Nonlinear Waves In Elastic Media

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Nonlinear Waves In Elastic Media

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Author : A.G. Kulikovskii
language : en
Publisher: CRC Press
Release Date : 2021-06-30

Nonlinear Waves In Elastic Media written by A.G. Kulikovskii and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-06-30 with Mathematics categories.

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.

Selected Topics In Nonlinear Wave Mechanics

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Author : C.I. Christov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Selected Topics In Nonlinear Wave Mechanics written by C.I. Christov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This book gives an overview ofthe current state of nonlinear wave mechanics with emphasis on strong discontinuities (shock waves) and localized self preserving shapes (solitons) in both elastic and fluid media. The exposition is intentionallyat a detailed mathematical and physical level, our expectation being that the reader will enjoy coming to grips in a concrete manner with advances in this fascinating subject. Historically, modern research in nonlinear wave mechanics began with the famous 1858 piston problem paper of Riemann on shock waves and con tinued into the early part of the last century with the work of Hadamard, Rankine, and Hugoniot. After WWII, research into nonlinear propagation of dispersive waves rapidly accelerated with the advent of computers. Works of particular importance in the immediate post-war years include those of von Neumann, Fermi, and Lax. Later, additional contributions were made by Lighthill, Glimm, Strauss, Wendroff, and Bishop. Dispersion alone leads to shock fronts of the propagating waves. That the nonlinearity can com pensate for the dispersion, leading to propagation with a stable wave having constant velocity and shape (solitons) came as a surprise. A solitary wave was first discussed by J. Scott Russell in 1845 in "Report of British Asso ciations for the Advancement of Science. " He had, while horseback riding, observed a solitary wave travelling along a water channel and followed its unbroken progress for over a mile.

Nonlinear Waves In Active Media

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Author : Jüri Engelbrecht
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Nonlinear Waves In Active Media written by Jüri Engelbrecht and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

TIlis volume contains the contributions to the Euromech Colloquium No. 241 on Nonlinear Waves in Active Media at the Institute of Cybernetics of the Estonian Academy of Sciences, Tallinn, Estonia, USSR, September 27-30, 1988. The Co-chairmen of the Euromech Colloquium felt that it would be a good service to the community to publish these proceedings. First, the topic itself dealing with various wave processes with energy influx is extremely interesting and attracted a much larger number of participants than usual - a clear sign of its importance to the scientific community. Second, Euromech No. 241 was actually the first Euromech Colloquium held in the Soviet Union and could thus be viewed as a milestone in the extending scientific contacts between East and West. At the colloquium 50 researchers working in very different branches of sci ence met to lecture on their results and to discuss problems of common interest. An introductory paper by I. Engelbrecht presents the common motivation and background of the topics covered. Altogether 36 speakers presented their lectures, of which 30 are gathered here. The remaining six papers which will appear elsewhere are listed on page X. In addition, three contributions by authors who could not attend the colloquium are included. The two lectures given by A.S. Mikhailov, V.S. Davydov and V.S. Zykov are here published as one long paper.

Nonlinear Waves In Bounded Media The Mathematics Of Resonance

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Author : Seymour Brian R
language : en
Publisher: World Scientific
Release Date : 2017-01-18

Nonlinear Waves In Bounded Media The Mathematics Of Resonance written by Seymour Brian R and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-18 with Technology & Engineering categories.

This unique book aims to treat a class of nonlinear waves that are reflected from the boundaries of media of finite extent. It involves both standing (unforced) waves and resonant oscillations due to external periodic forcing. The waves are both hyperbolic and dispersive. To achieve this aim, the book develops the necessary understanding of linear waves and the mathematical techniques of nonlinear waves before dealing with nonlinear waves in bounded media. The examples used come mainly from gas dynamics, water waves and viscoelastic waves.

Nonlinear Waves In Inhomogeneous And Hereditary Media

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Author : Aleksandr Aleksandrovich Lokshin
language : en
Publisher: Springer
Release Date : 1992

Nonlinear Waves In Inhomogeneous And Hereditary Media written by Aleksandr Aleksandrovich Lokshin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Science categories.

Wave Dynamics Of Generalized Continua

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Author : Alexander G. Bagdoev
language : en
Publisher: Springer
Release Date : 2015-09-25

Wave Dynamics Of Generalized Continua written by Alexander G. Bagdoev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-25 with Science categories.

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.

Introduction To Elastic Wave Propagation

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Author : A. Bedford
language : en
Publisher:
Release Date : 1994-09-06

Introduction To Elastic Wave Propagation written by A. Bedford and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-09-06 with Science categories.

This volume outlines the basic concepts and methods of the theory of wave propagation in elastic materials. The linear theory of elasticity is covered, culminating in the displacement equations of motion. One-dimensional waves are analyzed through the D'Alembert solution.

