BOOK REVIEWS P. L. Marston Physics Department, Washington State University, Pullman, Washington 99164 Thesereviewsofbooksandotherformsofinformationexpresstheopinionsoftheindividualreviewers andarenotnecessarilyendorsedbytheEditorialBoardofthisJournal. EditorialPolicy:Ifthereisanegativereview,theauthorofthebookwillbegivenachancetorespondto the review in this section of the Journal and the reviewer will be allowed to respond to the author’s comments.[See‘‘BookReviewsEditor’sNote,’’J.Acoust.Soc.Am.81,1651(May1987).] Ultrasonic Waves in Solid Media Joseph L. Rose Cambridge University Press, 1999. Price: $90.00 (hardcover), ISBN: 0521640431. This new book by Joseph L. Rose of The Pennsylvania State Univer- sity is a comprehensive review of ultrasonic wave propagation in solid me- dia with special emphasis on ultrasonic nondestructive evaluation ~NDE! and quantitative materials characterization. During the last 20–30 years, NDE in general, and ultrasonic NDE in particular, has become a mature engineering principle that is taught at both undergraduate and graduate lev- els at many of the leading academic institutions all over the world. Still, there have been very few successful efforts to write a textbook connecting the fundamental physics of elastic wave propagation to practical engineering applications and, in particular, the inherently rather elaborate analytical methods to the design and evaluation of experimental measurements. Rose’s new textbook provides a seamless connection between the two conventional, often unnecessarily separated, poles of theory and experiments. Throughout the book, the author presents a rigorous summary of the relevant fundamen- tals, that can be found only in the best theoretical works that have been used as textbooks by graduate students and practicing researchers for years, like B. A. Auld’s Acoustic Fields and Waves in Solids ~Krieger, Malabar, 1990! or J. D. Achenbach’s Wave Propagation in Elastic Solids ~Elsevier Science, Amsterdam, 1984!. Still, his approach is clearly that of somebody who is ultimately interested in the experimental aspects of acoustic wave propaga- tion in solids, like K. F. Graff’s widely used textbook of similar inception, Wave Motion in Elastic Solids ~Dover, New York, 1991!. However, Rose focuses on the high-frequency aspects of acoustic wave propagation and his main goal is to lay down the foundations for applied research in ultrasonic nondestructive evaluation and materials testing. This practicality is unparal- leled in other basic textbooks written on the subject and could be found previously only in textbooks specifically written for experimentalists, such as J. Krautkramer and H. Krautkramer’s celebrated Ultrasonic Testing of Materials ~Springer, Berlin, 1990!. The book is organized into 20 chapters followed by five appendices containing additional information that might be especially valuable in graduate studies. Parts of the book could serve as reading material for senior-level undergraduate or dual-level graduate courses, but the bulk of the material is more suitable for advanced graduate courses and could easily support a three-quarter or two-semester series on ultrasonic wave propagation and nondestructive evaluation. After a short Introduction in Chap. 1, the following two chapters present the fundamental dispersion principles and wave equations in both isotropic and anisotropic media. As in most standard texts, the distinction between phase and group velocities is brought out and the most important anisotropic wave propagation phenomena are discussed in detail. In Chaps. 4 through 6, acoustic reflection, refraction, and scattering are reviewed. Chapter 4 starts with the simple case of normal incidence reflection/ transmission at a plane interface separating semi-infinite media and contin- ues with the discussion of the basic concepts of oblique incidence wave refraction including Snell’s Law, critical angles, and mode conversion. Chapter 5 builds on these concepts and demonstrates how the reflection and transmission coefficients can be calculated generally for different boundary conditions. Chapter 6 briefly introduces the most important methods used in wave-scattering calculations. With the exception of the normal-mode de- composition technique, which is well demonstrated through the example of shear horizontal wave scattering from a cylindrical cavity, the rest of this short summary dealing with the boundary element method, the Born ap- proximation, and the T-matrix approach, is perhaps a bit ambitious and is merely introduced in order to make the reader aware of the different possi- bilities. Chapters 7 through 13 deal with different types of guided waves that represent the main area of focus in this book. The topics include the funda- mental Rayleigh-type surface mode propagating on the free surface of a solid half-space, Lamb-type guided modes propagating in thin plates, Stoneley-type interface waves propagating along the interface separating two elastic half-spaces, Scholte-type interface waves propagating along the surface of a fluid-loaded solid half-space, both vertically and horizontally polarized surface modes propagating on a layered half-space, longitudinal, torsional, and flexural waves in cylindrical rods, both circumferential and axial guided waves in hollow cylinders, leaky guided waves along immersed shells, and generalized guided waves in multiple-layer structures such as coated plates, adhesively bonded and diffusion-bonded plates. Although the presentation of the fundamental dispersion relationship is fairly straightfor- ward in each particular case, the sheer number of the elements in the corre- sponding characteristic matrix and the algebraic complexity of the resulting dispersion equation is sometimes overwhelming. Possibly, it would have been beneficial to present all the explicit expressions for the characteristic matrices separately in one of the appendices so that the underlying physics could be more apparent for less experienced readers who do not necessarily want to experiment with numerical evaluation of a six-by-six or even higher-order secular determinant. The one minor difficulty this reviewer experienced while otherwise thoroughly enjoying reading through this part of the book was the rather casual, alternating use of the e i(kx2vt) and e i(vt2kx) complex amplitude con- ventions for harmonic waves. Undoubtedly, either convention is as good as the other, since only the real part of the complex quantity is assumed to represent the actual physical quantity. However, inexperienced students might be confused by a sign that changes from chapter to chapter and, in some cases, even within the same chapter. Furthermore, the sign convention does make an important physical difference in some cases, for