3R3. Statistical Dynamics and Reliability Theory for Mechanical Structures. - VA Svetlitsky (Dept of Appl Mech, Bauman Moscow State Tech Univ, 2-nd Baumanskaya St 5, Moscow, 107005, Russia). Springer-Verlag, Berlin. 2003. 446 pp. ISBN 3-540-44297-9. $169.00.

Reviewed by AM Vinogradov (Dept of Mech Eng, Montana State Univ, 220 Roberts Hall, Bozeman MT 59717).

The book deals with the subject of random vibrations of mechanical systems. In addition, it contains a brief outline of reliability theory, focusing on the response of structural members subjected to random loads. The book represents a translation of Russian text, based primarily on course lectures taught by the author at the Moscow Bauman Technical University.

In the introduction, the author demonstrates that it is often impossible to correctly determine the response of dynamic systems based on deterministic formulations due to various oversimplifications of reality required to implement the deterministic approach. In particular, examples illustrate that it is impossible to solve deterministically such problems as the vibration response of structures to wind gusts or vehicles traveling on rough roads.

The book consists of ten chapters and four appendices. Chapter 1 provides the fundamentals of probability theory, which is expanded in Chapters 2 and 3 to characterize non-stationary and stationary stochastic processes. A brief description of Markov processes is given in Chapter 4. In general, Chapters 1-4 contains reference material intended to establish the background necessary for understanding the content of the following sections. The presentation of this material is brief. It is assumed that the reader should have prior knowledge of probability theory.

Chapter 5 concerns random vibration analysis of single degree of freedom (SDOF) systems, the motion of which is characterized by a single coordinate. The main focus of this chapter is on random vibrations of linear systems, including such problems as free vibrations under stochastic initial conditions, and non-stationary and stationary forced vibration analyses. In addition, Chapter 5 deals with random vibrations of SDOF systems with nonlinear stiffness characteristics.

Chapter 6 deals with the stochastic response of linear multiple degree of freedom (MDOF) systems characterized in terms of a limited number of coordinates. Both free and forced random vibration responses of linear MDOF systems are considered, including stationary and non-stationary problems involving random excitations.

Chapters 7 and 8 concern stochastic vibration analysis of continuous systems, focusing on the response of elastic rods. Initially, the random vibration problem under consideration is formulated in general terms, aiming at nonlinear analyses. However, certain approximations introduced in the subsequent sections reduce the problem to the analysis of linear MDOF systems.

The material presented in Chapters 9 and 10 is largely independent of the preceding text. Thus, Chapter 9 discusses some aspects of reliability theory using probabilistic approach. Chapter 10 considers special cases of random excitations of structural members and some issues of passive vibration control of mechanical systems. Appendices 1-4 contain information that appears redundant since it is either common knowledge or of little practical value in terms of the technical content of the book.

In general, Statistical Dynamics and Reliability Theory for Mechanical Systems is of certain interest, however, several factors tend to undermine its quality. In particular, the technical translation of the Russian text leaves much to be desired. The book is difficult to read and in many instances its technical content is either distorted or lost in translation. Besides, the text contains a number of typographic errors. Figures and illustrations appear adequate, but no figure captions are provided. The list of references is outdated and incomplete. It contains primarily Russian publications with little demonstrated knowledge of the Western literature. In view of the indicated deficiencies it is hard to identify a potential reader that would benefit from or express compelling interest in this book.