Theory of Elastic Waves in Crystals

Theory of Elastic Waves in Crystals
Title Theory of Elastic Waves in Crystals PDF eBook
Author Fedor I. Fedorov
Publisher Springer Science & Business Media
Pages 377
Release 2013-04-17
Genre Science
ISBN 1475712758

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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.

Elastic wave propagation in transversely isotropic media

Elastic wave propagation in transversely isotropic media
Title Elastic wave propagation in transversely isotropic media PDF eBook
Author R.C. Payton
Publisher Springer Science & Business Media
Pages 214
Release 1983-10-31
Genre Science
ISBN 9789024728435

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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 in Solids I

Elastic Waves in Solids I
Title Elastic Waves in Solids I PDF eBook
Author DANIEL ROYER
Publisher Springer Science & Business Media
Pages 394
Release 1999-11-29
Genre Science
ISBN 9783540659327

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Elastic waves possess some remarkable properties and have become ever more important to applications in fields such as telecommunications (signal processing), medicine (echography), and metallurgy (non-destructive testing). These volumes serve as a bridge between basic books on wave phenomena and more technically oriented books on specific applications of wave phenomena. The first volume studies the different mechanisms of propagation in isotropic and anisotropic media. The second volume describes the generation and applications of free and guided waves.

Elastic Waves in Solids

Elastic Waves in Solids
Title Elastic Waves in Solids PDF eBook
Author E. Dieulesaint
Publisher John Wiley & Sons
Pages 536
Release 1980
Genre Science
ISBN

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The Physics of Phonons

The Physics of Phonons
Title The Physics of Phonons PDF eBook
Author G.P Srivastava
Publisher CRC Press
Pages 448
Release 1990-01-01
Genre Science
ISBN 9780852741535

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There have been few books devoted to the study of phonons, a major area of condensed matter physics. The Physics of Phonons is a comprehensive theoretical discussion of the most important topics, including some topics not previously presented in book form. Although primarily theoretical in approach, the author refers to experimental results wherever possible, ensuring an ideal book for both experimental and theoretical researchers. The author begins with an introduction to crystal symmetry and continues with a discussion of lattice dynamics in the harmonic approximation, including the traditional phenomenological approach and the more recent ab initio approach, detailed for the first time in this book. A discussion of anharmonicity is followed by the theory of lattice thermal conductivity, presented at a level far beyond that available in any other book. The chapter on phonon interactions is likewise more comprehensive than any similar discussion elsewhere. The sections on phonons in superlattices, impure and mixed crystals, quasicrystals, phonon spectroscopy, Kapitza resistance, and quantum evaporation also contain material appearing in book form for the first time. The book is complemented by numerous diagrams that aid understanding and is comprehensively referenced for further study. With its unprecedented wide coverage of the field, The Physics of Phonons will be indispensable to all postgraduates, advanced undergraduates, and researchers working on condensed matter physics.

Nonlinear Waves in Elastic Crystals

Nonlinear Waves in Elastic Crystals
Title Nonlinear Waves in Elastic Crystals PDF eBook
Author Gérard A. Maugin
Publisher
Pages 328
Release 1999
Genre Mathematics
ISBN 9780198534846

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The mathematical modelling of changing structures in materials is of increasing importance to industry where applications of the theory are found in subjects as diverse as aerospace and medicine. This book deals with aspects of the nonlinear dynamics of deformable ordered solids (known as elastic crystals) where the nonlinear effects combine or compete with each other. Physical and mathematical models are discused and computational aspects are also included. Different models are considered - on discrete as well as continuum scales - applying heat, electricity, or magnetism to the crystal structure and these are analysed using the equations of rational mechanics. Students are introduced to the important equations of nonlinear science that describe shock waves, solitons and chaos and also the non-exactly integrable systems or partial differential equations. A large number of problems and examples are included, many taken from recent research and involving both one-dimensional and two-dimensional problems as well as some coupled degress of freedom.

Nonlinear Elastic Waves in Materials

Nonlinear Elastic Waves in Materials
Title Nonlinear Elastic Waves in Materials PDF eBook
Author Jeremiah J. Rushchitsky
Publisher Springer Science & Business
Pages 445
Release 2014-04-23
Genre Science
ISBN 3319004646

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The main goal of the book is a coherent treatment of the theory of propagation in materials of nonlinearly elastic waves of displacements, which corresponds to one modern line of development of the nonlinear theory of elastic waves. The book is divided on five basic parts: the necessary information on waves and materials; the necessary information on nonlinear theory of elasticity and elastic materials; analysis of one-dimensional nonlinear elastic waves of displacement – longitudinal, vertically and horizontally polarized transverse plane nonlinear elastic waves of displacement; analysis of one-dimensional nonlinear elastic waves of displacement – cylindrical and torsional nonlinear elastic waves of displacement; analysis of two-dimensional nonlinear elastic waves of displacement – Rayleigh and Love nonlinear elastic surface waves. The book is addressed first of all to people working in solid mechanics – from the students at an advanced undergraduate and graduate level to the scientists, professionally interesting in waves. But mechanics is understood in the broad sense, when it includes mechanical and other engineering, material science, applied mathematics and physics and so forth. The genesis of this book can be found in author’s years of research and teaching while a head of department at SP Timoshenko Institute of Mechanics (National Academy of Sciences of Ukraine), a member of Center for Micro and Nanomechanics at Engineering School of University of Aberdeen (Scotland) and a professor at Physical-Mathematical Faculty of National Technical University of Ukraine “KPI”. The book comprises 11 chapters. Each chapter is complemented by exercises, which can be used for the next development of the theory of nonlinear waves.