Introduction to Aircraft Aeroelasticity and Loads

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Series Preface xxi <
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Preface to the Second Edition xxiii <
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Preface to the First Edition xxv <
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Abbreviations xxix <
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Introduction 1 <
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PART I BACKGROUND MATERIAL 7 <
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1 Vibration of Single Degree of Freedom Systems 9 <
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1.1 Setting up Equations of Motion for SDoF Systems 9 <
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1.2 Free Vibration of SDoF Systems 11 <
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1.3 Forced Vibration of SDoF Systems 13 <
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1.4 Harmonic Forced Vibration     Frequency Response Functions 14 <
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1.5 Transient/Random Forced Vibration     Time Domain Solution 17 <
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1.6 Transient Forced Vibration     Frequency Domain Solution 21 <
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1.7 Random Forced Vibration     Frequency Domain Solution 23 <
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1.8 Examples 24 <
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2 Vibration of Multiple Degree of Freedom Systems 27 <
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2.1 Setting up Equations of Motion 27 <
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2.2 Undamped Free Vibration 29 <
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2.3 Damped Free Vibration 31 <
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2.4 Transformation to Modal Coordinates 34 <
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2.5 Two-DoF Rigid Aircraft in Heave and Pitch 38 <
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2.6    Free   Free    Systems 40 <
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2.7 Harmonic Forced Vibration 41 <
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2.8 Transient/Random Forced Vibration     Time Domain Solution 43 <
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2.9 Transient Forced Vibration     Frequency Domain Solution 44 <
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2.10 Random Forced Vibration     Frequency Domain Solution 44 <
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2.11 Examples 45 <
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3 Vibration of Continuous Systems     Assumed Shapes Approach 49 <
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3.1 Continuous Systems 49 <
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3.2 Modelling Continuous Systems 49 <
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3.3 Elastic and Flexural Axes 51 <
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3.4 Rayleigh   Ritz    Assumed Shapes    Method 52 <
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3.5 Generalized Equations of Motion     Basic Approach 53 <
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3.6 Generalized Equations of Motion     Matrix Approach 58 <
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3.7 Generating Whole Aircraft    Free   Free    Modes from    Branch    Modes 61 <
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3.8 Whole Aircraft    Free   Free    Modes 64 <
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3.9 Examples 65 <
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4 Introduction to Steady Aerodynamics 69 <
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4.1 The Standard Atmosphere 69 <
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4.2 Effect of Air Speed on Aerodynamic Characteristics 71 <
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4.3 Flows and Pressures Around a Symmetric Aerofoil 73 <
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4.4 Forces on an Aerofoil 74 <
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4.5 Variation of Lift for an Aerofoil at an Angle of Incidence 76 <
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4.6 Pitching Moment Variation and the Aerodynamic Centre 77 <
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4.7 Lift on a Three-dimensional Wing 78 <
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4.8 Drag on a Three-dimensional Wing 82 <
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4.9 Control Surfaces 83 <
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4.10 Transonic Flows 84 <
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4.11 Examples 85 <
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5 Introduction to Loads 87 <
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5.1 Laws of Motion 88 <
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5.2 D   Alembert   s Principle     Inertia Forces and Couples 90 <
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5.3 External Loads     Applied and Reactive 94 <
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5.4 Free Body Diagrams 95 <
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5.5 Internal Loads 96 <
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5.6 Internal Loads for a Continuous Member 96 <
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5.7 Internal Loads for a Discretized Member 101 <
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5.8 Intercomponent Loads 103 <
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5.9 Obtaining Stresses from Internal Loads     Structural Members with Simple Load Paths 103 <
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5.10 Examples 104 <
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6 Introduction to Control 109 <
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6.1 Open and Closed Loop Systems 109 <
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6.2 Laplace Transforms 110 <
