Nonlinear Waves In Elastic Crystals

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Nonlinear Waves in Elastic Crystals

Gérard A. Maugin
Nonlinear Waves in Elastic Crystals Book PDF

Author : Gérard A. Maugin
Publisher : Unknown
Page : 328 pages
File Size : 44,8 Mb
Release : 1999
Category : Mathematics
ISBN : 0198534841

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Nonlinear Waves in Elastic Crystals by Gérard A. Maugin Pdf

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 Waves in Elastic Media

A.G. Kulikovskii,Elena I. Sveshnikova
Nonlinear Waves in Elastic Media Book PDF

Author : A.G. Kulikovskii,Elena I. Sveshnikova
Publisher : CRC Press
Page : 252 pages
File Size : 53,7 Mb
Release : 2021-07-01
Category : Mathematics
ISBN : 9781000446418

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Nonlinear Waves in Elastic Media by A.G. Kulikovskii,Elena I. Sveshnikova Pdf

Nonlinear Waves in Elastic Media explores the theoretical results of one-dimensional nonlinear waves, including shock waves, in elastic media. It is the first book to provide an in-depth and comprehensive presentation of the nonlinear wave theory while taking anisotropy effects into account. The theory is completely worked out and draws on 15 years of research by the authors, one of whom also wrote the 1965 classic Magnetohydrodynamics. Nonlinear Waves in Elastic Media emphasizes the behavior of quasitransverse waves and analyzes arbitrary discontinuity disintegration problems, illustrating that the solution can be non-unique - a surprising result. The solution is shown to be especially interesting when anisotropy and nonlinearity effects interact, even in small-amplitude waves. In addition, the text contains an independent mathematical chapter describing general methods to study hyperbolic systems expressing the conservation laws. The theoretical results described in Nonlinear Waves in Elastic Media allow, for the first time, discovery and interpretation of many new peculiarities inherent to the general problem of discontinuous solutions and so provide a valuable resource for advanced students and researchers involved with continuum mechanics and partial differential equations.

Theory of Elastic Waves in Crystals

Fedor I. Fedorov
Theory of Elastic Waves in Crystals Book PDF

Author : Fedor I. Fedorov
Publisher : Springer
Page : 424 pages
File Size : 45,6 Mb
Release : 1968
Category : Science
ISBN : STANFORD:36105030123629

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Theory of Elastic Waves in Crystals by Fedor I. Fedorov Pdf

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.

Nonlinear Elastic Waves in Materials

Jeremiah J. Rushchitsky
Nonlinear Elastic Waves in Materials Book PDF

Author : Jeremiah J. Rushchitsky
Publisher : Springer Science & Business
Page : 440 pages
File Size : 55,5 Mb
Release : 2014-04-23
Category : Science
ISBN : 9783319004648

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Nonlinear Elastic Waves in Materials by Jeremiah J. Rushchitsky Pdf

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.

Nonlinear Mechanics of Crystals

John D. Clayton
Nonlinear Mechanics of Crystals Book PDF

Author : John D. Clayton
Publisher : Springer Science & Business Media
Page : 700 pages
File Size : 40,8 Mb
Release : 2010-11-01
Category : Science
ISBN : 9789400703506

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Nonlinear Mechanics of Crystals by John D. Clayton Pdf

This book describes behavior of crystalline solids primarily via methods of modern continuum mechanics. Emphasis is given to geometrically nonlinear descriptions, i.e., finite deformations. Primary topics include anisotropic crystal elasticity, plasticity, and methods for representing effects of defects in the solid on the material's mechanical response. Defects include crystal dislocations, point defects, twins, voids or pores, and micro-cracks. Thermoelastic, dielectric, and piezoelectric behaviors are addressed. Traditional and higher-order gradient theories of mechanical behavior of crystalline solids are discussed. Differential-geometric representations of kinematics of finite deformations and lattice defect distributions are presented. Multi-scale modeling concepts are described in the context of elastic and plastic material behavior. Representative substances towards which modeling techniques may be applied are single- and poly- crystalline metals and alloys, ceramics, and minerals. This book is intended for use by scientists and engineers involved in advanced constitutive modeling of nonlinear mechanical behavior of solid crystalline materials. Knowledge of fundamentals of continuum mechanics and tensor calculus is a prerequisite for accessing much of the text. This book could be used as supplemental material for graduate courses on continuum mechanics, elasticity, plasticity, micromechanics, or dislocation mechanics, for students in various disciplines of engineering, materials science, applied mathematics, and condensed matter physics.

Waves in Nonlinear Pre-Stressed Materials

M. Destrade,G. Saccomandi
Waves in Nonlinear Pre Stressed Materials Book PDF

Author : M. Destrade,G. Saccomandi
Publisher : Springer Science & Business Media
Page : 281 pages
File Size : 43,6 Mb
Release : 2007-11-08
Category : Technology & Engineering
ISBN : 9783211735725

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Waves in Nonlinear Pre-Stressed Materials by M. Destrade,G. Saccomandi Pdf

Papers in this book provide a state-of-the-art examination of waves in pre-stressed materials. You’ll gain new perspectives via a multi-disciplinary approach that interweaves key topics. These topics include the mathematical modeling of incremental material response (elastic and inelastic), an analysis of the governing differential equations, and boundary-value problems. Detailed illustrations help you visualize key concepts and processes.

