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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 xv
Introduction xix
Abbreviations xxv
Part I Background Material 1
1 Vibration of Single Degree of Freedom 3
Systems
1.1 Setting up equations of motion for 3
single DoF systems
1.2 Free vibration of single DoF systems 5
1.3 Forced vibration of single DoF systems 7
1.4 Harmonic forced vibration frequency 7
response functions
1.5 Transient/random forced vibration 10
time domain solution
1.6 Transient forced vibration 14
frequency domain solution
1.7 Random forced vibration frequency 16
domain solution
1.8 Examples 17
2 Vibration of Multiple Degree of Freedom 19
Systems
2.1 Setting up equations of motion 19
2.2 Undamped free vibration 21
2.3 Damped free vibration 24
2.4 Transformation to modal coordinates 27
2.5 'Free庸ree' systems 31
2.6 Harmonic forced vibration 31
2.7 Transient/random forced vibration 33
time domain solution
2.8 Transient forced vibration 34
frequency domain solution
2.9 Random forced vibration frequency 34
domain solution
2.10 Examples 35
3 Vibration of Continuous Systems Assumed 37
Shapes Approach
3.1 Rayleigh由itz assumed shapes' method 38
3.2 Generalized equations of motion 39
basic approach
3.3 Generalized equations of motion 44
matrix approach
3.4 Generating aircraft 'free庸ree' modes 46
from 'branch' modes
3.5 Whole aircraft 'free庸ree' modes 49
3.6 Examples 50
4 Vibration of Continuous Systems - 53
Discretization Approach
4.1 Introduction to the finite element 53
(FE) approach
4.2 Formulation of the beam bending 54
element
4.3 Assembly and solution for a structure 58
with beam elements
4.4 Torsion element 63
4.5 Combined bending/torsion element 64
4.6 Comments on modelling 65
4.7 Examples 66
5 Introduction to Steady Aerodynamics 69
5.1 The standard atmosphere 69
5.2 Effect of air speed on aerodynamic 71
characteristics
5.3 Flows and pressures around a 72
symmetric aerofoil
5.4 Forces on an aerofoil 74
5.5 Variation of lift for an aerofoil at 75
an angle of incidence
5.6 Pitching moment variation and the 76
aerodynamic centre
5.7 Lift on a three-dimensional wing 77
5.8 Drag on a three-dimensional wing 81
5.9 Control surfaces 82
5.10 Supersonic aerodynamics - piston 83
theory
5.11 Transonic flows 84
5.12 Examples 84
6 Introduction to Loads 87
6.1 Laws of motion 87
6.2 D'Alembert's principle - inertia 90
forces and couples
6.3 Externally applied/reactive loads 93
6.4 Free body diagrams 94
6.5 Internal loads 95
6.6 Internal loads for continuous 96
representation of a structure
6.7 Internal loads for discretized 100
representation of a structure
6.8 Intercomponent loads 102
6.9 Obtaining stresses from internal 103
loads - structural members with simple
load paths
6.10 Examples 103
7 Introduction to Control 107
7.1 Open and closed loop systems 107
7.2 Laplace transforms 108
7.3 Modelling of open and closed loop 110
systems using Laplace and frequency
domains
7.4 Stability of systems 111
7.5 PID control 118
7.6 Examples 119
Part II Introduction to Aeroelasticity and Loads 121
8 Static Aeroelasticity - Effect of Wing 123
Flexibility on Lift Distribution and
Divergence
8.1 Static aeroelastic behaviour of a 124
two-dimensional rigid aerofoil with
spring attachment
8.2 Static aeroelastic behaviour of a 127
fixed root flexible wing
8.3 Effect of trim on static aeroelastic 129
behaviour
8.4 Effect of wing sweep on static 134
aeroelastic behaviour
8.5 Examples 139
9 Static Aeroelasticity - Effect of Wing 141
Flexibility on Control Effectiveness
9.1 Rolling effectiveness of a flexible 141
wing - the steady roll case
9.2 Rolling effectiveness of a flexible 146
wing - the fixed wing root case
9.3 Effect of spanwise position of the 149
control surface
9.4 Full aircraft model - control 149
effectiveness
9.5 Effect of trim on reversal speed 151
9.6 Examples 151
