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Table of Contents

CHAPTER 1. INTRODUCTION TO AEROELASTICITY 1-1 Definitions 1-2 Historical background 1-3 Influence of aeroelastic phenomena on design 1-4 Comparison of wing critical speeds CHAPTER 2. DEFORMATIONS OF AIRPLANE STRUCTURES UNDER STATIC LOADS 2-1 Introduction 2-2 Elastic properties of structure 2-3 Deformation due to several forces. Influence coefficients 2-4 Properties of influence coefficients 2-5 Strain energy in terms of influence coefficients 2-6 Deformations under distributed forces. Influence functions 2-7 Properties of influence functions 2-8 The simplified elastic airplane 2-9 Deformations of airplane wings 2-10 Integration by weighting matrices 2-11 Energy methods in deflection calculations 2-12 Deformations of slender unswept wings 2-13 Influence functions and coefficients of slender swept wings 2-14 Deformations and influence coefficients of low aspect-ratio wings 2-15 Influence coefficients of complex built-up wings by the principle of minimum strain energy 2-16 Influence coefficients of complex built-up wings by the principle of minimum potential energy 2-17 Calculation of deformations of solid wings of variable thickness and complex built-up wings by the Rayleigh-Ritz method CHAPTER 3. DEFORMATION OF AIRPLANE STRUCTURES UNDER DYNAMIC LOADS 3-1 Introduction 3-2 Differential equations of motion of a beam 3-3 Integral equation of motion of a slender beam 3-4 Dynamic equilibrium of slender rotating beams in torsion 3-5 Dynamic equilibrium of slender beams in torsion 3-6 Dynamic equilibrium of restrained airplane wing 3-7 Dynamic equilibrium of the unrestrained elastic airplane 3-8 Energy methods 3-9 Approximate methods of solution to practical problems 3-10 Approximate solutions by the Rayleigh-Ritz method 3-11 Approximate solutions by the lumped parameter method CHAPTER 4. APPROXIMATE METHODS OF COMPUTING NATURAL MODE SHAPES AND FREQUENCIES 4-1 Introduction 4-2 Natural modes and frequencies by energy methods 4-3 Natural mode shapes and frequencies derived from the integral equation 4-4 Natural mode shapes and frequencies derived from the differential equation 4-5 Solution of characteristic equations 4-6 Natural modes and frequencies of complex airplane structures 4-7 Natural modes and frequencies of rotating beams CHAPTER 5. AERODYNAMIC TOOLS: TWO- AND THREE-DIMENSIONAL INCOMPRESSIBLE FLOW 5-1 Fundamentals: the concept of small disturbances 5-2 Properties of incompressible flow with and without circulation 5-3 Vortex flow 5-4 Thin airfoils in steady motion 5-5 Finite wings in steady motion 5-6 Thin airfoils oscillating in incompressible flow 5-7 Arbitrary motion of the thin airfoils in incompressible flow; the gust problem CHAPTER 6. AERODYNAMIC TOOLS: COMPRESSIBLE FLOW 6-1 Introduction 6-2 Wings and airfoils in steady subsonic flow; the Prandtl-Glauert transformation 6-3 Airfoils and wings in steady supersonic flow 6-4 Oscillating airfoils in subsonic flow 6-5 Arbitrary small motions of airfoils in subsonic flow 6-6 Oscillating airfoils in supersonic speeds 6-7 Indicial airfoil motions in supersonic flow 6-8 Unsteady motion of airfoils at Mach number one CHAPTER 7. WINGS AND BODIES IN THREE-DIMENSIONAL UNSTEADY FLOW 7-1 Introduction 7-2 Oscillating finite wings in incompressible flow 7-3 The influence of sweep 7-4 Wings of very low aspect ratio in unsteady motion 7-5 The influence of sweep 7-6 Unsteady motion of nonlifting bodies CHAPTER 8. STATIC AEROELASTIC PHENOMENA 8-1 Introduction 8-2 Twisting of simple two-dimensional wing with aileron 8-3 Slender straight wings 8-4 Swept wings 8-5 Low aspect-ratio lifting surfaces of arbitrary planform and stiffness CHAPTER 9. FLUTTER 9-1 Introduction. The nature of flutter 9-2 Flutter of a simple system with two degrees of freedom 9-3 Exact treatment of the bending-torsion flutter of a uniform cantilever wing 9-4 Aeroelastic modes 9-5 Flutter analysis by assumed-mode methods 9-6 Inclusion of finite span effects in flutter calculations 9-7 The effect of compressibility on flutter 9-8 Flutter of swept wings 9-9 Wings of low aspect ratio 9-10 Single-degree-of-freedom flutter 9-11 Certain other interesting types of flutter CHAPTER 10. DYNAMIC RESPONSE PHENOMENA 10-1 Introduction 10-2 Equations of disturbed motion of an elastic airplane 10-3 Systems with prescribed time-dependent external forces 10-4 Transient stresses during landing 10-5 Systems with external forces depending upon the motion 10-6 Dynamic response to a discrete gust 10-7 Dynamic response to continuous atmospheric turbulence CHAPTER 11. AEROELASTIC MODEL THEORY 11-1 Introduction 11-2 Dimensional concepts 11-3 Equations of motion 11-4 Vibration model similarity laws 11-5 Similarity laws for systems under steady airloads 11-6 Flutter model similarity laws 11-7 The unrestrained flutter model 11-8 The dynamic stability model CHAPTER 12. MODEL DESIGN AND CONSTRUCTION 12-1 Introduction 12-2 Structural simulation 12-3 Elastic properties as functions of one variable 12-4 Elastic properties as functions of two variables 12-5 Shape simulation 12-6 Inertial simulation CHAPTER 13. TESTING TECHNIQUES 13-1 Introduction 13-2 Measurement of structural flexibility 13-3 Measurement of natural frequencies and mode shapes 13-4 Steady-state aeroelastic testing 13-5 Dynamic aeroelastic testing - full scale 13-6 Dynamic aeroelastic testing - model scale APPENDICES. MATHEMATICAL TOOLS A Matrices B Integration by weighting numbers C Linear systems REFERENCES AUTHOR INDEX SUBJECT INDEX

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