Nonlinear Wave Dynamics of Materials and Structures

Holm Altenbach,Victor A. Eremeyev,Igor S. Pavlov,Alexey V. Porubov
Nonlinear Wave Dynamics of Materials and Structures Book PDF

Author : Holm Altenbach,Victor A. Eremeyev,Igor S. Pavlov,Alexey V. Porubov
Publisher : Springer Nature
Page : 473 pages
File Size : 49,9 Mb
Release : 2020-04-22
Category : Technology & Engineering
ISBN : 9783030387082

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Nonlinear Wave Dynamics of Materials and Structures by Holm Altenbach,Victor A. Eremeyev,Igor S. Pavlov,Alexey V. Porubov Pdf

This book marks the 60th birthday of Prof. Vladimir Erofeev – a well-known specialist in the field of wave processes in solids, fluids, and structures. Featuring a collection of papers related to Prof. Erofeev’s contributions in the field, it presents articles on the current problems concerning the theory of nonlinear wave processes in generalized continua and structures. It also discusses a number of applications as well as various discrete and continuous dynamic models of structures and media and problems of nonlinear acoustic diagnostics.

Wave Processes in Solids with Microstructure

Vladimir I. Erofeyev
Wave Processes in Solids with Microstructure Book PDF

Author : Vladimir I. Erofeyev
Publisher : World Scientific
Page : 276 pages
File Size : 42,7 Mb
Release : 2003
Category : Technology & Engineering
ISBN : 9789812382276

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Wave Processes in Solids with Microstructure by Vladimir I. Erofeyev Pdf

Wave Processes in Solids with Microstructure is useful for undergraduates, graduate students, researchers and practitioners in the mechanics of solids as well as in physical and technical acoustics.

Surface Waves in Geomechanics: Direct and Inverse Modelling for Soils and Rocks

Carlo G. Lai,Krzysztof Wilmanski
Surface Waves in Geomechanics Direct and Inverse Modelling for Soils and Rocks Book PDF

Author : Carlo G. Lai,Krzysztof Wilmanski
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 40,7 Mb
Release : 2007-03-23
Category : Science
ISBN : 9783211380659

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Surface Waves in Geomechanics: Direct and Inverse Modelling for Soils and Rocks by Carlo G. Lai,Krzysztof Wilmanski Pdf

Theories of surface waves develop since the end of XIX century and many fundamental problems like existence, phase and group velocities, attenuation (quality factor), mode conversion, etc. have been, in part successfully, solved within the framework of such simple models as ideal fluids^ or linear elasticity. However, a sufficiently complete presentation of this subject, particularly for solids, is still missing in the literature. The sole exception is the book of I. A. Viktorov^ which contains an extensive discussion of fundamental properties of surface waves in homogeneous and stratified linear elastic solids with particular emphasis on contributions of Russian scientists. Unfortunately, the book has never been translated to English and its Russian version is also hardly available. Practical applications of surface waves develop intensively since a much shorter period of time than theories even though the motivation of discoverers of surface waves such as Lord Rayleigh stems from their appearance in geophysics and seismology. Nowadays the growing interest in practical applications of surface waves stem from the following two main factors: surface waves are ideal for developing relatively cheap and convenient methods of nondestructive testing of various systems spanning from nanomaterials (e.g.

Acoustic Metamaterials and Phononic Crystals

Pierre A. Deymier
Acoustic Metamaterials and Phononic Crystals Book PDF

Author : Pierre A. Deymier
Publisher : Springer Science & Business Media
Page : 388 pages
File Size : 45,7 Mb
Release : 2013-01-13
Category : Technology & Engineering
ISBN : 9783642312328

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Acoustic Metamaterials and Phononic Crystals by Pierre A. Deymier Pdf

This comprehensive book presents all aspects of acoustic metamaterials and phononic crystals. The emphasis is on acoustic wave propagation phenomena at interfaces such as refraction, especially unusual refractive properties and negative refraction. A thorough discussion of the mechanisms leading to such refractive phenomena includes local resonances in metamaterials and scattering in phononic crystals.

Wave Dynamics of Generalized Continua

Alexander G. Bagdoev,Vladimir I. Erofeyev,Ashot V. Shekoyan
Wave Dynamics of Generalized Continua Book PDF

Author : Alexander G. Bagdoev,Vladimir I. Erofeyev,Ashot V. Shekoyan
Publisher : Springer
Page : 274 pages
File Size : 40,5 Mb
Release : 2015-09-25
Category : Science
ISBN : 9783642372674

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Wave Dynamics of Generalized Continua by Alexander G. Bagdoev,Vladimir I. Erofeyev,Ashot V. Shekoyan Pdf

This monograph is devoted to problems of propagation and stability of linear and nonlinear waves in continuous media with complex structure. It considers the different media, such as solid with cavities, preliminary deformed disperse medium, solid with porosity filled by the electrically conductive and non-conductive liquid, magnetoelastic, piezo-semiconductors, crystals with dislocations, composites with inclusions, an electrically conductive asymmetrical liquid, a mixture of gas with a drop liquid. The book also considers the propagation of a laser beam through a two-level medium. The presented results are based on methods of evolution and modulation equations that were developed by the authors. The book is intended for scientific and technical researchers, students and post-graduate students specializing in mechanics of continuous media, physical acoustics, and physics of the solid state.

