Introduction to Nonlinear Aeroelasticity.

Intro -- Title Page -- Copyright Page -- Contents -- Preface -- Dimitriadis: Nonlinear Aeroelasticity - Series Preface Oct 2016 -- About the Companion Website -- Chapter 1 Introduction -- 1.1 Sources of Nonlinearity -- 1.2 Origins of Nonlinear Aeroelasticity -- References -- Chapter 2 Nonlinear Dynamics -- 2.1 Introduction -- 2.2 Ordinary Differential Equations -- 2.3 Linear Systems -- 2.3.1 Stable Oscillatory Response -- 2.3.2 Neutral Oscillatory Response -- 2.3.3 Unstable Oscillatory Response -- 2.3.4 Stable Non-oscillatory Response -- 2.3.5 Unstable Non-oscillatory Response -- 2.3.6 Fixed Point Summary -- 2.4 Nonlinear Systems -- 2.4.1 Linearisation Around Fixed Points -- 2.4.2 The Pitching Wing Section with Cubic Stiffness -- 2.4.3 The Pitchfork Bifurcation -- 2.5 Stability in the Lyapunov Sense -- 2.6 Asymmetric Systems -- 2.6.1 The Fold Bifurcation -- 2.6.2 The Transcritical Bifurcation -- 2.7 Existence of Periodic Solutions -- 2.7.1 Nonlinear Aeroelastic Galloping -- 2.8 Estimating Periodic Solutions -- 2.8.1 Periodic Solutions of the Nonlinear Galloping Oscillator -- 2.8.2 The Hopf Bifurcation -- 2.9 Stability of Periodic Solutions -- 2.9.1 Stability of Galloping Oscillations -- 2.9.3 The Fold Bifurcation of Cycles -- 2.10 Concluding Remarks -- References -- Chapter 3 Time Integration -- 3.1 Introduction -- 3.2 Euler Method -- 3.2.1 Linear Systems -- 3.2.2 Nonlinear Systems -- 3.3 Central Difference Method -- 3.3.1 Explicit Solution of Nonlinear Systems -- 3.3.2 Implicit Solution of Nonlinear Systems -- 3.4 Runge-Kutta Method -- 3.5 Time-Varying Linear Approximation -- 3.6 Integrating Backwards in Time -- 3.7 Time Integration of Systems with Multiple Degrees of Freedom -- 3.8 Forced Response -- 3.9 Harmonic Balance -- 3.9.1 Newton-Raphson -- 3.9.2 Discrete Fourier Transform Techniques -- 3.10 Concluding Remarks -- References.

Chapter 4 Determining the Vibration Parameters -- 4.1 Introduction -- 4.2 Amplitude and Frequency Determination -- 4.2.1 Event Detection -- 4.3 Equivalent Linearisation -- 4.4 Hilbert Transform -- 4.5 Time-Varying Linear Approximation -- 4.6 Short Time Fourier Transform -- 4.7 Pinpointing Bifurcations -- 4.7.1 Newton-Raphson -- 4.7.2 Successive Bisection -- 4.8 Limit Cycle Study -- 4.9 Poincaré Sections -- 4.10 Stability of Periodic Solutions -- 4.10.1 Floquet Analysis -- 4.11 Concluding Remarks -- References -- Chapter 5 Bifurcations of FundamentalAeroelastic Systems -- 5.1 Introduction -- 5.2 Two-Dimensional Unsteady Pitch-Plunge-ControlWing -- 5.3 Linear Aeroelastic Analysis -- 5.4 Hardening Stiffness -- 5.4.1 Supercritical Hopf Bifurcation -- 5.4.2 Subcritical Hopf Bifurcation -- 5.4.3 Fold Bifurcation of Cycles -- 5.4.4 Flutter of Nonlinear Systems -- 5.4.5 Period-Doubling Bifurcation -- 5.4.6 Torus Bifurcation -- 5.5 Softening Stiffness -- 5.6 Damping Nonlinearity -- 5.6.1 Subcritical Hopf Bifurcation -- 5.6.2 Static Divergence of Cycles -- 5.6.3 Pitchfork Bifurcation of Cycles -- 5.7 Two-Parameter Bifurcations -- 5.7.1 Generalised Hopf Bifurcation -- 5.7.2 Pitchfork-Hopf Bifurcation -- 5.7.3 Hopf-Hopf Bifurcation -- 5.8 Asymmetric Nonlinear Aeroelastic Systems -- 5.8.1 Fold Bifurcation of Fixed Points and Cycles -- 5.8.2 Transcritical Bifurcation of Fixed Points and Cycles -- 5.8.3 Fold-Hopf Bifurcation -- 5.9 Concluding Remarks -- References -- Chapter 6 Discontinuous Nonlinearities -- 6.1 Introduction -- 6.2 Piecewise Linear Stiffness -- 6.2.1 Underlying and Overlying Linear Systems -- 6.2.2 Fixed Points and Boundary Equilibrium Bifurcations -- 6.2.3 Equivalent Linearisation of Piecewise Linear Stiffness -- 6.2.4 Three-Domain Limit Cycles -- 6.2.5 Two-Domain Limit Cycles -- 6.2.6 Time Domain Solutions.