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6.3 Modelling of Open and Closed Loop Systems using Laplace and Frequency Domains 112 <
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6.4 Stability of Systems 114 <
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6.5 PID Control 121 <
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6.6 Examples 122 <
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PART II INTRODUCTION TO AEROELASTICITY AND LOADS 123 <
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7 Static Aeroelasticity     Effect of Wing Flexibility on Lift Distribution and Divergence 125 <
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7.1 Static Aeroelastic Behaviour of a Two-dimensional Rigid Aerofoil with a Torsional Spring Attachment 126 <
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7.2 Static Aeroelastic Behaviour of a Fixed Root Flexible Wing 130 <
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7.3 Effect of Trim on Static Aeroelastic Behaviour 133 <
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7.4 Effect of Wing Sweep on Static Aeroelastic Behaviour 137 <
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7.5 Examples 142 <
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8 Static Aeroelasticity     Effect of Wing Flexibility on Control Effectiveness 143 <
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8.1 Rolling Effectiveness of a Flexible Wing     Fixed Wing Root Case 144 <
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8.2 Rolling Effectiveness of a Flexible Wing     Steady Roll Case 147 <
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8.3 Effect of Spanwise Position of the Control Surface 151 <
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8.4 Full Aircraft Model     Control Effectiveness 152 <
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8.5 Effect of Trim on Reversal Speed 153 <
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8.6 Examples 153 <
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9 Introduction to Unsteady Aerodynamics 155 <
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9.1 Quasi-steady Aerodynamics 156 <
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9.2 Unsteady Aerodynamics related to Motion 156 <
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9.3 Aerodynamic Lift and Moment for an Aerofoil Oscillating Harmonically in Heave and Pitch 161 <
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9.4 Oscillatory Aerodynamic Derivatives 162 <
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9.5 Aerodynamic Damping and Stiffness 163 <
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9.6 Approximation of Unsteady Aerodynamic Terms 164 <
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9.7 Unsteady Aerodynamics related to Gusts 164 <
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9.8 Examples 168 <
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10 Dynamic Aeroelasticity     Flutter 171 <
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10.1 Simplified Unsteady Aerodynamic Model 172 <
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10.2 Binary Aeroelastic Model 173 <
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10.3 General Form of the Aeroelastic Equations 176 <
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10.4 Eigenvalue Solution of the Flutter Equations 176 <
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10.5 Aeroelastic Behaviour of the Binary Model 177 <
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10.6 Aeroelastic Behaviour of a Multiple Mode System 185 <
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10.7 Flutter Speed Prediction for Binary Systems 185 <
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10.8 Divergence of Dynamic Aeroelastic Systems 188 <
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10.9 Inclusion of Unsteady Reduced Frequency Effects 189 <
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10.10 Control Surface Flutter 193 <
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10.11 Whole Aircraft Model     Inclusion of Rigid Body Modes 199 <
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10.12 Flutter in the Transonic Regime 202 <
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10.13 Effect of Non-Linearities     Limit Cycle Oscillations 202 <
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10.14 Examples 204 <
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11 Aeroservoelasticity 207 <
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11.1 Mathematical Modelling of a Simple Aeroelastic System with a Control Surface 208 <
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11.2 Inclusion of Gust Terms 209 <
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11.3 Implementation of a Control System 210 <
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11.4 Determination of Closed Loop System Stability 211 <
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11.5 Gust Response of the Closed Loop System 213 <
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11.6 Inclusion of Control Law Frequency Dependency in Stability Calculations 214 <
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11.7 Response Determination via the Frequency Domain 215 <
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11.8 State Space Modelling 216 <
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11.9 Examples 217 <
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12 Equilibrium Manoeuvres 219 <
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12.1 Equilibrium Manoeuvre     Rigid Aircraft under Normal Acceleration 221 <
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12.2 Manoeuvre Envelope 226 <
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12.3 Equilibrium Manoeuvre     Rigid Aircraft Pitching 227 <
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12.4 Equilibrium Manoeuvre     Flexible Aircraft Pitching 235 <
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12.5 Representation of the Flight Control System (FCS) 250 <
