Introduction to Aircraft Aeroelasticity and Loads

by Wright, Jan Robert; Cooper, Jonathan Edward

• ISBN13: 9780470858400
• ISBN10: 0470858400
• Format: Hardcover
• Copyright: 2008-01-22
• Publisher: WILEY

Summary

Aircraft performance is influenced significantly both by aeroelastic phenomena, arising from the interaction of elastic, inertial and aerodynamic forces, and by load variations resulting from flight and ground manoeuvres and gust / turbulence encounters. There is a strong link between aeroelasticity and loads, and these topics have become increasingly integrated in recent years. Introduction to Aircraft Aeroelasticity and Loads introduces the reader to the main principles involved in a wide range of aeroelasticity and loads topics. Divided into three sections, the book begins by reviewing the underlying disciplines of vibrations, aerodynamics, loads and control. It goes on to describe simplified models to illustrate aeroelastic behaviour and aircraft response before introducing more advanced methodologies. Finally, it explains how industrial certification requirements for aeroelasticity and loads may be met and relates these to the earlier theoretical approaches used. Presents fundamentals of structural dynamics, aerodynamics, static and dynamic aeroelasticity, response and load calculations and testing techniques. Covers performance issues related to aeroelasticity such as flutter, control effectiveness, divergence and redistribution of lift. Includes up-to-date experimental methods and analysis. Accompanied by a website with MatLAB and SIMULINK programs that relate to the models used. Introduction to Aircraft Aeroelasticity and Loads enables the reader to understand the aeroelastic and loads principles and procedures employed in a modern aircraft design office. It will appeal to final year undergraduate and masters students as well as engineers who are new to the aerospace industry.

