Dynamic Stability of Structures

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. The emphasis falls 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.

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.

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 several approaches. This volume is suitable as a graduate textbook or for self-study.