Linearization Methods for Stochastic Dynamic Systems

Leslaw Socha (auth.)3540729968, 9783540729969

For most cases of interest, exact solutions to nonlinear equations describing stochastic dynamical systems are not available. The aim of this book is to give a systematic introduction to and overview of the relatively simple and popular linearization methods available. The scope is limited to models with continous external and parametric excitations, yet these cover the majority of known approaches. The book contains an application chapter with emphasis on vibration analysis of stochastic mechanical structures as well as a chapter devoted to the assessment of the accuracy of the theoretical methods presented, both with respect to numerical and to experimental studies. The material derives partly from graduate course notes developed by the author for courses and seminars over the past 20 years.

Table of contents :
Front Matter….Pages I-XI
Introduction….Pages 1-5
Mathematical Preliminaries….Pages 7-58
Moment Equations for Linear Stochastic Dynamic Systems (LSDS)….Pages 59-84
Moment Equations for Nonlinear Stochastic Dynamic Systems (NSDS)….Pages 85-102
Statistical Linearization of Stochastic Dynamic Systems Under External Excitations….Pages 103-146
Equivalent Linearization of Stochastic Dynamic Systems Under External Excitation….Pages 147-210
Nonlinearization Methods….Pages 211-249
Linearization of Dynamic Systems with Stochastic Parametric Excitations….Pages 251-280
Applications of Linearization Methods in Vibration Analysis of Stochastic Mechanical Structures….Pages 281-340
Accuracy of Linearization Methods….Pages 341-376
Back Matter….Pages 377-383