Introduction to Experimental Nonlinear Dynamics: A Case Study in Mechanical Vibration

by Lawrence N. Virgin

Overview

Nonlinear behavior can be found in such highly disparate areas as population biology and aircraft wing flutter. For this reason, nonlinear dynamics and chaos have become very active fields of research. This work uses an extended case study—an experiment in mechanical vibration—to introduce and explore the subject of nonlinear behavior and chaos from an engineering perspective. After a review of basic principles, the text then describes a cart-on-a-track oscillator and shows what happens when it is gradually subjected to greater excitation, thereby encountering the full spectrum of nonlinear behavior, from simple free decay to chaos. Advanced undergraduate and graduate students, as well as practicing engineers, will find this book a lively, accessible introduction to the subject.

Product Details

ISBN-13:	9780521662864
Publisher:	Cambridge University Press
Publication date:	03/28/2000
Pages:	274
Product dimensions:	6.30(w) x 9.49(h) x 1.02(d)

Table of Contents

Preface; 1. Brief introductory remarks; 2. Background: linear behavior; 3. Some useful concepts; 4. The paradigm; 5. Mathematical description; 6. The experimental model; 7. Free oscillations; 8. Forced response: periodic; 9. Forced response: non-periodic; 10. Escape from a potential energy well; 11. A hardening spring oscillator; 12. The effect of a stiffness discontinuity; 13. Two-frequency excitation; 14. Global issues; Appendix A. A nonlinear electric circuit; Appendix B. A continuous system; References.

Editorial Reviews

"This well-written textbook...is highly recommended to researchers and students of nonlinear mechanical phenomena and should be available in all mathematics and mechanics libraries."
Applied Mechanics Reviews

"A novel feature of the book is that it introduces many of the concepts using experimental examples...The book very nicely motivates a lot of the theoretical material from experimental results, and successfully brings across the idea that, far from being pathological, complicated dynamics and bifurcation behaviours are widespread even in simple nonlinear systems."
Mathematical Reviews

"A unique book.... Novices to the field of nonlinear dynamics and chaos theory will find the book's introduction of concepts both easy to understand and presented in a physically meaningful manner. The book will also be useful for specialists in chaos and nonlinearity in the comparison of experiments with theoretical models.... This book is recommended for the libraries of both students and researches in nonlinear science."
Physics Today

"The pleasant presentation of the field of nonlinear oscillations and chaos is continually reinforced by the good agreement that is obtained and shown between numerical and experimental results...this book will surely be of great interest to students, engineers, and researchers involved in the field."
Measurement Science and Technology

"This book is highly recommended...clearly written with the novice in mind, and both engineers and physicists will find it worthwhile."
SIAM Review

From the Publisher