6.3 Discontinuity-Induced Bifurcations -- 6.3.1 The Boundary Equilibrium Bifurcation -- 6.3.2 The Grazing Bifurcation -- 6.4 Freeplay and Friction -- 6.5 Concluding Remarks -- References -- Chapter 7 Numerical Continuation -- 7.1 Introduction -- 7.2 Algebraic Problems -- 7.2.1 Prediction Correction -- 7.2.2 Arclength Continuation -- 7.2.3 Pseudo-Arclength Continuation -- 7.3 Direct Location of Folds -- 7.4 Fixed Point Solutions of Dynamic Systems -- 7.4.1 Branch Points -- 7.4.2 Arclength Step Control -- 7.5 Periodic Solutions of Dynamic Systems -- 7.5.1 Starting the Continuation Scheme -- 7.5.2 Folds and Branch Points -- 7.5.3 Branch Switching -- 7.6 Stability of Periodic Solutions Calculated from Numerical Continuation -- 7.7 Shooting -- 7.7.1 Starting the Continuation Scheme -- 7.7.2 Arclength Continuation -- 7.7.3 Stability Analysis -- 7.7.4 Branch Point Location and Branch Switching -- 7.7.5 Grazing -- 7.8 Harmonic Balance -- 7.9 Concluding Remarks -- References -- Chapter 8 Low-Speed AerodynamicNonlinearities -- 8.1 Introduction -- 8.2 Vortex-Induced Vibrations -- 8.3 Galloping -- 8.4 Stall Flutter -- 8.4.1 Dynamic Stall -- 8.4.2 Leishman-Beddoes Model -- 8.4.3 ONERA Model -- 8.4.4 Aeroelastic Simulations using Dynamic Stall Models -- 8.5 Concluding Remarks -- References -- Chapter 9 High-Speed AeroelasticNonlinearities -- 9.1 Introduction -- 9.2 Piston Theory -- 9.3 Panel Flutter -- 9.3.1 Buckling -- 9.3.2 Limit Cycle Oscillations -- 9.4 Concluding Remarks -- References -- Chapter 10 Finite Wings -- 10.1 Introduction -- 10.2 Cantilever Plate in Supersonic Flow -- 10.3 Three-Dimensional Aerodynamic Modelling by the Vortex Lattice Method -- 10.3.1 Aeroelastic Coupling -- 10.3.2 Transforming to the Time Domain -- 10.3.3 Nonlinear Response -- 10.4 Concluding Remarks -- References -- Appendix A Aeroelastic Models -- A.1 Galloping Oscillator.

A.2 Two-Dimensional Pitch-Plunge-Control Wing Section with Unsteady Aerodynamics -- A.3 Two-Dimensional Pitch-Plunge-Control Wing Section with Quasi-Steady Aerodynamics -- A.4 Two-Dimensional Pitch-Plunge Wing Section with Quasi-Steady Aerodynamics -- A.5 Two-Dimensional Pitching Wing Section with Quasi-Steady Aerodynamics -- A.6 Two-Dimensional Pitch-Plunge Wing with Leishman-Beddoes Aerodynamic Mode -- A.7 Two-Dimensional Pitch-Plunge Wing with ONERA Aerodynamic Model -- A.8 Two-Dimensional Pitch-Plunge-Control Wing Section with Supersonic Aerodynamics -- A.9 Two-Dimensional Pitch-Plunge Wing Section with Supersonic Aerodynamics -- References -- Index.

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