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Wave Propagation In An Elastic Medium Generalized Davey Stewartson Equations
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Book Synopsis Wave Propagation in an Elastic Medium: Generalized Davey-Stewartson Equations by : Ceni Babaoğlu
Download or read book Wave Propagation in an Elastic Medium: Generalized Davey-Stewartson Equations written by Ceni Babaoğlu and published by . This book was released on 2006 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: In the present study, the problem of (2 + 1) (two spatial and one temporal) dimensional nonlinear wave propagation in a generalized elastic medium is considered. The modulation of (2 + 1) dimensional waves is examined in an infinite; homogenous, weakly nonlinear and weakly dispersive elastic medium. The study corıtaİns five ınaİrı sections. In the first section, a general introduction is given including some information about the nonlinear systems characterizing the modulation problems and the special solutions of these systems. In the second section, nonlinear evolution equations are derived describing the asymptotic behavior of waves for (2 + 1 ) dimensional wave modulation problem. While deriving the equations an asymptotic technique called reductive perturbation method is used and it is shown that the problem of wave modulation is characterİzed by a system of three nonlinear partial differential equations. These equations involve interactions of a free short transverse, a free long longitudinal and a free long transverse wave modes, and is called the ''generalized Davey-Stewartson equations''. Under some restrictions on parameter values, it is .. shown that the generalized Davey-Stewartson equations reduce to the well-known Davey-Stewartson and to the nonlinear Schrödinger equations. Besides, some special solutions of the generalized Davey-Stewartson equations are calculated by two different methods. Whİle calculatİng the special solutions by the help of the first method, travelling wave transformations are used in order to reduce the partial differential equations to ordinary differential equations and special solutions are given in terms of Jacobian elliptic functions. It is shown that these solutions reduce to hyperbolic functions for some cases and that they involve sech-tanh-tanh and tanh-tanh-tanh type solutions under some constraints on the parameter values. The second method is based on coupled Riccati equations and their travelling wave transformatİons. By using the second method, the special solutions of the generalized Davey-Stewartson equations are obtained in terms of hyperbolic functions. In the third section, it is observed that the generalized Davey-Stewartson equations are not valid for the long-wave short-wave resonant case. In the case where the phase velocity of the long longitudinal wave is equal to the group velocity of the short transverse wave, new evolution equations are derived characterizing the problem and are called long-wave short-wave interaction equations. The special solutions of the long-wave short-wave interaction equations are obtained by Jacobian elliptic functions and tanh method. In the fourth section, degenerate generalized Davey-Stewartson equations, which are obtained when one of thei,coefficients of the generalized Davey-Stewartson equations becomes zero, are considered. The special solutions of the degenerate generalized Davey-Stewartson equations are obtained by using the two methods given in the second and third sections. ...
Book Synopsis Wave Propagation in Elastic Solids by : J. D. Achenbach
Download or read book Wave Propagation in Elastic Solids written by J. D. Achenbach and published by Elsevier. This book was released on 2016-01-21 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wave Propagation in Elastic Solids focuses on linearized theory and perfectly elastic media. This book discusses the one-dimensional motion of an elastic continuum; linearized theory of elasticity; elastodynamic theory; and elastic waves in an unbounded medium. The plane harmonic waves in elastic half-spaces; harmonic waves in waveguides; and forced motions of a half-space are also elaborated. This text likewise covers the transient waves in layers and rods; diffraction of waves by a slit; and thermal and viscoelastic effects, and effects of anisotropy and nonlinearity. Other topics include the summary of equations in rectangular coordinates, time-harmonic plane waves, approximate theories for rods, and transient in-plane motion of a layer. This publication is a good source for students and researchers conducting work on the wave propagation in elastic solids.
Book Synopsis Symmetry And Perturbation Theory - Proceedings Of The International Conference On Spt2004 by : Giuseppe Gaeta
Download or read book Symmetry And Perturbation Theory - Proceedings Of The International Conference On Spt2004 written by Giuseppe Gaeta and published by World Scientific. This book was released on 2005-01-25 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume is a collection of papers presented at the International Conference on SPT2004 focusing on symmetry, perturbation theory, and integrability.The book provides an updated overview of the recent developments in the various different fields of nonlinear dynamics, covering both theory and applications. Special emphasis is given to algebraic and geometric integrability, solutions to the N-body problem of the “choreography” type, geometry and symmetry of dynamical systems, integrable evolution equations, various different perturbation theories, and bifurcation analysis.The contributors to this volume include some of the leading scientists in the field, among them: I Anderson, D Bambusi, S Benenti, S Bolotin, M Fels, W Y Hsiang, V Matveev, A V Mikhailov, P J Olver, G Pucacco, G Sartori, M A Teixeira, S Terracini, F Verhulst and I Yehorchenko.
