations of Motion – Basic Approach 53
3.6 Generalized Equations of Motion – Matrix Approach 58
3.7 Generating Whole Aircraft ‘Free–Free’ Modes from ‘Branch’ Modes 61
3.8 Whole Aircraft ‘Free–Free’ Modes 64
3.9 Examples 65
4 Introduction to Steady Aerodynamics 69
4.1 The Standard Atmosphere 69
4.2 Effect of Air Speed on Aerodynamic Characteristics 71
4.3 Flows and Pressures Around a Symmetric Aerofoil 73
4.4 Forces on an Aerofoil 74
4.5 Variation of Lift for an Aerofoil at an Angle of Incidence 76
4.6 Pitching Moment Variation and the Aerodynamic Centre 77
4.7 Lift on a Three-dimensional Wing 78
4.8 Drag on a Three-dimensional Wing 82
4.9 Control Surfaces 83
4.10 Transonic Flows 84
4.11 Examples 85
5 Introduction to Loads 87
5.1 Laws of Motion 88
5.2 D’Alembert’s Principle – Inertia Forces and Couples 90
5.3 External Loads – Applied and Reactive 94
5.4 Free Body Diagrams 95
5.5 Internal Loads 96
5.6 Internal Loads for a Continuous Member 96
5.7 Internal Loads for a Discretized Member 101
5.8 Intercomponent Loads 103
5.9 Obtaining Stresses from Internal Loads – Structural Members with Simple Load Paths 103
5.10 Examples 104
6 Introduction to Control 109
6.1 Open and Closed Loop Systems 109
6.2 Laplace Transforms 110
6.3 Modelling of Open and Closed Loop Systems using Laplace and Frequency Domains 112
6.4 Stability of Systems 114
6.5 PID Control 121
6.6 Examples 122
PART II INTRODUCTION TO AEROELASTICITY AND LOADS 123
7 Static Aeroelasticity – Effect of Wing Flexibility on Lift Distribution and Divergence 125
7.1 Static Aeroelastic Behaviour of a Two-dimensional Rigid Aerofoil with a Torsional Spring Attachment 126
7.2 Static Aeroelastic Behaviour of a Fixed Root Flexible Wing 130
7.3 Effect of Trim on Static Aeroelastic Behaviour 133
7.4 Effect of Wing Sweep on Static Aeroelastic Behaviour 137
7.5 Examples 142
8 Static Aeroelasticity – Effect of Wing Flexibility on Control Effectiveness 143
8.1 Rolling Effectiveness of a Flexible Wing – Fixed Wing Root Case 144
8.2 Rolling Effectiveness of a Flexible Wing – Steady Roll Case 147
8.3 Effect of Spanwise Position of the Control Surface 151
8.4 Full Aircraft Model – Control Effectiveness 152
8.5 Effect of Trim on Reversal Speed 153
8.6 Examples 153
9 Introduction to Unsteady Aerodynamics 155
9.1 Quasi-steady Aerodynamics 156
9.2 Unsteady Aerodynamics related to Motion 156
9.3 Aerodynamic Lift and Moment for an Aerofoil Oscillating Harmonically in Heave and Pitch 161
9.4 Oscillatory Aerodynamic Derivatives 162
9.5 Aerodynamic Damping and Stiffness 163
9.6 Approximation of Unsteady Aerodynamic Terms 164
9.7 Unsteady Aerodynamics related to Gusts 164
9.8 Examples 168
10 Dynamic Aeroelasticity – Flutter 171
10.1 Simplified Unsteady Aerodynamic Model 172
10.2 Binary Aeroelastic Model 173
10.3 General Form of the Aeroelastic Equations 176
10.4 Eigenvalue Solution of the Flutter Equations 176
10.5 Aeroelastic Behaviour of the Binary Model 177
10.6 Aeroelastic Behaviour of a Multiple Mode System 185
10.7 Flutter Speed Prediction for Binary Systems 185
10.8 Divergence of Dynamic Aeroelastic Systems 188
10.9 Inclusion of Unsteady Reduced Frequency Effects 189
10.10 Control Surface Flutter 193
10.11 Whole Aircraft Model – Inclusion of Rigid Body Modes 199
10.12 Flutter in the Transonic Regime 202
10.13 Effect of Non-Linearities – Limit Cycle Oscillations 202
10.14 Examples 204
11 Aeroservoelasticity 207
11.1 Mathematical Modelling of a Simple Aeroelastic System with a Control Surface 208
11.2 Inclusion of Gust Terms 209
11.3 Implementation of a Control System 210