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12.6 Examples 250 <
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13 Dynamic Manoeuvres 253 <
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13.1 Aircraft Axes 255 <
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13.2 Motion Variables 257 <
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13.3 Axes Transformations 257 <
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13.4 Velocity and Acceleration Components for Moving Axes in 2D 259 <
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13.5 Flight Mechanics Equations of Motion for a Rigid Symmetric Aircraft in 2D 262 <
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13.6 Representation of Disturbing Forces and Moments 265 <
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13.7 Modelling the Flexible Aircraft 267 <
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13.8 Solution of Flight Mechanics Equations for the Rigid Aircraft 272 <
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13.9 Dynamic Manoeuvre     Rigid Aircraft in Longitudinal Motion 273 <
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13.10 Dynamic Manoeuvre     Flexible Aircraft Heave/Pitch 279 <
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13.11 General Form of Longitudinal Equations 287 <
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13.12 Dynamic Manoeuvre for Rigid Aircraft in Lateral Motion 288 <
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13.13 Bookcase Manoeuvres for Rigid Aircraft in Lateral Motion 289 <
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13.14 Flight Control System (FCS) 293 <
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13.15 Representation of the Flight Control System (FCS) 295 <
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13.16 Examples 295 <
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14 Gust and Turbulence Encounters 299 <
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14.1 Gusts and Turbulence 300 <
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14.2 Gust Response in the Time Domain 301 <
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14.3 Time Domain Gust Response     Rigid Aircraft in Heave 303 <
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14.4 Time Domain Gust Response     Rigid Aircraft in Heave/Pitch 310 <
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14.5 Time Domain Gust Response     Flexible Aircraft 316 <
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14.6 General Form of Equations in the Time Domain 321 <
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14.7 Turbulence Response in the Frequency Domain 321 <
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14.8 Frequency Domain Turbulence Response     Rigid Aircraft in Heave 324 <
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14.9 Frequency Domain Turbulence Response     Rigid Aircraft in Heave/Pitch 329 <
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14.10 Frequency Domain Turbulence Response     Flexible Aircraft 330 <
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14.11 General Form of Equations in the Frequency Domain 333 <
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14.12 Representation of the Flight Control System (FCS) 334 <
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14.13 Examples 334 <
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15 Ground Manoeuvres 337 <
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15.1 Landing Gear 337 <
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15.2 Taxi, Take-Off and Landing Roll 342 <
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15.3 Landing 351 <
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15.4 Braking 359 <
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15.5 Turning 360 <
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15.6 Shimmy 361 <
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15.7 Representation of the Flight Control System (FCS) 363 <
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15.8 Examples 363 <
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16 Aircraft Internal Loads 367 <
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16.1 Limit and Ultimate Loads 368 <
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16.2 Internal Loads for an Aircraft 368 <
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16.3 General Internal Loads Expressions     Continuous Wing 370 <
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16.4 Effect of Wing-mounted Engines and Landing Gear 372 <
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16.5 Internal Loads     Continuous Flexible Wing 373 <
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16.6 General Internal Loads Expressions     Discretized Wing 379 <
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16.7 Internal Loads     Discretized Fuselage 384 <
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16.8 Internal Loads     Continuous Turbulence Encounter 387 <
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16.9 Loads Generation and Sorting to yield Critical Cases 388 <
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16.10 Aircraft Dimensioning Cases 390 <
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16.11 Stresses derived from Internal Loads     Complex Load Paths 391 <
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16.12 Examples 391 <
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17 Vibration of Continuous Systems     Finite Element Approach 395 <
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17.1 Introduction to the Finite Element Approach 395 <
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17.2 Formulation of the Beam Bending Element 397 <
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17.3 Assembly and Solution for a Beam Structure 401 <
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17.4 Torsion Element 406 <
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17.5 Combined Bending/Torsion Element 407 <