Table of Contents

Preface	p. xv
Introduction	p. xix
Abbreviations	p. xxv
Background Material	p. 1
Vibration of Single Degree of Freedom Systems	p. 3
Setting up equations of motion for single DoF systems	p. 3
Free vibration of single DoF systems	p. 5
Forced vibration of single DoF systems	p. 7
Harmonic forced vibration - frequency response functions	p. 7
Transient/random forced vibration - time domain solution	p. 10
Transient forced vibration - frequency domain solution	p. 14
Random forced vibration - frequency domain solution	p. 16
Examples	p. 17
Vibration of Multiple Degree of Freedom Systems	p. 19
Setting up equations of motion	p. 19
Undamped free vibration	p. 21
Damped free vibration	p. 24
Transformation to modal coordinates	p. 27
'Free-free' systems	p. 31
Harmonic forced vibration	p. 31
Transient/random forced vibration - time domain solution	p. 33
Transient forced vibration - frequency domain solution	p. 34
Random forced vibration - frequency domain solution	p. 34
Examples	p. 35
Vibration of Continuous Systems - Assumed Shapes Approach	p. 37
Rayleigh-Ritz 'assumed shapes' method	p. 38
Generalized equations of motion - basic approach	p. 39
Generalized equations of motion - matrix approach	p. 44
Generating aircraft 'free-free' modes from 'branch' modes	p. 46
Whole aircraft 'free-free' modes	p. 49
Examples	p. 50
Vibration of Continuous Systems - Discretization Approach	p. 53
Introduction to the finite element (FE) approach	p. 53
Formulation of the beam bending element	p. 54
Assembly and solution for a structure with beam elements	p. 58
Torsion element	p. 63
Combined bending/torsion element	p. 64
Comments on modelling	p. 65
Examples	p. 66
Introduction to Steady Aerodynamics	p. 69
The standard atmosphere	p. 69
Effect of air speed on aerodynamic characteristics	p. 71
Flows and pressures around a symmetric aerofoil	p. 72
Forces on an aerofoil	p. 74
Variation of lift for an aerofoil at an angle of incidence	p. 75
Pitching moment variation and the aerodynamic centre	p. 76
Lift on a three-dimensional wing	p. 77
Drag on a three-dimensional wing	p. 81
Control surfaces	p. 82
Supersonic aerodynamics - piston theory	p. 83
Transonic flows	p. 84
Examples	p. 84
Introduction to Loads	p. 87
Laws of motion	p. 87
D'Alembert's principle - inertia forces and couples	p. 90
Externally applied/reactive loads	p. 93
Free body diagrams	p. 94
Internal loads	p. 95
Internal loads for continuous representation of a structure	p. 96
Internal loads for discretized representation of a structure	p. 100
Intercomponent loads	p. 102
Obtaining stresses from internal loads - structural members with simple load paths	p. 103
Examples	p. 103
Introduction to Control	p. 107
Open and closed loop systems	p. 107
Laplace transforms	p. 108
Modelling of open and closed loop systems using Laplace and frequency domains	p. 110
Stability of systems	p. 111
PID control	p. 118
Examples	p. 119
Introduction to Aeroelasticity and Loads	p. 121
Static Aeroelasticity - Effect of Wing Flexibility on Lift Distribution and Divergence	p. 123
Static aeroelastic behaviour of a two-dimensional rigid aerofoil with spring attachment	p. 124
Static aeroelastic behaviour of a fixed root flexible wing	p. 127
Effect of trim on static aeroelastic behaviour	p. 129
Effect of wing sweep on static aeroelastic behaviour	p. 134
Examples	p. 139
Static Aeroelasticity - Effect of Wing Flexibility on Control Effectiveness	p. 141
Rolling effectiveness of a flexible wing - the steady roll case	p. 141
Rolling effectiveness of a flexible wing - the fixed wing root case	p. 146
Effect of spanwise position of the control surface	p. 149
Full aircraft model - control effectiveness	p. 149
Effect of trim on reversal speed	p. 151
Examples	p. 151
Introduction to Unsteady Aerodynamics	p. 153
Quasi-steady aerodynamics	p. 153
Unsteady aerodynamics	p. 154
Aerodynamic lift and moment for a harmonically oscillating aerofoil	p. 157
Oscillatory aerodynamic derivatives	p. 159
Aerodynamic damping and stiffness	p. 160
Unsteady aerodynamics related to gusts	p. 161
Examples	p. 165
Dynamic Aeroelasticity - Flutter	p. 167
Simplified unsteady aerodynamic model	p. 167
Binary aeroelastic model	p. 168
General form of the aeroelastic equations	p. 171
Eigenvalue solution of flutter equations	p. 171
Aeroelastic behaviour of the binary model	p. 172
Aeroelastic behaviour of a flexible wing	p. 180
Aeroelastic behaviour of a multiple mode system	p. 182
Flutter speed prediction for binary systems	p. 182
Flutter conic	p. 184
Divergence of aeroelastic systems	p. 186
Inclusion of unsteady reduced frequency effects	p. 187
Control surface flutter	p. 191
Whole aircraft model - inclusion of rigid body modes	p. 193
Flutter in the transonic regime	p. 194
Flutter in the supersonic regime - wing and panel flutter	p. 194
Effect of nonlinearities - limit cycle oscillations	p. 197
Examples	p. 198
Aeroservoelasticity	p. 201
Mathematical modelling of a simple aeroelastic system with a control surface	p. 202
Inclusion of gust terms	p. 203
Implementation of a control system	p. 204
Determination of closed loop system stability	p. 204
Gust response of the closed loop system	p. 205
Inclusion of control law frequency dependency in stability calculations	p. 206
Response determination via the frequency domain	p. 208
State space modelling	p. 208
Examples	p. 209
Equilibrium Manoeuvres	p. 211
Equilibrium manoeuvre - rigid aircraft under normal acceleration	p. 213
Manoeuvre envelope	p. 217
Equilibrium manoeuvre - rigid aircraft pitching	p. 218
Equilibrium manoeuvre - flexible aircraft pitching	p. 225
Flexible corrections to rigid aircraft pitching derivatives	p. 238
Equilibrium manoeuvres - aircraft rolling and yawing	p. 239
Representation of the flight control system (FCS)	p. 243
Examples	p. 243
Flight Mechanics Model for Dynamic Manoeuvres	p. 245
Aircraft axes	p. 246
Motion variables	p. 247
Axes transformations	p. 248
Velocity and acceleration components for moving axes	p. 250