example, in choosing between the first and second kind of Hankel functions for the appropriate leaky field produced by axial guided waves in an immersed cylinder or whether the attenuation coefficient of the guided wave is equal to the imaginary part of the wave number or to its negative value. Chapter 14 deals with the influence of nonideal sources, a topic of great practical importance that is entirely missing from almost all textbooks written about ultrasonic wave propagation in solid media. The two particular examples discussed in greater detail include dispersive guided wave genera- tion and detection in traction-free plates and bulk wave generation and de- tection in three-dimensional anisotropic media. In the first case, the selec- tivity of an ultrasonic angle-beam transducer for a particular plate mode is analyzed by the normal-mode expansion technique and the role of the trans- ducer’s size, through its effect on the directivity pattern, is shown to be as important as its center frequency and bandwidth. In the case of an aniso- tropic medium, beam skewing in other than principal directions often results in specific problems such as apparent energy loss, anomalous focusing, beam splitting, etc. A simple numerical integration method using Green’s functions is shown to accurately predict the previously mentioned aniso- tropic distortions of the acoustic beam in transversely isotropic materials as well as in more generally anisotropic media. Following the main line of the book, Chaps. 15 and 16 continue the discussion of different types of guided waves in plates. First, the family of horizontally polarized guided modes is presented. Traditionally, the Rayleigh–Lamb modes of sagital polarization are primarily associated with wave propagation in plates. These modes, which are combinations of longi- tudinal and vertically polarized shear partial waves, can be readily generated 1807 J. Acoust. Soc. Am. 107 (4), April 2000 0001-4966/2000/107(4)/1807/2/$17.00 © 2000 Acoustical Society of America 1807 

and detected via normal surface tractions in either immersion or contact inspection and they allow a more complete characterization of material properties than the horizontally polarized family, which contains only shear partial waves. However, with the recent development of electromagnetic acoustic transducers ~EMATs!, horizontally polarized plate modes can also be relatively easily exploited for flaw detection or texture assessment in sheet metal, and these guided modes are expected to play an increasing role in future ultrasonic NDE applications. As a final note on guided wave propa- gation, ultrasonic waves propagating in a free anisotropic layer, such as a composite lamina, are considered in Chap. 16. The main differences be- tween the isotropic and anisotropic cases are briefly explained and the char- acteristic anisotropic features are demonstrated through the example of a typical unidirectional composite plate. It would have been beyond the scope of Rose’s book to extent this discussion to the case of multilayered com- posite laminates; interested readers are referred to A. H. Nayfeh’s recent book on this subject, Wave Propagation in Layered Anisotropic Media with Applications to Composites ~North-Holland, Amsterdam, 1995!. The following three chapters of the book are dedicated to three special topics of great interest in ultrasonic materials characterization. Chapter 17 discusses the most crucial issues of data inversion, i.e., how the sought elastic moduli of the material can be obtained from the actually measured velocity data. This inversion is particularly difficult in the case of aniso- tropic media, when often as many as five to nine independent constants need to be determined and sufficient accuracy cannot be achieved unless the measurements are made not just arbitrarily based on the convenience of the experimental arrangement but more systematically based on the sensitivity of given modes to a limited number of elastic moduli. Chapter 18 outlines the basic concepts of viscoelasticity and briefly reviews its impact on ultra- sonic wave propagation. The well-known Maxwell and Kelvin–Voight models are analyzed in detail, but the readers are advised that overwhelming experimental evidence suggests that the actual behavior of most viscoelastic materials, such as plastics, adhesives, and epoxy matrix composites, appear to be best modeled at ultrasonic frequencies by assuming that both the real and imaginary parts of the elastic moduli are independent of frequency. Finally, Chap. 19 discusses the influence of stress on the velocity of ultra- sonic waves propagating in solid media. This so-called acousto-elastic effect is arguably the most important nonlinear phenomenon that can be exploited for ultrasonic materials evaluation and plays a unique role in nondestructive residual stress assessment. The last chapter of the book presents a short introduction to the most efficient analytical tool available for numerical modeling of ultrasonic wave propagation in solid media, namely the boundary element method. By its nature, Chap. 20 belongs a little more to the following excellent and very useful appendices rather than to the rest of the book, which is focused mainly on the physical concepts of ultrasonic wave propagation. These ap- pendices include a short review of the special methods and instrumentation used in ultrasonic NDE, a list of basic formulas from the theory of elasticity, that are particularly relevant to ultrasonic wave propagation, a very useful introduction to the use of complex variables, some examples of Schlieren imaging and dynamic photoelasticity, and a series of key wave propagation experiments. This last appendix contains seven basic experiments that pro- vide the students with sufficient laboratory experience not only to better understand the theoretical concepts learned from this textbook but also to start individual graduate research in ultrasonic NDE. Along with the excel- lent series of questions and problems presented in the exercise sections at the end of each chapter, this extensive set of appendices makes this textbook especially valuable for both graduate students and educators. Overall, Rose’s Ultrasonic Waves in Solid Media is clearly the product of many years of combined experience in teaching and research in the subject area and it will undoubtedly serve as one of the most influential textbooks for generations of graduate students in ultrasonic nondestructive testing and materials characterization all over the country as well as in other parts of the world. PETER B. NAGY Department of Aerospace Engineering and Engineering Mechanics University of Cincinnati Cincinnati, Ohio 45221-0070 1808 J. Acoust. Soc. Am., Vol. 107, No. 4, April 2000 Book Reviews 1808