Wave Processes In Solids With Microstructure

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Author : Vladimir I. Erofeyev
language : en
Publisher: World Scientific
Release Date : 2003

Wave Processes In Solids With Microstructure written by Vladimir I. Erofeyev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Science categories.

1. The fundamental hypothesis of microstructured elastic solids. Structural-phenomenological model. 1.1. Mathematical models of solids with microstructure. 1.2. Definition of material constants -- 2. Gradient elasticity media. Dispersion. Dissipation. Non-linearity. 2.1. Dynamic equations. Energy and momentum variation law. 2.2. Dispersion properties of longitudinal and shear waves. Surface Rayleigh waves. 2.3. Dissipative properties. 2.4. Nonlinear plain stationary waves. 2.5. Quasi-plain wave beams. 2.6. Self-modulation of quasi-harmonic shear waves. 2.7. Resonant interaction of quasi-harmonic waves. 2.8. Noise waves -- 3. Gradient elasticity media. Damaged medium. Magnetoelasticity. 3.1. Waves in damaged medium with microstructure. 3.2. Magneto-elastic waves in the medium with microstructure -- 4. Cosserat continuum. 4.1. Basic equations of micropolar elasticity theory. 4.2. Dispersion properties of volume waves. 4.3. Wave reflection from the free interface of micropolar halfspace. Rayleigh surface waves. 4.4. Normal waves in a micropolar layer. 4.5. Nonlinear resonant interaction of longitudinal and rotation waves. 4.6. Waves in Cosserat pseudocontinuum. 4.7. Waves in the Cosserat continuum with symmetric stress tensor -- 5. Waves in two-component mixture of solids. 5.1. Dispersion properties. 5.2. Some nonlinear wave effects -- 6. Waves in micromorphic solids. 6.1. Dynamics equations. 6.2. Different types of volume waves and their dispersion properties. 6.3. Surface shear waves in the gradient-elastic half-space with surface energy -- 7. Elasto-plastic waves in the medium with dislocations. 7.1. Equations of dynamics. 7.2. Dispersion properties. 7.3. Some nonlinear problems. 7.4. Correlation of elasto-plastic continuum and Cosserat continuum. 7.5. Example of research of the influence of dislocations on dispersion and damping of ultrasound in solid body -- 8. Wave problems of micropolar hydrodynamics. 8.1. Rotational waves in micropolar liquids. 8.2. Shear surface wave at the interface of elastic body and micropolar liquid. 8.3. Shear surface wave at the interface between elastic half-space and conducting viscous liquid in a magnetic field.

Introduction To Elastic Wave Propagation

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Author : Anthony Bedford
language : en
Publisher: Springer Nature
Release Date : 2023-11-05

Introduction To Elastic Wave Propagation written by Anthony Bedford and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-05 with Technology & Engineering categories.

This revised and updated edition expands on its explanations of methods used to analyze waves in solid materials, such as the waves created by earthquakes and the ultrasonic waves used to detect flaws in materials and for medical diagnoses. In addition to the traditional methods used to analyze steady-state and transient waves in elastic materials, the book contains introductions to advanced areas that no other single text covers. These topics include the use of finite elements to solve wave problems, the Cagniard-de Hoop method, the four-pole technique for analyzing waves in layered media, and the growth and decay of shock and acceleration waves. The authors explain the theory of linear elasticity through the displacement equations of motion, methods used to analyze steady-state and transient waves in layered media, and include an appendix on functions of a complex variable. Originally developed for a graduate course for which no suitable text existed, the new edition retains its classroom-tested treatment of the theories of linear elasticity and complex variables for students needing background in those subjects.

Linear And Nonlinear Waves In Microstructured Solids

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Author : Igor V. Andrianov
language : en
Publisher: CRC Press
Release Date : 2021-04-22

Linear And Nonlinear Waves In Microstructured Solids written by Igor V. Andrianov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-22 with Technology & Engineering categories.

This book uses asymptotic methods to obtain simple approximate analytic solutions to various problems within mechanics, notably wave processes in heterogeneous materials. Presenting original solutions to common issues within mechanics, this book builds upon years of research to demonstrate the benefits of implementing asymptotic techniques within mechanical engineering and material science. Focusing on linear and nonlinear wave phenomena in complex micro-structured solids, the book determines their global characteristics through analysis of their internal structure, using homogenization and asymptotic procedures, in line with the latest thinking within the field. The book’s cutting-edge methodology can be applied to optimal design, non-destructive control and in deep seismic sounding, providing a valuable alternative to widely used numerical methods. Using case studies, the book covers topics such as elastic waves in nonhomogeneous materials, regular and chaotic dynamics based on continualisation and discretization and vibration localization in 1D Linear and Nonlinear lattices. The book will be of interest to students, research engineers, and professionals specialising in mathematics and physics as well as mechanical and civil engineering.