Dynamic Stability of Structures

This book explores the theory of parametric stability of structures under deterministic and stochastic loadings.

Wei-Chau Xie (Author)

9780521852661, Cambridge University Press

Hardback, published 5 June 2006

454 pages
25.6 x 18.4 x 3.4 cm, 1.123 kg

Review of the hardback: 'Writing a monograph intended for engineers on advanced applications of stochastic modelling is a difficult challenge: the subject is extremely mathematical and one runs the risk of either writing for a very small target audience of experts or one has to include entire chapters of background material. Professor Wei-Chau Xie has managed to strike a difficult balance between these two extremes.' Journal of Sound and Vibration

This 2006 book presents a systematic introduction to the theory of parametric stability of structures under both deterministic and stochastic loadings. A comprehensive range of theories are presented and various application problems are formulated and solved, often using more than one approach. Investigation of an elastic system's dynamic stability frequently leads to the study of dynamic behaviour of the solutions of parametrically excited systems. Parametric instability or resonance is more dangerous than ordinary resonance as it is characterised by exponential growth of the response amplitudes even in the presence of damping. The emphasis in this book is on the applications and various analytical and numerical methods for solving engineering problems. The materials presented are as self-contained as possible, with all of the important steps of analysis provided in order to make the book suitable as a graduate-level textbook and especially for self-study.

1. Introduction
Part I. Dynamic Stability of Structures under Deterministic Loadings: 2. Linear differential equations with periodic coefficients
3. Approximate methods
4. Nonlinear systems under periodic excitations
Part II. Dynamic Stability of Structures under Stochastic Loadings: 5. Random processes and stochastic differential equations
6. Almost-sure stability of systems under ergodic excitations
7. Moment stability of stochastic systems
8. Lyapunov exponents
9. Moment Lyapunov exponents
Appendix A. Maple programs
Bibliography.

Subject Areas: Dynamics & vibration [TGMD4], Mechanics of solids [TGMD], Mechanical engineering [TGB]