The Duffing Equation: nonlinear oscillators and their behaviour

INDICE: Biographies of the Contributors Preface 1 Background: On Georg Duffing and the Duffing Equation Ivana Kovacic and Michael Brennan 1.1 Introduction 1.2 Historical Perspective 1.3 A Brief Biography of Georg Duffing 1.4 The Work of Georg Duffing 1.5 Contents of Duffing's Book 1.6 Research Inspired by Duffing's Work 1.7 Some other Books on Nonlinear Dynamics 1.8 Overview of this Book References 2 Examples of Physical Systems Described by the Duffing Equation Michael Brennan and Ivana Kovacic 2.1 Introduction 2.2 Nonlinear Stiffness 2.3 The Pendulum 2.4 Example of Geometrical Nonlinearity 2.5 A System Consisting of the Pendulum and Nonlinear Stiffness 2.6 Snap-Through Mechanism 2.7. Nonlinear Isolator 2.8 Large Deflection of a Beam with Nonlinear Stiffness 2.9 Beam with Nonlinear Stiffness due to in-plane Tension 2.10 Nonlinear Cable Vibrations 2.11 Nonlinear Electrical Circuit 2.12 Summary References 3 Free Vibration of a Duffing Oscillator with Viscous Damping Hiroshi Yabuno 3.1 Introduction3.2 Fixed Points and their Stability 3.3 Local Bifurcation Analysis 3.4 Global Analysis for Softening Nonlinear Stiffness 3.5 Global Analysis for HardeningNonlinear Stiffness 3.6 Summary Acknowledgments References 4 Analysis Techniques for the Various Forms of the Duffing Equation Livija Cveticanin 4.1 Introduction 4.2 Exact Solution for Free Oscillations of the Duffing Equation with Cubic Nonlinearity 4.3 The Elliptic Harmonic Balance Method 4.4 The Elliptic Galerkin Method 4.5 The Straightforward Expansion Method 4.6 The Elliptic Lindstedt-Poincaré Method 4.7 Averaging Methods 4.8 Elliptic Homotopy Methods 4.9 Summary References Appendix 4AI: Jacobi Elliptic Functions and Elliptic Integrals Appendix 4AII: The Best L2 Norm Approximation 5 Forced Harmonic Vibration ofa Duffing Oscillator with Linear Viscous Damping Tamás Kalmár-Nagy and Balakumar Balachandran 5.1 Introduction 5.2 Free and Forced Responses of the Linear Oscillator 5.3 Amplitude and Phase Responses of the Duffing Oscillator 5.4 Periodic Solutions, Poincaré Sections, and Bifurcations 5.5 Global Dynamics 5.6 Summary References 6 Forced Harmonic Vibration of a Duffing oscillator with Different Damping Mechanisms Asok Kumar Mallik 6.1 Introduction 6.2 Classification of Nonlinear Characteristics 6.3 Harmonically Excited Duffing Oscillator with Generalized Damping 6.4 Viscous Damping 6.5 Nonlinear Damping in a HardeningSystem 6.6 Nonlinear Damping in a Softening System 6.7 Nonlinear Damping in Double-Well Potential Oscillator 6.8 Summary Acknowledgments References 7 Forced Harmonic Vibration in a Duffing Oscillator with Negative Linear Stiffness and Linear Viscous Damping Stefano Lenci and Giuseppe Rega 7.1 Introduction 7.2 Literature Survey 7.3 Dynamics of Conservative and Non-Conservative Systems 7.4 Nonli

• ISBN: 978-0-470-71549-9
• Editorial: John Wiley & Sons
• Encuadernacion: Cartoné
• Páginas: 400
• Fecha Publicación: 04/03/2011
• Nº Volúmenes: 1
• Idioma: Inglés