Non-Classical Continuum Mechanics

Gérard A. Maugin
Non Classical Continuum Mechanics Book PDF

Author : Gérard A. Maugin
Publisher : Springer
Page : 259 pages
File Size : 45,7 Mb
Release : 2016-09-24
Category : Science
ISBN : 9789811024344

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Non-Classical Continuum Mechanics by Gérard A. Maugin Pdf

This dictionary offers clear and reliable explanations of over 100 keywords covering the entire field of non-classical continuum mechanics and generalized mechanics, including the theory of elasticity, heat conduction, thermodynamic and electromagnetic continua, as well as applied mathematics. Every entry includes the historical background and the underlying theory, basic equations and typical applications. The reference list for each entry provides a link to the original articles and the most important in-depth theoretical works. Last but not least, ever y entry is followed by a cross-reference to other related subject entries in the dictionary.

Nonlinear Waves in Solids

A. Jeffrey,J. Engelbrecht
Nonlinear Waves in Solids Book PDF

Author : A. Jeffrey,J. Engelbrecht
Publisher : Springer
Page : 385 pages
File Size : 43,5 Mb
Release : 2014-05-04
Category : Technology & Engineering
ISBN : 9783709124444

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Nonlinear Waves in Solids by A. Jeffrey,J. Engelbrecht Pdf

Travelling wave processes and wave motion are of great importance in many areas of mechanics, and nonlinearity also plays a decisive role there. The basic mathematical models in this area involve nonlinear partial differential equations, and predictability of behaviour of wave phenomena is of great importance. Beside fluid dynamics and gas dynamics, which have long been the traditional nonlinear scienes, solid mechanics is now taking an ever increasing account of nonlinear effects. Apart from plasticity and fracture mechanics, nonlinear elastic waves have been shown to be of great importance in many areas, such as the study of impact, nondestructive testing and seismology. These lectures offer a thorough account of the fundamental theory of nonlinear deformation waves, and in the process offer an up to date account of the current state of research in the theory and practice of nonlinear waves in solids.

Mechanics of Generalized Continua

Gérard A. Maugin,Andrei V. Metrikine
Mechanics of Generalized Continua Book PDF

Author : Gérard A. Maugin,Andrei V. Metrikine
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 43,5 Mb
Release : 2010-03-24
Category : Mathematics
ISBN : 9781441956958

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Mechanics of Generalized Continua by Gérard A. Maugin,Andrei V. Metrikine Pdf

In their 1909 publication Théorie des corps déformables, Eugène and François Cosserat made a historic contribution to materials science by establishing the fundamental principles of the mechanics of generalized continua. The chapters collected in this volume showcase the many areas of continuum mechanics that grew out of the foundational work of the Cosserat brothers. The included contributions provide a detailed survey of the most recent theoretical developments in the field of generalized continuum mechanics and can serve as a useful reference for graduate students and researchers in mechanical engineering, materials science, applied physics and applied mathematics.

Configurational Forces

Gerard A. Maugin
Configurational Forces Book PDF

Author : Gerard A. Maugin
Publisher : CRC Press
Page : 562 pages
File Size : 41,5 Mb
Release : 2016-04-19
Category : Mathematics
ISBN : 1439846138

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Configurational Forces by Gerard A. Maugin Pdf

Exploring recent developments in continuum mechanics, Configurational Forces: Thermomechanics, Physics, Mathematics, and Numerics presents the general framework for configurational forces. It also covers a range of applications in engineering and condensed matter physics. The author presents the fundamentals of accepted standard continuum mechanics, before introducing Eshelby material stress, field theory, variational formulations, Noether’s theorem, and the resulting conservation laws. In the chapter on complex continua, he compares the classical perspective of B.D. Coleman and W. Noll with the viewpoint linked to abstract field theory. He then describes the important notion of local structural rearrangement and its relationship to Eshelby stress. After looking at the relevance of Eshelby stress in the thermodynamic description of singular interfaces, the text focuses on fracture problems, microstructured media, systems with mass exchanges, and electromagnetic deformable media. The concluding chapters discuss the exploitation of the canonical conservation law of momentum in nonlinear wave propagation, the application of canonical-momentum conservation law and material force in numerical schemes, and similarities of fluid mechanics and aerodynamics. Written by a long-time researcher in mechanical engineering, this book provides a detailed treatment of the theory of configurational forces—one of the latest and most fruitful advances in macroscopic field theories. Through many applications, it shows the depth and efficiency of this theory.