11.4 Determination of Closed Loop System Stability 211
11.5 Gust Response of the Closed Loop System 213
11.6 Inclusion of Control Law Frequency Dependency in Stability Calculations 214
11.7 Response Determination via the Frequency Domain 215
11.8 State Space Modelling 216
11.9 Examples 217
12 Equilibrium Manoeuvres 219
12.1 Equilibrium Manoeuvre – Rigid Aircraft under Normal Acceleration 221
19.6 2D Coupled Dynamic Aeroelastic Model – Bending/Torsion 447
19.7 3D Flutter Analysis 448
19.8 Inclusion of Frequency Dependent Aerodynamics for State–Space Modelling – Rational Function Approximation 450
PART III INTRODUCTION TO INDUSTRIAL PRACTICE 455
20 Aircraft Design and Certification 457
20.1 Aeroelastics and Loads in the Aircraft Design Process 457
20.2 Aircraft Certification Process 459
21 Aeroelasticity and Loads Models 465
21.1 Structural Model 465
21.2 Aerodynamic Model 471
21.3 Flight Control System 473
21.4 Other Model Issues 474
21.5 Loads Transformations 474
22 Static Aeroelasticity and Flutter 475
22.1 Static Aeroelasticity 475
22.2 Flutter 478
23 Flight Manoeuvre and Gust/Turbulence Loads 481
23.1 Evaluation of Internal Loads 481
23.2 Equilibrium/Balanced Flight Manoeuvres 481
23.3 Dynamic Flight Manoeuvres 485
23.4 Gusts and Turbulence 489
24 Ground Manoeuvre Loads 495
24.1 Aircraft/Landing Gear Models for Ground Manoeuvres 495
24.2 Landing Gear/Airframe Interface 496
24.3 Ground Manoeuvres – Landing 496
24.4 Ground Manoeuvres – Ground Handling 497
24.5 Loads Processing 498
25 Testing Relevant to Aeroelasticity and Loads 501
25.1 Introduction 501
25.2 Wind Tunnel Tests 501
25.3 Ground Vibration Test 502
25.4 Structural Coupling Test 503
25.5 Flight Simulator Test 504
25.6 Structural Tests 504
25.7 Flight Flutter Test 505
25.8 Flight Loads Validation 507
Appendices 509
A Aircraft Rigid Body Modes 511
B Table of Longitudinal Aerodynamic Derivatives 513
C Aircraft Symmetric Flexible Modes 517
D Model Condensation 527
E Aerodynamic Derivatives in Body Fixed Axes 531
References 535
Index 539
Introduction to Aircraft aeroelasticity and Loads, SecondEdition is an updated new edition offering comprehensivecoverage of the main principles of aircraft aeroelasticity andloads. For ease of reference, the book is divided into three partsand begins by reviewing the underlying disciplines of vibrations, aerodynamics, loads and control, and then goes on to describesimplified models to illustrate aeroelastic behaviour and aircraftresponse and loads for the flexible aircraft before introducingsome more advanced methodologies. Finally, it explains howindustrial certification requirements for aeroelasticity and loadsmay be met and relates these to the earlier theoretical approachesused. Key features of this new edition include: -Uses a unified simple aeroelastic model throughout thebook -Major revisions to chapters on aeroelasticity -Updates and reorganisation of chapters involving FiniteElements -Some reorganisation of loads material -Updates on certification requirements -Accompanied by a website containing a solutions manual, andMATLAB and SIMULINK programs that relate to the modelsused -For instructors who recommend this textbook, a series oflecture slides are also available Introduction to Aircraft aeroelasticity and Loads, SecondEdition is a must-have reference for researchers andpractitioners working in the aeroelasticity and loads fields, andis also an excellent textbook for senior undergraduate and graduatestudents in aerospace engineering.
About the Author Jan R. Wright University of Manchester, UK