Flight mechanics equations of motion for a rigid aircraft	p. 252
Representation of disturbing forces and moments	p. 255
Equations for flexible aircraft in longitudinal motion	p. 257
Solution of flight mechanics equations	p. 262
Flight control system (FCS)	p. 263
Dynamic Manoeuvres	p. 265
Dynamic manoeuvre - rigid aircraft heave/pitch due to elevator input	p. 266
Dynamic manoeuvre - flexible aircraft heave/pitch due to elevator input	p. 271
General form of longitudinal equations	p. 278
Dynamic manoeuvre - rigid aircraft roll due to aileron input	p. 279
Dynamic manoeuvre - flexible aircraft roll due to aileron input	p. 283
Flexible corrections to flight mechanics equations	p. 290
Representation of the flight control system (FCS)	p. 290
Examples	p. 290
Gust and Turbulence Encounters	p. 293
Gusts and turbulence	p. 294
Gust response in the time domain	p. 295
Time domain gust response - rigid aircraft in heave	p. 297
Time domain gust response - rigid aircraft in heave/pitch	p. 303
Time domain gust response - flexible aircraft	p. 306
General form of equations in the time domain	p. 312
Turbulence response in the frequency domain	p. 314
Frequency domain turbulence response - rigid aircraft in heave	p. 317
Frequency domain turbulence response - rigid aircraft in heave/pitch	p. 320
Frequency domain turbulence response - flexible aircraft	p. 323
General form of equations in the frequency domain	p. 325
Representation of the flight control system (FCS)	p. 326
Examples	p. 326
Ground Manoeuvres	p. 329
Landing gear	p. 329
Taxi, take-off and landing roll	p. 333
Landing	p. 340
Braking	p. 345
'Spin-up' and 'spring-back' condition	p. 348
Turning	p. 350
Shimmy	p. 350
Representation of the flight control system (FCS)	p. 353
Examples	p. 353
Aircraft Internal Loads	p. 355
Limit and ultimate loads	p. 356
Internal loads for an aircraft	p. 356
General internal loads expressions - continuous wing	p. 358
Effect of wing-mounted engines/landing gear	p. 360
Internal loads - continuous flexible wing	p. 361
General internal loads expressions - discretized wing	p. 366
Internal loads - discretized fuselage	p. 370
Internal loads - continuous turbulence encounter	p. 373
Loads generation and sorting to yield critical cases	p. 374
Aircraft dimensioning cases	p. 376
Stresses from internal loads - complex load paths	p. 377
Examples	p. 377
Potential Flow Aerodynamics	p. 381
Elements of inviscid, incompressible flow analysis	p. 381
Inclusion of vorticity	p. 386
Numerical steady aerodynamic modelling of thin two-dimensional aerofoils	p. 388
Steady aerodynamic modelling of three-dimensional wings using a panel method	p. 391
Unsteady aerodynamic modelling of wings undergoing harmonic motion	p. 394
AICs in modal space	p. 397
Examples	p. 400
Coupling of Structural and Aerodynamic Computational Models	p. 401
Mathematical modelling - static aeroelastic case	p. 401
Two-dimensional coupled static aeroelastic model - pitch	p. 403
Two-dimensional coupled static aeroelastic model - heave/pitch	p. 404
Three-dimensional coupled static aeroelastic model	p. 405
Mathematical modelling - dynamic aeroelastic response	p. 409
Two-dimensional coupled dynamic aeroelastic model - bending and torsion	p. 410
Three-dimensional flutter analysis	p. 411
Inclusion of frequency-dependent aerodynamics for state space modelling - rational fraction approximation	p. 412
Introduction to Industrial Practice	p. 417
Aircraft Design and Certification	p. 419
Aeroelastics and loads in the aircraft design process	p. 419
Aircraft certification process	p. 421
Aeroelasticity and Loads Models	p. 427
Structural model	p. 427
Aerodynamic model	p. 432
Flight control system	p. 435
Other model issues	p. 435
Loads transformations	p. 436
Static Aeroelasticity and Flutter	p. 437
Static aeroelasticity	p. 437
Flutter	p. 439
Flight Manoeuvre and Gust/Turbulence Loads	p. 443
Evaluation of internal loads	p. 443
Equilibrium/balanced flight manoeuvres	p. 443
Dynamic flight manoeuvres	p. 446
Gusts and turbulence	p. 449
Ground Manoeuvre Loads	p. 455
Aircraft/landing gear models for ground manoeuvres	p. 455
Landing gear/airframe interface	p. 456
Ground manoeuvres - landing	p. 456
Ground manoeuvres - ground handling	p. 457
Loads processing	p. 458
Testing Relevant to Aeroelasticity and Loads	p. 461
Introduction	p. 461
Wind tunnel tests	p. 461
Ground vibration test	p. 462
Structural coupling test	p. 463
Flight simulator test	p. 464
Structural tests	p. 464
Flight flutter test	p. 465
Flight loads validation	p. 466
Appendices	p. 467
Aircraft Rigid Body Modes	p. 469
Rigid body translation modes	p. 469
Rigid body rotation modes	p. 469
Table of Longitudinal Aerodynamic Derivatives	p. 471
Aircraft Symmetric Flexible Modes	p. 473
Aircraft model	p. 473
Symmetric free-free flexible mode	p. 474
Model Condensation	p. 481
Introduction	p. 481
Static condensation	p. 481
Dynamic condensation - Guyan reduction	p. 482
Static condensation for aeroelastic models	p. 483
Modal condensation	p. 483
Modal reduction	p. 484
Aerodynamic Derivatives in Body Fixed Axes	p. 485
Longitudinal derivative Z[subscript w]	p. 485
Lateral derivatives L[subscript p], L[subscript xi]	p. 486
Aircraft Antisymmetric Flexible Modes	p. 489
Aircraft model	p. 489
Antisymmetric free-free flexible modes	p. 489
References	p. 491
Index	p. 495
Programs Accessible (on the Companion Website) via the Internet
MATLAB/SIMULINK Programs for Vibration
Forced response of an SDoF system
Modal solution for an MDoF system
Finite element solution
MATLAB/SIMULINK Programs for Flutter
Dynamic aeroelastic calculations
Aeroservoelastic system
MATLAB/SIMULINK Programs for Flight/Ground Manoeuvres and Gust/Turbulence Encounters
Rigid aircraft data
Flexible aircraft data
Flight case data
Aerodynamic derivative calculation
Equilibrium manoeuvres
Dynamic manoeuvres
Gust response in the time domain
Gust response in the frequency domain
Ground manoeuvres
Table of Contents provided by Ingram. All Rights Reserved.