10 Introduction to Unsteady Aerodynamics 153
10.1 Quasi-steady aerodynamics 153
10.2 Unsteady aerodynamics 154
10.3 Aerodynamic lift and moment for a 157
harmonically oscillating aerofoil
10.4 Oscillatory aerodynamic derivatives 159
10.5 Aerodynamic damping and stiffness 160
10.6 Unsteady aerodynamics related to 161
gusts
10.7 Examples 165
11 Dynamic Aeroelasticity - Flutter 167
11.1 Simplified unsteady aerodynamic 167
model
11.2 Binary aeroelastic model 168
11.3 General form of the aeroelastic 171
equations
11.4 Eigenvalue solution of flutter 171
equations
11.5 Aeroelastic behaviour of the binary 172
model
11.6 Aeroelastic behaviour of a flexible 180
wing
11.7 Aeroelastic behaviour of a multiple 182
mode system
11.8 Flutter speed prediction for binary 182
systems
11.9 Flutter conic 184
11.10 Divergence of aeroelastic systems 186
11.11 Inclusion of unsteady reduced 187
frequency effects
11.12 Control surface flutter 191
11.13 Whole aircraft model - inclusion of 193
rigid body modes
11.14 Flutter in the transonic regime 194
11.15 Flutter in the supersonic regime - 194
wing and panel flutter
11.16 Effect of nonlinearities - limit 197
cycle oscillations
11.17 Examples 198
12 Aeroservoelasticity 201
12.1 Mathematical modelling of a simple 202
aeroelastic system with a control surface
12.2 Inclusion of gust terms 203
12.3 Implementation of a control system 204
12.4 Determination of closed loop system 204
stability
12.5 Gust response of the closed loop 205
system
12.6 Inclusion of control law frequency 206
dependency in stability calculations
12.7 Response determination via the 208
frequency domain
12.8 State space modelling 208
12.9 Examples 209
13 Equilibrium Manoeuvres 211
13.1 Equilibrium manoeuvre - rigid 213
aircraft under normal acceleration
13.2 Manoeuvre envelope 217
13.3 Equilibrium manoeuvre - rigid 218
aircraft pitching
13.4 Equilibrium manoeuvre - flexible 225
aircraft pitching
13.5 Flexible corrections to rigid 238
aircraft pitching derivatives
13.6 Equilibrium manoeuvres - aircraft 239
rolling and yawing
13.7 Representation of the flight control 243
system (FCS)
13.8 Examples 243
14 Flight Mechanics Model for Dynamic 245
Manoeuvres
14.1 Aircraft axes 246
14.2 Motion variables 247
14.3 Axes transformations 248
14.4 Velocity and acceleration components 250
for moving axes
14.5 Flight mechanics equations of motion 252
for a rigid aircraft
14.6 Representation of disturbing forces 255
and moments
14.7 Equations for flexible aircraft in 257
longitudinal motion
14.8 Solution of flight mechanics 262
equations
14.9 Flight control system (FCS) 263
15 Dynamic Manoeuvres 265
15.1 Dynamic manoeuvre - rigid aircraft 266
heave/pitch due to elevator input
15.2 Dynamic manoeuvre - flexible 271
aircraft heave/pitch due to elevator input
15.3 General form of longitudinal 278
equations
15.4 Dynamic manoeuvre - rigid aircraft 279
roll due to aileron input
15.5 Dynamic manoeuvre - flexible 283
aircraft roll due to aileron input
15.6 Flexible corrections to flight 290
mechanics equations
15.7 Representation of the flight control 290
system (FCS)
15.8 Examples 290
16 Gust and Turbulence Encounters 293
16.1 Gusts and turbulence 294
16.2 Gust response in the time domain 295
16.3 Time domain gust response - rigid 297
aircraft in heave
16.4 Time domain gust response - rigid 303
aircraft in heave/pitch
16.5 Time domain gust response - 306
flexible aircraft
16.6 General form of equations in the 312
time domain
16.7 Turbulence response in the 314
frequency domain
16.8 Frequency domain turbulence 317
response - rigid aircraft in heave
16.9 Frequency domain turbulence 320
response-rigid aircraft in heave/pitch
16.10 Frequency domain turbulence 323
response - flexible aircraft
16.11 General form of equations in the 325
frequency domain
16.12 Representation of the flight 326
control system (FCS)
