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Author : Jüri Engelbrecht
Publisher : Pitman Advanced Publishing Program
Page : 248 pages
File Size : 55,8 Mb
Release : 1983
Category : Deformation (Mechanics).
ISBN : UCAL:B4406513
Author : J. Engelbrecht
Publisher : Halsted Press
Page : 234 pages
File Size : 54,6 Mb
Release : 1986-05-01
Category : Electronic
ISBN : 0470204737
Author : A. Jeffrey,J. Engelbrecht
Publisher : Springer
Page : 385 pages
File Size : 46,6 Mb
Release : 2014-05-04
Category : Technology & Engineering
ISBN : 9783709124444
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.
Author : Vladimir I Erofeyev
Publisher : World Scientific
Page : 276 pages
File Size : 47,8 Mb
Release : 2003-08-12
Category : Technology & Engineering
ISBN : 9789814487047
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
Author : Igor V. Andrianov,Jan Awrejcewicz,Vladyslav Danishevskyy
Publisher : CRC Press
Page : 322 pages
File Size : 45,8 Mb
Release : 2021-04-22
Category : Technology & Engineering
ISBN : 9781000372212
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.
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 43,9 Mb
Release : 2024-06-23
Category : Electronic
ISBN : 9789814486354
Author : Alexey V. Porubov
Publisher : World Scientific
Page : 229 pages
File Size : 54,9 Mb
Release : 2003
Category : Science
ISBN : 9789812794291
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.
Author : Vladimir I. Erofeyev
Publisher : World Scientific
Page : 276 pages
File Size : 51,6 Mb
Release : 2003
Category : Technology & Engineering
ISBN : 9789812382276
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.
Author : D. S. Drumheller
Publisher : Cambridge University Press
Page : 546 pages
File Size : 40,9 Mb
Release : 1998-02-13
Category : Science
ISBN : 0521587468
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.
Author : C.I. Christov,Arde Guran
Publisher : Springer Science & Business Media
Page : 274 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461200956
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.
Author : Gérard A. Maugin
Publisher : Unknown
Page : 328 pages
File Size : 54,6 Mb
Release : 1999
Category : Mathematics
ISBN : 0198534841
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.
Author : J.-F. Ganghoffer,Franco Pastrone
Publisher : Springer Science & Business Media
Page : 133 pages
File Size : 44,7 Mb
Release : 2009-05-14
Category : Science
ISBN : 9783642009112
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.
Author : Ewald Quak,Tarmo Soomere
Publisher : Springer Science & Business Media
Page : 467 pages
File Size : 46,6 Mb
Release : 2009-08-29
Category : Mathematics
ISBN : 9783642005855
This edited volume consists of twelve contributions related to the EU Marie Curie Transfer of Knowledge Project Cooperation of Estonian and Norwegian Scienti c Centres within Mathematics and its Applications, CENS-CMA (2005-2009), - der contract MTKD-CT-2004-013909, which ?nanced exchange visits to and from CENS, the Centre for Nonlinear Studies at the Institute of Cybernetics of Tallinn University of Technology in Estonia. Seven contributions describe research highlights of CENS members, two the work of members of CMA, the Centre of Mathematics for Applications,Univ- sity of Oslo, Norway, as the partner institution of CENS in the Marie Curie project, and three the ?eld of work of foreign research fellows, who visited CENS as part of theproject. Thestructureofthebookre?ectsthedistributionofthetopicsaddressed: Part I Waves in Solids Part II Mesoscopic Theory Part III Exploiting the Dissipation Inequality Part IV Waves in Fluids Part V Mathematical Methods The papers are written in a tutorial style, intended for non-specialist researchers and students, where the authors communicate their own experiences in tackling a problem that is currently of interest in the scienti?c community. The goal was to produce a book, which highlights the importance of applied mathematics and which can be used for educational purposes, such as material for a course or a seminar. To ensure the scienti?c quality of the contributions, each paper was carefully - viewed by two international experts. Special thanks go to all authors and referees, without whom making this book would not have been possible.
Author : Holm Altenbach,Victor A. Eremeyev,Igor S. Pavlov,Alexey V. Porubov
Publisher : Springer Nature
Page : 473 pages
File Size : 55,5 Mb
Release : 2020-04-22
Category : Technology & Engineering
ISBN : 9783030387082
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.
Author : Carlo G. Lai,Krzysztof Wilmanski
Publisher : Springer Science & Business Media
Page : 390 pages
File Size : 51,8 Mb
Release : 2007-03-23
Category : Science
ISBN : 9783211380659
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.