§16§§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 continuous 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. § §04§Mathematical Preliminaries.- Moment Equations for Linear Stochastic Dynamic Systems (LSDS).- Moment Equations for Nonlinear Stochastic Dynamic Systems (NSDS).- Statistical Linearization of Stochastic Dynamic Systems Under External Excitations.- Equivalent Linearization of Stochastic Dynamic Systems Under External Excitation.- Nonlinearization Methods.- Linearization of Dynamic Systems with Stochastic Parametric Excitations.- Applications of Linearization Methods in Vibration Analysis of Stochastic Mechanical Structures.- Accuracy of Linearization Methods. §13§§From the reviews:§ §§ §"This book deals with numerous linearization techniques for stochastic dynamic systems. ... As a textbook, it can serve for both advanced undergraduate and graduate courses. ... At the end of each chapter one finds bibliographic references. ... The author provides a very valuable toolbox on the basic idea of statistical linearization methods." (Henri Schurz, Mathematical Reviews, Issue 2008 m)§
