Introduction to Experimental Nonlinear Dynamics A Case Study in Mechanical Vibration

General Comments

• Aims and Scope

Nonlinear dynamics and chaos have been popular areas of research for more than twenty years. One of the most interesting aspects of nonlinear behavior is its ubiquity. Population biology, celestial mechanics, cardiac fibrillation, and aircraft wing flutter are just a few of the highly disparate areas in which nonlinear dynamics and chaos have shed new light. Interdisciplinary research and the cross fertilization of ideas between different areas has provided much of the impetus. There is hardly a branch of applied science that is not touched by nonlinear dynamics: Witness the range of interdisciplinary books and meetings spread within, and between, research boundaries. However, it is the sheer intrigue provided by nonlinear systems, and chaos in particular, that has caught the imagination of so many people in science and engineering and has led to continued growth in the field.

The aim of this book is to provide a relatively concise pedagogical approach to nonlinear dynamics based on the evolution of an experimental paradigm. In contrast to most other books in this general area, this book will use real data, generated from the laboratory, to introduce, rather than occasionally confirm, the fascinating array of behavior encountered even in a relatively restricted subset of the nonlinear world. In this way, the material will span the gap between abstract, often chaos-driven, ideas and practical engineering reality.

This book uses experimental mechanical vibration as the backbone, or theme, on which the material is developed. We focus attention on this specific branch of engineering to tell a story: one of expanding the horizon from a linear to a nonlinear view, without losing sight of the exigent world of experimentally verifiable behavior. An advantage of this approach is that mechanical vibration, as well as being an important area of research in its own right, has a well-founded history based on linear behavior, and using experimental data as a key component emphasizes the robustness of the described behavior. Thus the narrative of the present book evolves from a local, linear, largely analytical, foundation toward the rich and often unpredictable world of nonlinearity. This book does not attempt to cover the whole range of nonlinear phenomena and experimental techniques.