604 nOOK I~.EVI E~,VS Chapter 8 is the chapter which has been most revised in this second edition and deals with the finite element method. Whereas its early sections may be taught to undergraduates, its later sections are definitely for the post-graduate. The treatment is restricted to bars (undergoing longitudinal vibration), beams, and to assemblies of bars and will easily be assimilated by the good undergraduate. The later sections introduce the hierarchical finite element approach and serve as an excellent (though brief) introduction into this new and important area. Attention is drawn to the Inclusion and Embedding principles. Chapters 9 and 10 deal with non-linear systems. The first is devoted to such qualitative questions as the stability of equilibrium, and places emphasis on geometric descriptions of the system motion by means of phase-plane techniques. The second of the chapters (Chapter 10) introduces perturbation techniques to yield quantitative solutions to the problems of non-linear response. Duffing's equation, Linstedt's method, the jump phenomenon, subharmonics and combination harmonics are all considered for systems under harmonic excitation. Mathieu's equation, for systems with time-dependent (har- monic) coefficients is also discussed. Chapter 11 considers random vibrations. It introduces the necessary statistical tools and requires no prior knowledge of statistics. In consequence, most of the chapter is given to what is now termed time-series analysis, and relatively little to the actual random vibration of mechanical systems. This is inevitable in such a complex problem, if no prior statistical knowledge is assumed. Chapter 12 is a brand-new chapter dealing with modern techniques for the application of digital computers to vibration analysis. The response of linear systems in continuous time is considered by means of the transition matrix and a later section presents discrete- time techniques. The response of non-linear systems by the Runge-Kutta method is introduced. Subsequent sections deal with sampled functions, the discrete Fourier trans- form and the FFT. Some brief Appendices deal with Fourier Series, Laplace Transforms and the elements of linear (matrix) algebra. The book is well produced and illustrated, but is not without its printing errors. One of these (in Rayleigh's Quotient, equation (5.98) will be obvious to the discerning reader, but will be perplexing to the student. This error, which was not in the fi_tst edition, shows that the second edition is not just a modified reprint. It is actually a re-set edition. Apart from this, there is little to criticize. This reviewer would have preferred that the term "impedance" in Chapter 2 had not been used to describe the quantity "harm6nic force per unit harmonic displacement". Attempts at standardization over the years have tried to assign "dynamic stiffness" to this quantity. "Impedance" is reserved for the force per unit velocity. In addition, it would have been desirable for the real and imaginary parts of the frequency response function G(ito) to have been discussed in chapter 2. Such data and the corresponding Nyquist diagrams are invariably sought and interpreted in contemporary experimental modal analysis. Much useful theoretical analysis can also be conducted making use of these terms. The reviewer strongly recommends this book to every teachcr of vibration analysis and to all of those who work or research in that field. He found the book to be fascinating reading, and only wishes he had a month to spare in which to study it in much more detail, page by page! D. J. MEAD SOUND AND STRUCTURAL VIBRATION 1987, by Frank Fahy, Orlando: Academic Press. 309 pages; price (paper-back) s Students of Physical Acoustics and Acoustical Engineering are soon made aware of the fact that, despite an apparent plethora of books on the subject, few can be recommended