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Linear And Nonlinear Waves In Microstructured Solids
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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.
Book Synopsis Linear and Nonlinear Waves in Microstructured Solids by : Igorʹ Vasilʹevich Andrianov
Download or read book Linear and Nonlinear Waves in Microstructured Solids written by Igorʹ Vasilʹevich Andrianov and published by CRC Press. This book was released on 2021 with total page 0 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.
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 251 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.
Book Synopsis Wave Processes in Solids with Microstructure by : Vladimir I. Erofeyev
Download or read book Wave Processes in Solids with Microstructure written by Vladimir I. Erofeyev and published by World Scientific. This book was released on 2003 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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. Contents: Basic Concepts; Mathematical Tools for the Governing Equations Analysis; Strain Solitary Waves in an Elastic Rod; Amplification of Strain Waves in Absence of External Energy Influx; Influence of Dissipative (Active) External Medium; Bulk Active or Dissipative Sources of the Amplification and Selection. Readership: Graduate students, academics and researchers in mechanics, nonlinear science and mechanical engineering.
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.
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.
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:
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.
Book Synopsis Mechanics of Microstructured Solids by : J.-F. Ganghoffer
Download or read book Mechanics of Microstructured Solids written by J.-F. Ganghoffer and published by Springer Science & Business Media. This book was released on 2009-05-14 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a compendium of reviewed articles presented at the 11th EUROMECH-MECAMAT conference entitled, "Mechancis of microstructured solids: cellular materials, fibre reinforced solids and soft tissues." It provides all the latest information in the field.
Book Synopsis Waves in Nonlinear Pre-Stressed Materials by : M. Destrade
Download or read book Waves in Nonlinear Pre-Stressed Materials written by M. Destrade and published by Springer Science & Business Media. This book was released on 2007-11-08 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Applied Wave Mathematics II by : Arkadi Berezovski
Download or read book Applied Wave Mathematics II written by Arkadi Berezovski and published by Springer Nature. This book was released on 2019-11-16 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers contributions on various aspects of the theory and applications of linear and nonlinear waves and associated phenomena, as well as approaches developed in a global partnership of researchers with the national Centre of Excellence in Nonlinear Studies (CENS) at the Department of Cybernetics of Tallinn University of Technology in Estonia. The papers chiefly focus on the role of mathematics in the analysis of wave phenomena. They highlight the complexity of related topics concerning wave generation, propagation, transformation and impact in solids, gases, fluids and human tissues, while also sharing insights into selected mathematical methods for the analytical and numerical treatment of complex phenomena. In addition, the contributions derive advanced mathematical models, share innovative ideas on computing, and present novel applications for a number of research fields where both linear and nonlinear wave problems play an important role. The papers are written in a tutorial style, intended for non-specialist researchers and students. The authors first describe the basics of a problem that is currently of interest in the scientific community, discuss the state of the art in related research, and then share their own experiences in tackling the problem. Each chapter highlights the importance of applied mathematics for central issues in the study of waves and associated complex phenomena in different media. The topics range from basic principles of wave mechanics up to the mathematics of Planet Earth in the broadest sense, including contemporary challenges in the mathematics of society. In turn, the areas of application range from classic ocean wave mathematics to material science, and to human nerves and tissues. All contributions describe the approaches in a straightforward manner, making them ideal material for educational purposes, e.g. for courses, master class lectures, or seminar presentations.
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.
Book Synopsis Generalized Models and Non-classical Approaches in Complex Materials 1 by : Holm Altenbach
Download or read book Generalized Models and Non-classical Approaches in Complex Materials 1 written by Holm Altenbach and published by Springer. This book was released on 2018-03-24 with total page 760 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first of 2 special volumes dedicated to the memory of Gérard Maugin. Including 40 papers that reflect his vast field of scientific activity, the contributions discuss non-standard methods (generalized model) to demonstrate the wide range of subjects that were covered by this exceptional scientific leader. The topics range from micromechanical basics to engineering applications, focusing on new models and applications of well-known models to new problems. They include micro–macro aspects, computational endeavors, options for identifying constitutive equations, and old problems with incorrect or non-satisfying solutions based on the classical continua assumptions.
Book Synopsis Questions About Elastic Waves by : Jüri Engelbrecht
Download or read book Questions About Elastic Waves written by Jüri Engelbrecht and published by Springer. This book was released on 2015-03-05 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the modelling of mechanical waves by asking the right questions about them and trying to find suitable answers. The questions follow the analytical sequence from elementary understandings to complicated cases, following a step-by-step path towards increased knowledge. The focus is on waves in elastic solids, although some examples also concern non-conservative cases for the sake of completeness. Special attention is paid to the understanding of the influence of microstructure, nonlinearity and internal variables in continua. With the help of many mathematical models for describing waves, physical phenomena concerning wave dispersion, nonlinear effects, emergence of solitary waves, scales and hierarchies of waves as well as the governing physical parameters are analysed. Also, the energy balance in waves and non-conservative models with energy influx are discussed. Finally, all answers are interwoven into the canvas of complexity.
Book Synopsis Wave Processes in Solids with Microstructure by : Vladimir I Erofeyev
Download or read book Wave Processes in Solids with Microstructure written by Vladimir I Erofeyev and published by World Scientific. This book was released on 2003-08-12 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book systematically discusses the modern theory of propagation and interaction of elastic waves in solids with microstructure. Mathematical models of solids taking into account microstructure, geometrical and physical nonlinearity, damage media, interaction of deformation and magnetic field are obtained. Different wave effects characteristic of solids with microstructure are studied. The opportunity to use these effects in problems of ultrasonic testing of materials and devices of constructions is considered. Contents:The Fundamental Hypothesis of Microstructured Elastic Solids. Structural–Phenomenological ModelGradient Elasticity Media. Dispersion. Dissipation. NonlinearityGradient Elasticity Media. Damaged Medium. MagnetoelasticityCosserat ContinuumWaves in Two-Component Mixture of SolidsWaves in Micromorphic SolidsElasto-Plastic Waves in the Medium with DislocationsWave Problems of Micropolar Hydrodynamics Readership: Undergraduates, graduate students, researchers and practitioners in the mechanics of solids as well as in physical and technical acoustics. Keywords:Wave;Microstructure;Dispersion;Nonlinearity;Soliton;Damaged
Book Synopsis Nonlinear Wave Dynamics of Materials and Structures by : Holm Altenbach
Download or read book Nonlinear Wave Dynamics of Materials and Structures written by Holm Altenbach and published by Springer Nature. This book was released on 2020-04-22 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