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17.6 Concentrated Mass Element 408 <
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17.7 Stiffness Element 408 <
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17.8 Rigid Body Elements 409 <
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17.9 Other Elements 410 <
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17.10 Comments on Modelling 411 <
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17.11 Examples 413 <
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18 Potential Flow Aerodynamics 415 <
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18.1 Components of Inviscid, Incompressible Flow Analysis 415 <
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18.2 Inclusion of Vorticity 420 <
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18.3 Numerical Steady Aerodynamic Modelling of Thin Two-dimensional Aerofoils 422 <
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18.4 Steady Aerodynamic Modelling of Three-Dimensional Wings using a Panel Method 425 <
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18.5 Unsteady Aerodynamic Modelling of Wings undergoing Harmonic Motion 429 <
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18.6 Aerodynamic Influence Coefficients in Modal Space 432 <
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18.7 Examples 436 <
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19 Coupling of Structural and Aerodynamic Computational Models 437 <
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19.1 Mathematical Modelling     Static Aeroelastic Case 438 <
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19.2 2D Coupled Static Aeroelastic Model     Pitch 439 <
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19.3 2D Coupled Static Aeroelastic Model     Heave/Pitch 440 <
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19.4 3D Coupled Static Aeroelastic Model 441 <
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19.5 Mathematical Modelling     Dynamic Aeroelastic Response 446 <
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19.6 2D Coupled Dynamic Aeroelastic Model     Bending/Torsion 447 <
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19.7 3D Flutter Analysis 448 <
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19.8 Inclusion of Frequency Dependent Aerodynamics for State   Space Modelling     Rational Function Approximation 450 <
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PART III INTRODUCTION TO INDUSTRIAL PRACTICE 455 <
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20 Aircraft Design and Certification 457 <
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20.1 Aeroelastics and Loads in the Aircraft Design Process 457 <
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20.2 Aircraft Certification Process 459 <
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21 Aeroelasticity and Loads Models 465 <
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21.1 Structural Model 465 <
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21.2 Aerodynamic Model 471 <
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21.3 Flight Control System 473 <
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21.4 Other Model Issues 474 <
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21.5 Loads Transformations 474 <
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22 Static Aeroelasticity and Flutter 475 <
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22.1 Static Aeroelasticity 475 <
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22.2 Flutter 478 <
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23 Flight Manoeuvre and Gust/Turbulence Loads 481 <
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23.1 Evaluation of Internal Loads 481 <
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23.2 Equilibrium/Balanced Flight Manoeuvres 481 <
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23.3 Dynamic Flight Manoeuvres 485 <
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23.4 Gusts and Turbulence 489 <
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24 Ground Manoeuvre Loads 495 <
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24.1 Aircraft/Landing Gear Models for Ground Manoeuvres 495 <
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24.2 Landing Gear/Airframe Interface 496 <
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24.3 Ground Manoeuvres     Landing 496 <
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24.4 Ground Manoeuvres     Ground Handling 497 <
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24.5 Loads Processing 498 <
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25 Testing Relevant to Aeroelasticity and Loads 501 <
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25.1 Introduction 501 <
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25.2 Wind Tunnel Tests 501 <
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25.3 Ground Vibration Test 502 <
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25.4 Structural Coupling Test 503 <
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25.5 Flight Simulator Test 504 <
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25.6 Structural Tests 504 <
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25.7 Flight Flutter Test 505 <
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25.8 Flight Loads Validation 507 <
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Appendices 509 <
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A Aircraft Rigid Body Modes 511 <
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B Table of Longitudinal Aerodynamic Derivatives 513 <
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C Aircraft Symmetric Flexible Modes 517 <
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D Model Condensation 527 <
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E Aerodynamic Derivatives in Body Fixed Axes 531 <
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References 535 <
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Index 539