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Nonlinear Waves in Solids

Author: A. Jeffrey

Publisher: Springer

Published: 2014-05-04

Total Pages: 385

ISBN-13: 3709124441

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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.

Book Synopsis Nonlinear Waves in Solids by : A. Jeffrey

Download or read book Nonlinear Waves in Solids written by A. Jeffrey and published by Springer. This book was released on 2014-05-04 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Nonlinear Waves in Solid State Physics

Author: A.D. Boardman

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 498

ISBN-13: 1468458981

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This book is based on the contributions to the 17th International School of Materials Sci ence and Technology, entitled Nonlinear Waves in Solid State Physics. This was held as a NATO Advanced Study Institute at the Ettore Majorana Centre in Erice, Sicily between the st th 1 and 15 July 1989, and attracted almost 100 participants from over 20 different countries. The book covers the fundamental properties of nonlinear waves in solid state materials, dealing with both theory and experiment. The aim is to emphasise the methods underpinning the important new developments in this area. The material is organised into subject areas that can broadly be classified into the following groups: the theory of nonlinear surface and guided waves in self-focusing magnetic and non-magnetic materials; nonlinear effects at in terfaces; nonlinear acoustoelectronic and surface acoustic waves; Lagrangian and Hamiltonian formulations of nonlinear problems; nonlinear effects in optical fibres; resonance phenomena; and nonlinear integrated optics. The chapters have been grouped together according to these classifications as closely as possible, but it should be borne in mind that although there is much overlap of ideas, each chapter is essentially independent of the others. We would like to acknowledge the sponsorship of the NATO Scientific Affairs Division, the European Physical Society, the National Science Foundation of the USA, the European Research Office, the Italian Ministry of Education, the Italian Ministry of Scientific and Technological Research, the Sicilian Regional Government and the Ugo Bordoni Foundation.

Book Synopsis Nonlinear Waves in Solid State Physics by : A.D. Boardman

Download or read book Nonlinear Waves in Solid State Physics written by A.D. Boardman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on the contributions to the 17th International School of Materials Sci ence and Technology, entitled Nonlinear Waves in Solid State Physics. This was held as a NATO Advanced Study Institute at the Ettore Majorana Centre in Erice, Sicily between the st th 1 and 15 July 1989, and attracted almost 100 participants from over 20 different countries. The book covers the fundamental properties of nonlinear waves in solid state materials, dealing with both theory and experiment. The aim is to emphasise the methods underpinning the important new developments in this area. The material is organised into subject areas that can broadly be classified into the following groups: the theory of nonlinear surface and guided waves in self-focusing magnetic and non-magnetic materials; nonlinear effects at in terfaces; nonlinear acoustoelectronic and surface acoustic waves; Lagrangian and Hamiltonian formulations of nonlinear problems; nonlinear effects in optical fibres; resonance phenomena; and nonlinear integrated optics. The chapters have been grouped together according to these classifications as closely as possible, but it should be borne in mind that although there is much overlap of ideas, each chapter is essentially independent of the others. We would like to acknowledge the sponsorship of the NATO Scientific Affairs Division, the European Physical Society, the National Science Foundation of the USA, the European Research Office, the Italian Ministry of Education, the Italian Ministry of Scientific and Technological Research, the Sicilian Regional Government and the Ugo Bordoni Foundation.

Nonlinear Wave Processes of Deformation in Solids

Author: Jüri Engelbrecht

Publisher: Pitman Advanced Publishing Program

Published: 1983

Total Pages: 248

ISBN-13:

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Book Synopsis Nonlinear Wave Processes of Deformation in Solids by : Jüri Engelbrecht

Download or read book Nonlinear Wave Processes of Deformation in Solids written by Jüri Engelbrecht and published by Pitman Advanced Publishing Program. This book was released on 1983 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Linear and Nonlinear Waves in Microstructured Solids

Author: Igor V. Andrianov

Publisher: CRC Press

Published: 2021-04-22

Total Pages: 322

ISBN-13: 1000372219

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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.

