7R11. Transient Aerohydroelasticity of Spherical Bodies. Foundations of Engineering Mechanics. - AG Gorshkov and DV Tarlakovsky (Dept of Appl Mech, Moscow Aviation Inst, Volokolamskoe Shosse 4, Moscow, 125871, Russia). Springer-Verlag, Berlin. 2001. 289 pp. ISBN 3-540-42151-3. $99.00.
Reviewed by GA Maugin (Lab de Modelisation en Mec, Univ Pierre et Marie Curie, Tour 66, 4 Place Jussieu, Case 162, Paris Cedex 05, 75252, France).
This book is authored by two scientists from the Department of Applied Mechanics of the Moscow Institute of Aviation. Although the title does not render justice to the contents, it is indeed a book about problems met with the transient interaction of deformable bodies with a surrounding medium, say a fluid or another solid, in special contact conditions. This involves interfaces, some of which being part of the looked-for solution. Here, however, as indicated by the title, homogeneous bodies and composite structures considered all have spherical shapes. This obviously greatly helps the authors in their essentially analytical considerations. Due to this privileged symmetry, the exact solutions derived for both external and internal problems, depending on where are situated the elastic and acoustic (ie, fluid-like) media with respect to one another, involve series expansions in terms of Legendre polynomials. In other words, solutions are sought in the form of generalized spherical waves. This gives a somewhat antiquated look to the book with a paraphernalia of special functions and representations of all kinds compared to modern books that would necessarily consider bodies with less symmetries, but certainly attractive computer-obtained diagrams. Remarkably enough, there is no such diagram in the whole book. Transient problems obviously involve Laplace transfoms in time for arbitrary functions corresponding to converging and diverging waves. An exact algorithm, in fact, is presented for the inversion of the Laplace transfom for the general class of problems under consideration. This calls for high mathematics such as the theory of self-adjoint differential operators.
To better grasp the aim of the authors in producing this book, perhaps more a collection of solved problems than anything else, it is of interest to give a representative list of some of the problems that are studied in detail. In a non-limitative list, we note among the classics of classics: vibrations of thin-walled isotropic shells in contact with an elastic medium and the vibrations of a thick-walled sphere in an elastic medium with special cases such as a fully solid sphere embedded in an elastic medium, propagation from a cavity, reflection of elastic waves from the wall of a rigid reservoir, and vibrations of a piecewise homogeneous elastic space with concentric spherical interfaces. Other typical problems that require some space for their treatment are the diffraction of waves by elastic spherical bodies, the axially symmetric vibrations of elastic media containing a spherical cavity or an embedded stiff inclusion, and the diffraction of plane and spherical waves by a spherical barrier supported by a thin-walled shell with all possible declinations of the latter problem. Perhaps more to the point is the study of the translational motion of a sphere in an elastic or acoustic medium, and the penetration of spherical bodies into a fluid half-space. More complicated media of propagation such as Biot’s porous medium are mentioned in a last chapter.
In all, the book is extremely technical and does not make easy reading. It does not mention explicitly applications, but some can easily be guessed. Transient Aerohydroelasticity of Spherical Bodies will be of interest to those specialists who directly deal with some of the just mentioned problems. The translation from the Russian language is correct, but this is not, as anyone can guess, high literature. But the bibliography offered is tremendous, containing about 500 items of which about two thirds of the works are from the former Soviet Union and the actual Russian Federation.