No abstract

Methods for determining the response of continuous systems with quadratic and cubic nonlinearities are discussed. We show by means of a simple example that perturbation and computational methods based on first discretizing the systems may lead to erroneous results whereas perturbation methods that attack directly the nonlinear partialdifferential equations and boundary conditions avoid the pitfalls associated with the analysis of the discretized systems. We describe a perturbation technique that applies either the method of multiple scales or the method of averaging to the Lagrangian of the system rather than the partial-differential equations and boundary conditions.

I shall survey the contents of this book before making some general comments. I close with a few specific comments on the organization, clarity, and viewpoint of the book, and on some of the topics omitted. Chapter 1 constitutes an extended abstract of the entire work. The next four chapters cover conservative, nonconservative, externally, and parametrically excited single-degree-of-freedom oscillators. The authors then go on to treat re-degree-of-freedom systems, continuous systems, and traveling waves. Each chapter ends with a set of exercises, many of which represent nontrivial pieces of research, and the 70-page bibliography contains over 1500 references. The book therefore provides a comprehensive sampler of the nonlinear vibration problems which occur in engineering. This text lies firmly within the classical engineering tradition of nonlinear oscillations; the first half of the book is essentially a new version of such texts as those by Minorsky, Hayashi, or Stoker. However, this serves as an introduction to the authors' main aim of covering recent work on multidegree of freedom and continuous systems, which they do in Chapters 5-8. Topics such as the forced oscillations of rc-degree-of-freedom systems with quadratic and cubic nonlinearities and of finite strings, beams, and plates are covered, as well as longitudinal and transverse traveling waves in bars. In connection with traveling waves, a nice presentation of the method of characteristics is given and shock fitting is discussed. The authors' recent work on modal saturation in coupled quadratic systems is also covered.

No abstract

No abstract