Random differential equations in science and engineering
Random differential equations in science and engineering
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DOI：
10.1115/1.3423466
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发表时间：
1974-12
期刊：
影响因子：
--
通讯作者：
T. Soong;J. Bogdanoff
中科院分区：
文献类型：
--
作者：
T. Soong;J. Bogdanoff
Random vibration and random processes began entering the engineering mechanics profession as a significant subject around 20 years ago. Since that time, the subject has grown and developed in a number of ways. Material which first appeared in research papers now is presented in books. Most engineering schools have one or more courses in random vibration; some have courses in random processes. Probabilistic concepts have entered codes in military specifications, nuclear power plant specifications, building codes in areas of high seismic risk, etc. Thus the subject has achieved a position of importance in the profession. The initial books on the subject were either over the heads of engineers mathematically (and ignored) or on an insecure basis mathematically. As a result, unsound and/or confused conclusions were occasionally put forward in the literature. Soong's excellent book indicates that the profession is now sure of the importance of the subject and expects its members to know the mathematical tools needed to pursue the subject in a competent manner. According to the author, the primary objective of the book is to give the reader a working knowledge of random differential equations... and it is also hoped that the contents will bridge the gap between introductory material on stochastic processes and advanced topics in science and technology involving probabilistic methods.The contents are as follows. Chapter 1 is an introduction. Chapter 2 briefly reviews some of the concepts of probability needed in succeeding chapters. Chapters 3 and 4 introduce the concept of a random process, classify random processes, and develop the mean square calculus. Chapters 5-8 concentrate on differential equations with stochastic elements including random initial conditions, random nonhomogeneous elements, and random coefficients. Chapter 9 considers stochastic stability. There are two Appendexes—one on sample treatment of random differential equations and the other on some useful properties of the solution processes. At the end of each chapter there are references and good problems. Concepts of probability theory and random processes are carefully defined and illustrated. Significant and useful results in the mean square calculus are presented as theorems and corollaries. Random differential equations are also given deliberate and careful treatment. Illustrations in the text and references are taken from the fields of dynamics, guidance control, physics, and structures. Stochastic stability is treated in the same careful manner, but coverage of this important topic is limited. The author has had to be selective in the topics presented in order to keep the size of
