Chaotic Vibrations: An Introduction for Applied Scientists and Engineers

Abstract

1. Introduction: A New Age of Dynamics. 1.1 What Is Chaotic Dynamics? 1.2 Classical Nonlinear Vibration Theory: A Brief Review. 1.3 Maps and Flows. 2. How to Identify Chaotic Vibrations. 3. A Survey of Systems with Chaotic Vibrations. 3.1 New Paradigms in Dynamics. 3.2 Mathematical Models of Chaotic Physical Systems. 3.3 Physical Experiments in Chaotic Systems. 4. Experimental Methods in Chaotic Vibrations. 4.1 Introduction: Experimental Goals. 4.2 Nonlinear Elements in Dynamical Systems. 4.3 Experimental Controls. 4.4 Phase Space Measurements. 4.5 Bifurcation Diagrams. 4.6 Experimental Poincare Maps. 4.7 Quantitative Measures of Chaotic Vibrations. 5. Criteria for Chaotic Vibrations. 5.1 Introduction. 5.2 Introduction Empirical Criteria for Chaos. 5.3 Theoretical Predictive Criteria. 5.4 Lyapunov Exponents. 6. Fractal Concepts in Nonlinear Dynamics. 6.1 Introduction. 6.2 Measures of Fractal Dimension. 6.3 Fractal Dimension of Strange Attractors. 6.4 Optical Measurement of Fractal Dimension. 6.5 Fractal Basin Boundaries. 6.6 complex Maps and the Mandelbrot Set. Appendix A. Glossary of Terms in Chaotic and Nonlinear Vibrations. Appendix B. Appendix C. Numerical Experiments in Chaos. Appendix C. Chaotic Toys. References. Author Index. Subject Index.