Book Synopsis Linear and Nonlinear Waves in Microstructured Solids by : Igor V. Andrianov

Download or read book Linear and Nonlinear Waves in Microstructured Solids written by Igor V. Andrianov and published by CRC Press. This book was released on 2021-04-22 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Wave Propagation in Nonlinear Fluids and Solids

Author: D. S. Drumheller

Publisher: Cambridge University Press

Published: 1998-02-13

Total Pages: 546

ISBN-13: 9780521587464

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Waves occur widely in nature and have innumerable commercial uses. Pressure waves are responsible for the transmission of speech, bow waves created by meteors can virtually ignite the earth's atmosphere, ultrasonic waves are used for medical imaging, and shock waves are used for the synthesis of new materials. This book provides a thorough, modern introduction to the study of linear and nonlinear waves. Beginning with fundamental concepts of motion, the book goes on to discuss linear and nonlinear mechanical waves, thermodynamics, and constitutive models. It covers gases, liquids, and solids as integral parts of the subject. Among the important areas of research and application are impact analysis, shock wave research, explosive detonation, nonlinear acoustics, and hypersonic aerodynamics. Graduate students, as well as professional engineers and applied physicists, will value this clear, comprehensive introduction to the study of wave phenomena.

Book Synopsis Introduction to Wave Propagation in Nonlinear Fluids and Solids by : D. S. Drumheller

Download or read book Introduction to Wave Propagation in Nonlinear Fluids and Solids written by D. S. Drumheller and published by Cambridge University Press. This book was released on 1998-02-13 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: Waves occur widely in nature and have innumerable commercial uses. Pressure waves are responsible for the transmission of speech, bow waves created by meteors can virtually ignite the earth's atmosphere, ultrasonic waves are used for medical imaging, and shock waves are used for the synthesis of new materials. This book provides a thorough, modern introduction to the study of linear and nonlinear waves. Beginning with fundamental concepts of motion, the book goes on to discuss linear and nonlinear mechanical waves, thermodynamics, and constitutive models. It covers gases, liquids, and solids as integral parts of the subject. Among the important areas of research and application are impact analysis, shock wave research, explosive detonation, nonlinear acoustics, and hypersonic aerodynamics. Graduate students, as well as professional engineers and applied physicists, will value this clear, comprehensive introduction to the study of wave phenomena.

Amplification of Nonlinear Strain Waves in Solids

Author: Alexey V. Porubov

Publisher: World Scientific

Published: 2003

Total Pages: 229

ISBN-13: 9812383263

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This book treats two problems simultaneously: sequential analytical consideration of nonlinear strain wave amplification and selection in wave guides and in a medium; demonstration of the use of even particular analytical solutions to nonintegrable equations in a design of numerical simulation of unsteady nonlinear wave processes. The text includes numerous detailed examples of the strain wave amplification and selection caused by the influence of an external medium, microstructure, moving point defects, and thermal phenomena. The main features of the book are: (1) nonlinear models of the strain wave evolution in a rod subjected by various dissipative/active factors; (2) an analytico-numerical approach for solutions to the governing nonlinear partial differential equations with dispersion and dissipation. This book is essential for introducing readers in mechanics, mechanical engineering, and applied mathematics to the concept of long nonlinear strain wave in one-dimensional wave guides. It is also suitable for self-study by professionals in all areas of nonlinear physics.

Book Synopsis Amplification of Nonlinear Strain Waves in Solids by : Alexey V. Porubov

Download or read book Amplification of Nonlinear Strain Waves in Solids written by Alexey V. Porubov and published by World Scientific. This book was released on 2003 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book treats two problems simultaneously: sequential analytical consideration of nonlinear strain wave amplification and selection in wave guides and in a medium; demonstration of the use of even particular analytical solutions to nonintegrable equations in a design of numerical simulation of unsteady nonlinear wave processes. The text includes numerous detailed examples of the strain wave amplification and selection caused by the influence of an external medium, microstructure, moving point defects, and thermal phenomena. The main features of the book are: (1) nonlinear models of the strain wave evolution in a rod subjected by various dissipative/active factors; (2) an analytico-numerical approach for solutions to the governing nonlinear partial differential equations with dispersion and dissipation. This book is essential for introducing readers in mechanics, mechanical engineering, and applied mathematics to the concept of long nonlinear strain wave in one-dimensional wave guides. It is also suitable for self-study by professionals in all areas of nonlinear physics.