16.13 Examples 326
17 Ground Manoeuvres 329
17.1 Landing gear 329
17.2 Taxi, take-off and landing roll 333
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 Representation of the flight control 353
system (FCS)
17.9 Examples 353
18 Aircraft Internal Loads 355
18.1 Limit and ultimate loads 356
18.2 Internal loads for an aircraft 356
18.3 General internal loads expressions 358
- continuous wing
18.4 Effect of wing-mounted 360
engines/landing gear
18.5 Internal loads - continuous 361
flexible wing
18.6 General internal loads expressions 366
- discretized wing
18.7 Internal loads - discretized 370
fuselage
18.8 Internal loads - continuous 373
turbulence encounter
18.9 Loads generation and sorting to 374
yield critical cases
18.10 Aircraft dimensioning cases 376
18.11 Stresses from internal loads - 377
complex load paths
18.12 Examples 377
19 Potential Flow Aerodynamics 381
19.1 Elements of inviscid, incompressible 381
flow analysis
19.2 Inclusion of vorticity 386
19.3 Numerical steady aerodynamic 388
modelling of thin two-dimensional
aerofoils
19.4 Steady aerodynamic modelling of 391
three-dimensional wings using a panel
method
19.5 Unsteady aerodynamic modelling of 394
wings undergoing harmonic motion
19.6 AICs in modal space 397
19.7 Examples 400
20 Coupling of Structural and Aerodynamic 401
Computational Models
20.1 Mathematical modelling - static 401
aeroelastic case
20.2 Two-dimensional coupled static 403
aeroelastic model - pitch
20.3 Two-dimensional coupled static 404
aeroelastic model - heave/pitch
20.4 Three-dimensional coupled static 405
aeroelastic model
20.5 Mathematical modelling - dynamic 409
aeroelastic response
20.6 Two-dimensional coupled dynamic 410
aeroelastic model - bending and torsion
20.7 Three-dimensional flutter analysis 411
20.8 Inclusion of frequency-dependent 412
aerodynamics for state space modelling -
rational fraction approximation
Part III Introduction to Industrial Practice 417
21 Aircraft Design and Certification 419
21.1 Aeroelastics and loads in the 419
aircraft design process
21.2 Aircraft certification process 421
22 Aeroelasticity and Loads Models 427
22.1 Structural model 427
22.2 Aerodynamic model 432
22.3 Flight control system 435
22.4 Other model issues 435
22.5 Loads transformations 436
23 Static Aeroelasticity and Flutter 437
23.1 Static aeroelasticity 437
23.2 Flutter 439
24 Flight Manoeuvre and Gust/Turbulence Loads 443
24.1 Evaluation of internal loads 443
24.2 Equilibrium/balanced flight 443
manoeuvres
24.3 Dynamic flight manoeuvres 446
24.4 Gusts and turbulence 449
25 Ground Manoeuvre Loads 455
25.1 Aircraft/landing gear models for 455
ground manoeuvres
25.2 Landing gear/airframe interface 456
25.3 Ground manoeuvres - landing 456
25.4 Ground manoeuvres - ground handling 457
25.5 Loads processing 458
26 Testing Relevant to Aeroelasticity and 461
Loads
26.1 Introduction 461
26.2 Wind tunnel tests 461
26.3 Ground vibration test 462
26.4 Structural coupling test 463
26.5 Flight simulator test 464
26.6 Structural tests 464
26.7 Flight flutter test 465
26.8 Flight loads validation 466
Appendices 467
A Aircraft Rigid Body Modes 469
A.1 Rigid body translation modes 469
A.2 Rigid body rotation modes 469
B Table of Longitudinal Aerodynamic 471
Derivatives
C Aircraft Symmetric Flexible Modes 473
C.1 Aircraft model 473
C.2 Symmetric free-free flexible mode 474
D Model Condensation 481
D.1 Introduction 481
D.2 Static condensation 481
D.3 Dynamic condensation - Guyan reduction 482
D.4 Static condensation for aeroelastic 483
models
D.5 Modal condensation 483
D.6 Modal reduction 484
E Aerodynamic Derivatives in Body Fixed Axes 485
E.1 Longitudinal derivative Zw 485
E.2 Lateral derivatives Lp, Lξ 486
F Aircraft Antisymmetric Flexible Modes 489
F.1 Aircraft model 489
F.2 Antisymmetric free庸ree flexible modes 489
References 491
Index 495
