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Self-contained coverage of topics ranging from elementary theory of waves and vibrations in strings to three-dimensional theory of waves in thick plates. Over 100 problems.
The translation into English of Academician Fedorov's ex cellent treatise on elastic wave propagation in solids has come at an opportune time. His systematic exposition of all aspects of this field is most lucid and straightforward. The author has gone to considerable pains to develop in his mathematical background a consistent tensor framework which acts as a unifying motif through out the various aspects of the subject. In many respects his approach will appear quite novel as his treatment introduces several concepts and parameters previously unfamiliar to the literature of the West. Extensive tables in the final chapters illustrate the application of these ideas to the exist ing body of experimental data. The book is both extensive and comprehensive in al1 phases of the subject. Workers in the fields of ultrasonic propagation and elastic properties will find this treatise of great interest and direct concern. H. B. Huntington Rensselaer Polytechnic Institute Troy, New York November 1967 v Preface to the American Edition In preparing this edition I have corrected various misprints and errors appearing in the Russian edition, but I have also incorpo rated some substantial changes and additions, the latter representing some results I and my colleagues have recently obtained and pub_ lished in Russian journals. For example, in section 32 I have added a general derivation of the equation for the seetion of the wave surface by a symmetry plane for cubic, hexagonal, tetragonal, and orthorhombic crystals.
Ultrasound has found an increasing number of applications in recent years due to greatly increased computing power. Ultrasound devices are often preferred over other devices because of their lower cost, portability, and non-invasive nature. Patients using ultrasound can avoid the dangers of radiological imaging devices such as x-rays, CT scans, and radioactive media injections. Ultrasound is also a preferred and practical method of detecting material fatique and defects in metals, composites, semiconductors, wood, etc. - Detailed appendices contain useful formulas and their derivations, technical details of relevant theories - The FAQ format is used where a concept in one answer leads to a new Q
This volume contains 16 classic essays from the 17th to the 21st centuries on aspects of elastic wave theory.
In this monograph I record those parts of the theory of transverse isotropic elastic wave propagation which lend themselves to an exact treatment, within the framework of linear theory. Emphasis is placed on transient wave motion problems in two- and three-dimensional unbounded and semibounded solids for which explicit results can be obtained, without resort to approximate methods of integration. The mathematical techniques used, many of which appear here in book form for the first time, will be of interest to applied mathematicians, engeneers and scientists whose specialty includes crystal acoustics, crystal optics, magnetogasdynamics, dislocation theory, seismology and fibre wound composites. My interest in the subject of anisotropic wave motion had its origin in the study of small deformations superposed on large deformations of elastic solids. By varying the initial stretch in a homogeneously deformed solid, it is possible to synthesize aniso tropic materials whose elastic parameters vary continuously. The range of the parameter variation is limited by stability considerations in the case of small deformations super posed on large deformation problems and (what is essentially the same thing) by the of hyperbolicity (solids whose parameters allow wave motion) for anisotropic notion solids. The full implication of hyperbolicity for anisotropic elastic solids has never been previously examined, and even now the constraints which it imposes on the elasticity constants have only been examined for the class of transversely isotropic (hexagonal crystals) materials.
Elastic Waves: High Frequency Theory is concerned with mathematical aspects of the theory of high-frequency elastic waves, which is based on the ray method. The foundations of elastodynamics are presented along with the basic theory of plane and spherical waves. The ray method is then described in considerable detail for bulk waves in isotropic and anisotropic media, and also for the Rayleigh waves on the surface of inhomogeneous anisotropic elastic solids. Much attention is paid to analysis of higher-order terms and to generation of waves in inhomogeneous media. The aim of the book is to present a clear, systematic description of the ray method, and at the same time to emphasize its mathematical beauty. Luckily, this beauty is usually not accompanied by complexity and mathematical ornateness.
An advanced level textbook on wave propagation and scattering directed at applied mathematicians, seismologists, and engineers.
This book treats various generalizations of the classical O'Doherty-Anstey formula in order to describe stratigraphic filtering effects. These are the effects that can be observed when elastic and electromagnetic waves propagate through multilayered structures. Our aim was to treat this topic in a comprehensive manner and present compact results in a didactically simple way, emphasizing the physics of the wave-propagation phenomena. We do not claim mathematical rigidity in all our derivations, however, we are pleased to have obtained quite simple descriptions of scattering, transmission and reflection of wavefields in acoustic, elastic, and poroelastic media which can be useful for various seismological and non-seismological applications.
Earthquakes are detected and studied by measuring the waves they create. Waves are transmitted through the Earth to detect oil and gas deposits and to study the Earth?s geological structure. Properties of materials are determined by measuring the behaviour of waves transmitted through them. In recent years, elastic waves transmitted through the human body have been used for medical diagnosis and therapy. Many students and professionals in various branches of engineering encounter problems requiring an understanding of elastic waves. In this book, they will find the basic concepts and methods of the theory of wave propagation in elastic materials. One-dimensional waves, transient waves and harmonic waves including reflections of plane waves at interfaces. Rayleigh waves, waves in elastic layers and in layered materials are discussed. Analytical methods in nonlinear wave propagation are presented. This book includes exercises with solutions and many explanatory figures.