This 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 behavior of the solutions of parametrically excited systems. Parametric instability or resonance is more dangerous than ordinary resonance as it is characterized 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.
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
"In addition to being very clearly written throughout, the book can boast an impeccable overall visual presentation, with numerous diagrams and charts illustrating graphically the mathematical treatments. It also contains an extensive list of references for those needing more background material or wishing to pursue a particular area further."
- Philippe Duffour, University of College London
"This monograph is a competent introduction to several models of structural dynamics and their asymptotic treatment. It guides the reader carefully through a list of models with periodic and random loads, and shows through step-by-step computations how classical and modern concepts can be combined to deliver stability results for structures under dynamic loading. The book will be a great companion for those who want to understand how dynamic models of structures are derived and how asymptotic stability results can be obtained."
- Wolfgang Kliemann, SIAM Review
"The book is an excellent textbook for an advanced level graduate course, and calls for slow and meditative reading. In the end, however, the reader will have the feeling of having been walked, in a methodical and scientific way, through a fascinating area of dynamics."
- Ricardo Foschi, The University of British Columbia