Nonlinear Waves in Fluids: Recent Advances and Modern Applications

Author: Roger Grimshaw

Publisher: Springer Science & Business Media

Published: 2007-03-23

Total Pages: 202

ISBN-13: 3211380256

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Although nonlinear waves occur in nearly all branches of physics and engi neering, there is an amazing degree of agreement about the fundamental con cepts and the basic paradigms. The underlying unity of the theory for linearized waves is already well-established, with the importance of such universal concepts as group velocity and wave superposition. For nonlinear waves the last few decades have seen the emergence of analogous unifying comcepts. The pervasiveness of the soliton concept is amply demonstrated by the ubiquity of such models as the Korteweg-de Vries equation and the nonlinear Schrodinger equation. Similarly, there is a universality in the study of wave-wave interactions, whether determin istic or statistical, and in the recent developments in the theory of wave-mean flow interactions. The aim of this text is to present the basic paradigms of weakly nonlinear waves in fluids. This book is the outcome of a CISM Summer School held at Udine from September 20-24, 2004. . Like the lectures given there the text covers asymptotic methods for the derivation of canonical evolution equations, such as the Kortew- de Vries and nonlinear Schrodinger equations, descriptions of the basic solution sets of these evolution equations, and the most relevant and compelling applica tions. These themes are interlocked, and this will be demonstrated throughout the text . The topics address any fluid flow application, but there is a bias towards geophysical fluid dynamics, reflecting for the most part the areas where many applications have been found.

Book Synopsis Nonlinear Waves in Fluids: Recent Advances and Modern Applications by : Roger Grimshaw

Download or read book Nonlinear Waves in Fluids: Recent Advances and Modern Applications written by Roger Grimshaw and published by Springer Science & Business Media. This book was released on 2007-03-23 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although nonlinear waves occur in nearly all branches of physics and engi neering, there is an amazing degree of agreement about the fundamental con cepts and the basic paradigms. The underlying unity of the theory for linearized waves is already well-established, with the importance of such universal concepts as group velocity and wave superposition. For nonlinear waves the last few decades have seen the emergence of analogous unifying comcepts. The pervasiveness of the soliton concept is amply demonstrated by the ubiquity of such models as the Korteweg-de Vries equation and the nonlinear Schrodinger equation. Similarly, there is a universality in the study of wave-wave interactions, whether determin istic or statistical, and in the recent developments in the theory of wave-mean flow interactions. The aim of this text is to present the basic paradigms of weakly nonlinear waves in fluids. This book is the outcome of a CISM Summer School held at Udine from September 20-24, 2004. . Like the lectures given there the text covers asymptotic methods for the derivation of canonical evolution equations, such as the Kortew- de Vries and nonlinear Schrodinger equations, descriptions of the basic solution sets of these evolution equations, and the most relevant and compelling applica tions. These themes are interlocked, and this will be demonstrated throughout the text . The topics address any fluid flow application, but there is a bias towards geophysical fluid dynamics, reflecting for the most part the areas where many applications have been found.

Wave Propagation in Electromagnetic Media

Author: Julian L. Davis

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 303

ISBN-13: 1461232848

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This is the second work of a set of two volumes on the phenomena of wave propagation in nonreacting and reacting media. The first, entitled Wave Propagation in Solids and Fluids (published by Springer-Verlag in 1988), deals with wave phenomena in nonreacting media (solids and fluids). This book is concerned with wave propagation in reacting media-specifically, in electro magnetic materials. Since these volumes were designed to be relatively self contained, we have taken the liberty of adapting some of the pertinent material, especially in the theory of hyperbolic partial differential equations (concerned with electromagnetic wave propagation), variational methods, and Hamilton-Jacobi theory, to the phenomena of electromagnetic waves. The purpose of this volume is similar to that of the first, except that here we are dealing with electromagnetic waves. We attempt to present a clear and systematic account of the mathematical methods of wave phenomena in electromagnetic materials that will be readily accessible to physicists and engineers. The emphasis is on developing the necessary mathematical tech niques, and on showing how these methods of mathematical physics can be effective in unifying the physics of wave propagation in electromagnetic media. Chapter 1 presents the theory of time-varying electromagnetic fields, which involves a discussion of Faraday's laws, Maxwell's equations, and their appli cations to electromagnetic wave propagation under a variety of conditions.

