Autoparametric Resonance in Mechanical Systems

When a mechanical system consists of two or more coupled vibrating components, the vibration of one of the component subsystems may destabilise the motion of the other components. This destabilisation effect is called autoparametric resonance. It is a concept that has important engineering applications. For example, flow-induced vibrations such as those caused by a rolling sea on ships, high-speed gas flows in pipelines, or turbulent air flow around aircraft wings must be considered in the design and the operation of such structures and systems. This book is the first completely devoted to the subject of autoparametric resonance in an engineering context. With examples taken from a variety of autoparametric systems, the authors show how to carry out the first crucial step, that is, how to determine the regions of parameter space where the semitrivial solution is unstable. Using the tools of nonlinear analysis, they describe what happens in these regions and the mathematical models used to analyse them. This analysis leads to a discussion of nontrivial solutions and their stability. The study of autoparametric systems is a lively area of current research in engineering and applied mathematics, and this book will appeal to graduate students and research workers in both disciplines.