
Introduction to Aircraft Aeroelasticity and Loads
by Wright, Jan Robert; Cooper, Jonathan Edward-
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Summary
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. |
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