Book Synopsis Wave Propagation in Electromagnetic Media by : Julian L. Davis

Download or read book Wave Propagation in Electromagnetic Media written by Julian L. Davis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 303 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second work of a set of two volumes on the phenomena of wave propagation in nonreacting and reacting media. The first, entitled Wave Propagation in Solids and Fluids (published by Springer-Verlag in 1988), deals with wave phenomena in nonreacting media (solids and fluids). This book is concerned with wave propagation in reacting media-specifically, in electro magnetic materials. Since these volumes were designed to be relatively self contained, we have taken the liberty of adapting some of the pertinent material, especially in the theory of hyperbolic partial differential equations (concerned with electromagnetic wave propagation), variational methods, and Hamilton-Jacobi theory, to the phenomena of electromagnetic waves. The purpose of this volume is similar to that of the first, except that here we are dealing with electromagnetic waves. We attempt to present a clear and systematic account of the mathematical methods of wave phenomena in electromagnetic materials that will be readily accessible to physicists and engineers. The emphasis is on developing the necessary mathematical tech niques, and on showing how these methods of mathematical physics can be effective in unifying the physics of wave propagation in electromagnetic media. Chapter 1 presents the theory of time-varying electromagnetic fields, which involves a discussion of Faraday's laws, Maxwell's equations, and their appli cations to electromagnetic wave propagation under a variety of conditions.

Nonlinear Waves in Solids

Author: T. C. T. Ting

Publisher:

Published: 1977

Total Pages:

ISBN-13:

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Book Synopsis Nonlinear Waves in Solids by : T. C. T. Ting

Download or read book Nonlinear Waves in Solids written by T. C. T. Ting and published by . This book was released on 1977 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Nonlinear Wave Dynamics

Author: J. Engelbrecht

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 197

ISBN-13: 9401588910

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At the end of the twentieth century, nonlinear dynamics turned out to be one of the most challenging and stimulating ideas. Notions like bifurcations, attractors, chaos, fractals, etc. have proved to be useful in explaining the world around us, be it natural or artificial. However, much of our everyday understanding is still based on linearity, i. e. on the additivity and the proportionality. The larger the excitation, the larger the response-this seems to be carved in a stone tablet. The real world is not always reacting this way and the additivity is simply lost. The most convenient way to describe such a phenomenon is to use a mathematical term-nonlinearity. The importance of this notion, i. e. the importance of being nonlinear is nowadays more and more accepted not only by the scientific community but also globally. The recent success of nonlinear dynamics is heavily biased towards temporal characterization widely using nonlinear ordinary differential equations. Nonlinear spatio-temporal processes, i. e. nonlinear waves are seemingly much more complicated because they are described by nonlinear partial differential equations. The richness of the world may lead in this case to coherent structures like solitons, kinks, breathers, etc. which have been studied in detail. Their chaotic counterparts, however, are not so explicitly analysed yet. The wavebearing physical systems cover a wide range of phenomena involving physics, solid mechanics, hydrodynamics, biological structures, chemistry, etc.

Book Synopsis Nonlinear Wave Dynamics by : J. Engelbrecht

Download or read book Nonlinear Wave Dynamics written by J. Engelbrecht and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the end of the twentieth century, nonlinear dynamics turned out to be one of the most challenging and stimulating ideas. Notions like bifurcations, attractors, chaos, fractals, etc. have proved to be useful in explaining the world around us, be it natural or artificial. However, much of our everyday understanding is still based on linearity, i. e. on the additivity and the proportionality. The larger the excitation, the larger the response-this seems to be carved in a stone tablet. The real world is not always reacting this way and the additivity is simply lost. The most convenient way to describe such a phenomenon is to use a mathematical term-nonlinearity. The importance of this notion, i. e. the importance of being nonlinear is nowadays more and more accepted not only by the scientific community but also globally. The recent success of nonlinear dynamics is heavily biased towards temporal characterization widely using nonlinear ordinary differential equations. Nonlinear spatio-temporal processes, i. e. nonlinear waves are seemingly much more complicated because they are described by nonlinear partial differential equations. The richness of the world may lead in this case to coherent structures like solitons, kinks, breathers, etc. which have been studied in detail. Their chaotic counterparts, however, are not so explicitly analysed yet. The wavebearing physical systems cover a wide range of phenomena involving physics, solid mechanics, hydrodynamics, biological structures, chemistry, etc.