Wei-Chau XieCambridge University Press, 8/10/2006EAN 9780521852661, ISBN10: 0521852668Hardcover, 454 pages, 25.6 x 18.4 x 3.4 cmLanguage: EnglishThis 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. IntroductionPart I. Dynamic Stability of Structures under Deterministic Loadings2. Linear differential equations with periodic coefficients3. Approximate methods4. Nonlinear systems under periodic excitationsPart II. Dynamic Stability of Structures under Stochastic Loadings5. Random processes and stochastic differential equations6. Almost-sure stability of systems under ergodic excitations7. Moment stability of stochastic systems8. Lyapunov exponents9. Moment Lyapunov exponentsAppendix A. Maple programsBibliography.
