3R14. Elastic Waves in Anisotropic Laminates. - GR Liu and ZC Xi (Natl Univ of Singapore, Singapore). CRC Press LLC, Boca Raton, FL. 2002. 452 pp. ISBN 0-8493-1070-9. $149.95.

Reviewed by Y Horie (Los Alamos Nat Lab, Group X-7, MS D413, Los Alamos, NM 87545).

Sound waves are a wonderful tool to probe the interiors of materials and structures that are invisible from outside. Ultrasounds are used to detect flaws and abnormalities not only in inanimate objects, but also in living bodies. A clear advantage of probing with sounds is that the examination can be carried out without destroying the object, nor changing the existing conditions of the object under investigation. It is, however, well known that the interpretation of probing with sounds is not always clear nor straightforward, particularly difficult are those that have complex interior structures and compositions. Examples are composites such as those used on aircraft and human bodies.

A modern foundation of probing with sounds is the study of wave propagation in materials. This book offers a combined analytical-numerical method for linear elastic wave analysis of anisotropic laminates, drawing heavily from the research work of the authors and their colleagues over the last 15 years. Attention is focused specially on two techniques: a hybrid numerical method (HNM) and a strip element method (SEM). These techniques are aimed at reducing the computational burden of direct finite element methods and obtaining insightful results that reveal important characteristics of complex wave phenomena, through use of judicially chosen discretizing elements (plates and strips) and a combined analytical-numerical method.

The book is intended primarily for senior university students, postgraduate students, and engineers in civil, mechanical, geophysical, aeronautical, and engineering mechanics. Prerequisites are matrix algebra, Fourier Transform, complex variables, and the linear theory of elasticity. To that we should add Green’s function method. The first chapter covers fundamentals of one dimensional wave propagation using bars as an example. Subsequent 17 chapters are written in a relatively independent manner and do not always follow a logical progression. Topics covered in these chapters include: waves in functionally graded plates, Lamb waves in anisotropic laminates, harmonic and transient waves in laminates, waves in piezoelectric plates, wave scattering by cracks and flaws, crack and flaw characterizations, bending wave in laminates, helical waves in laminated cylinders, inverse construction of impact loading, and inverse characterization of laminates properties. HNM and SEM methods are formulated in Chapter 8 and 11, respectively. HNM uses first a plate element to calculate modal solutions in the wave number domain and then inverse Fourier transform to obtain displacement in the spatial domain. SEM is similar to HNM, but it combines FEM, the modal analysis, and the Fourier transform technique. Strength of these methods are demonstrated through examples in Chapters 9-10, and 12-14, and 16, respectively. A useful feature of the book is that select software codes of these methods are available on a website.

The book is fairly easy to follow and numerous drawings and charts are useful in understanding concepts and theories, and appreciating the results. The writing of the book is guided by “the philosophy: make all the topics insightful but simple, informative but interesting, and theoretical but practical.” I think that the authors have succeeded in achieving the stated goals. However there are some minor, but recurring editorial questions. For example, the judgment of what is simple appears very uneven. Many trivial algebraic manipulations are shown in details, but derivations and explanations of some important subjects are not discussed at all. Examples are the quadratic shape function that plays an important in the layer method and Green’s function method. There are also many statements that are not informative, nor insightful without accompanying clarification. Again examples are “A laminate is mechanically governed by solid mechanics while a laminated plate is governed by a theory of laminated plates (p. 3),” and “Matrix G is generally ill-conditioned; it cannot be solved by directly using conventionally methods (p. 412).” You need to know the subjects to understand what he means in these passages.

Plus, there are some inaccurate statements. They are, eg, “a vibration is a motion of waves with very long wavelength” (no vibrations with short wavelengths?) and “waves in solids are invisible to human eyes” (no photoelasticity?).

These shortcomings may be explained in part by the impression that basically the book is a collection of expanded journal papers and introductory materials. This explains that most chapters can be read independent of others, as mentioned by the authors.

In spite of some minor glitches, Elastic Waves in Anisotropic Laminates is a useful compilation of recent advances in the numerical study of linear elastic waves in anisotropic laminates. It is recommended not only for engineers, but also students and researchers in non-engineering fields who are interested in ultrasonic-based non-destructive evaluation.