3R16. Random Vibration. Mechanical Vibration and Shock Series, Vol III. - C Lalanne (French Atomic Energy Authority, France). Hermes Sci Publ, Paris. Distributed in USA by Taylor & Francis Publ, New York NY. 2002. 346 pp. ISBN 1-56032-988-2. \$150.00.

Reviewed by YA Rossikhin (Dept of Theor Mech, Voronezh State Univ of Architec and Civil Eng, ul Kirova 3-75, Voronezh, 394018, Russia).

This book is the third volume in the series Mechanical Vibration and Shock published by Hermes Science Publications. The objective of the series is to provide state-of-the-art developments in different aspects of vibration and shock analysis from both theoretical and practical standpoints. This work is intended first of all for engineers.

This book is a fine handbook for engineers working in design and project teams and in laboratories dealing with the vibration tests, since it comprises the basics of random vibrations and stochastic mechanics, which are adapted to the needs of the mechanical engineer practicing design of structures and equipment subjected to random vibrations in real environments and in laboratory tests.

The book includes seven chapters followed by five appendices, a list of references, and an index. The first chapter is an introduction reviewing statistical properties of random processes occurring in engineering systems and the methods of analysis of random vibrations. The second chapter presents the fundamental concepts of probability theory and the statistical analysis of random variables and stochastic processes in the frequency domain. Chapter 3 is devoted to practical calculation of acceleration, velocity, and displacement mean square values. Practical calculation of power spectral density is discussed in Chapter 4 under the assumption that random vibrations are stationary and ergodic. Chapter 5 describes properties of random vibration in the time domain. The following two chapters are devoted to probability distribution of maxima of random vibration and statistics of extreme values, which is very useful information for the pre-sizing of a structure. The main results are summarized in tables given at the end of Chapter 7. Appendices contain some useful formulas for different laws of probability, in $1/nth$ octave analysis, power spectral density, mathematical functions, and transfer functions.

Random Vibration has features intended to support its use as primarily a reference book by engineers and graduate students. The book is well written, with good quality figures and tables to illustrate the subject. A list of references includes textbooks and monographs in the field, as well as original papers. The author provides a reasonable subject index. Consequently, this reviewer recommends purchase by libraries and individuals with an interest in stochastic mechanics.