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Informationen zum Autor Grigorios Dimitriadis, University of Liège, Belgium Klappentext Introduction to Nonlinear Aeroelasticity Introduces the latest developments and technologies in the area of nonlinear aeroelasticity Nonlinear aeroelasticity has become an increasingly popular research area in recent years. There have been many driving forces behind this development, increasingly flexible structures, nonlinear control laws, materials with nonlinear characteristics and so on. Introduction to Nonlinear Aeroelasticity covers the theoretical basics in nonlinear aeroelasticity and applies the theory to practical problems. As nonlinear aeroelasticity is a combined topic, necessitating expertise from different areas, the book introduces methodologies from a variety of disciplines such as nonlinear dynamics, bifurcation analysis, unsteady aerodynamics, non-smooth systems and others. The emphasis throughout is on the practical application of the theories and methods, so as to enable the reader to apply their newly acquired knowledge Key features: Covers the major topics in nonlinear aeroelasticity, from the galloping of cables to supersonic panel flutter Discusses nonlinear dynamics, bifurcation analysis, numerical continuation, unsteady aerodynamics and non-smooth systems Considers the practical application of the theories and methods Covers nonlinear dynamics, bifurcation analysis and numerical methods Accompanied by a website hosting Matlab code Introduction to Nonlinear Aeroelasticity is a comprehensive reference for researchers and workers in industry and is also a useful introduction to the subject for graduate and undergraduate students across engineering disciplines. Zusammenfassung Introduces the latest developments and technologies in the area of nonlinear aeroelasticity Nonlinear aeroelasticity has become an increasingly popular research area in recent years. Inhaltsverzeichnis Preface xi Dimitriadis: Nonlinear Aeroelasticity - Series Preface Oct 2016 xiii About the Companion Website xv 1 Introduction 1 1.1 Sources of Nonlinearity 3 1.2 Origins of Nonlinear Aeroelasticity 5 References 6 2 Nonlinear Dynamics 9 2.1 Introduction 9 2.2 Ordinary Differential Equations 9 2.3 Linear Systems 11 2.3.1 Stable Oscillatory Response 13 2.3.2 Neutral Oscillatory Response 15 2.3.3 Unstable Oscillatory Response 17 2.3.4 Stable Non-oscillatory Response 19 2.3.5 Unstable Non-oscillatory Response 21 2.3.6 Fixed Point Summary 23 2.4 Nonlinear Systems 24 2.4.1 Linearisation Around Fixed Points 25 2.4.2 The Pitching Wing Section with Cubic Stiffness 28 2.4.3 The Pitchfork Bifurcation 30 2.5 Stability in the Lyapunov Sense 34 2.6 Asymmetric Systems 37 2.6.1 The Fold Bifurcation 38 2.6.2 The Transcritical Bifurcation 41 2.7 Existence of Periodic Solutions 45 2.7.1 Nonlinear Aeroelastic Galloping 47 2.8 Estimating Periodic Solutions 49 2.8.1 Periodic Solutions of the Nonlinear Galloping Oscillator 50 2.8.2 The Hopf Bifurcation 52 2.9 Stability of Periodic Solutions 53 2.9.1 Stability of Galloping Oscillations 55 2.9.2 Supercritical and Subcritical Hopf Bifurcations 56 2.9.3 The Fold Bifurcation of Cycles 56 2.10 Concluding Remarks 61 References 61 3 Time Integration 63 3.1 Introduction 63 3.2 Euler Method 64 3.2.1 Linear Systems 65 3.2.2 Nonlinear Systems 66 3.3 Central Difference Method 68 3.3.1 Explicit Solution of Nonlinear Systems 69 3.3.2 Implicit Solution of Nonlinear Systems 72 3.4 Runge-Kutta Method 74 3.5 Time-Varying Linear Approximation 80 3.6 Integrating Backwards in Time 86