Book Synopsis Wave Propagation in Elastic Solids by : Jan Achenbach
Download or read book Wave Propagation in Elastic Solids written by Jan Achenbach and published by Elsevier. This book was released on 2012-12-02 with total page 440 pages. Available in PDF, EPUB and Kindle. Book excerpt: The propagation of mechanical disturbances in solids is of interest in many branches of the physical scienses and engineering. This book aims to present an account of the theory of wave propagation in elastic solids. The material is arranged to present an exposition of the basic concepts of mechanical wave propagation within a one-dimensional setting and a discussion of formal aspects of elastodynamic theory in three dimensions, followed by chapters expounding on typical wave propagation phenomena, such as radiation, reflection, refraction, propagation in waveguides, and diffraction. The treatment necessarily involves considerable mathematical analysis. The pertinent mathematical techniques are, however, discussed at some length.
Book Synopsis Wave Propagation in Solids and Fluids by : Julian L. Davis
Download or read book Wave Propagation in Solids and Fluids written by Julian L. Davis and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 396 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this volume is to present a clear and systematic account of the mathematical methods of wave phenomena in solids, gases, and water that will be readily accessible to physicists and engineers. The emphasis is on developing the necessary mathematical techniques, and on showing how these mathematical concepts can be effective in unifying the physics of wave propagation in a variety of physical settings: sound and shock waves in gases, water waves, and stress waves in solids. Nonlinear effects and asymptotic phenomena will be discussed. Wave propagation in continuous media (solid, liquid, or gas) has as its foundation the three basic conservation laws of physics: conservation of mass, momentum, and energy, which will be described in various sections of the book in their proper physical setting. These conservation laws are expressed either in the Lagrangian or the Eulerian representation depending on whether the boundaries are relatively fixed or moving. In any case, these laws of physics allow us to derive the "field equations" which are expressed as systems of partial differential equations. For wave propagation phenomena these equations are said to be "hyperbolic" and, in general, nonlinear in the sense of being "quasi linear" . We therefore attempt to determine the properties of a system of "quasi linear hyperbolic" partial differential equations which will allow us to calculate the displacement, velocity fields, etc.
Book Synopsis Some Wave Propagation Problems in a Bounded, Heterogeneous, Elastic Medium by : Glenn Leland Converse
Download or read book Some Wave Propagation Problems in a Bounded, Heterogeneous, Elastic Medium written by Glenn Leland Converse and published by . This book was released on 1965 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt: This report is a study of the relationships existing between the frequency, phase velocity, group velocity, and wave number of mechanical waves propagating in bounded, heterogeneous, linearly elastic media. For single wave systems, which include the Love and pressure waves and are governed by a single second-order ordinary differential equation, Sturmian theory is applicable. Due to the inapplicability of Sturmian theory to two or three coupled, second-order ordinary differential equations, general results of double wave systems, comprised of the pressure and shear-vertical waves and described by these two or three equations, are unobtainable. The analysis is directed towards either very short or very long wavelength waves and proceeds by perturbation or asymptotic methods. For both wave systems, the emphasis is on determining the way in which the phase velocity varies with the wave number. From this relationship, the frequency and group velocity can be found as functions of the wave number.
Book Synopsis Mathematics of Wave Propagation by : Julian L. Davis
Download or read book Mathematics of Wave Propagation written by Julian L. Davis and published by Princeton University Press. This book was released on 2021-01-12 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: Earthquakes, a plucked string, ocean waves crashing on the beach, the sound waves that allow us to recognize known voices. Waves are everywhere, and the propagation and classical properties of these apparently disparate phenomena can be described by the same mathematical methods: variational calculus, characteristics theory, and caustics. Taking a medium-by-medium approach, Julian Davis explains the mathematics needed to understand wave propagation in inviscid and viscous fluids, elastic solids, viscoelastic solids, and thermoelastic media, including hyperbolic partial differential equations and characteristics theory, which makes possible geometric solutions to nonlinear wave problems. The result is a clear and unified treatment of wave propagation that makes a diverse body of mathematics accessible to engineers, physicists, and applied mathematicians engaged in research on elasticity, aerodynamics, and fluid mechanics. This book will particularly appeal to those working across specializations and those who seek the truly interdisciplinary understanding necessary to fully grasp waves and their behavior. By proceeding from concrete phenomena (e.g., the Doppler effect, the motion of sinusoidal waves, energy dissipation in viscous fluids, thermal stress) rather than abstract mathematical principles, Davis also creates a one-stop reference that will be prized by students of continuum mechanics and by mathematicians needing information on the physics of waves.
Book Synopsis The Theory of Elastic Waves and Waveguides by : J. Miklowitz
Download or read book The Theory of Elastic Waves and Waveguides written by J. Miklowitz and published by Elsevier. This book was released on 2012-12-02 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary objective of this book is to give the reader a basic understanding of waves and their propagation in a linear elastic continuum. The studies of elastodynamic theory and its application to fundamental value problems should prepare the reader to tackle many physical problems of general interest in engineering and geophysics, and of particular interest in mechanics and seismology.
Book Synopsis Introduction to Elastic Wave Propagation by : Anthony Bedford
Download or read book Introduction to Elastic Wave Propagation written by Anthony Bedford and published by Springer Nature. This book was released on 2023-11-05 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Linear Elastic Waves by : John G. Harris
Download or read book Linear Elastic Waves written by John G. Harris and published by Cambridge University Press. This book was released on 2001-08-06 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: An advanced level textbook on wave propagation and scattering directed at applied mathematicians, seismologists, and engineers.
Book Synopsis Wave Propagation in Elastic Solids by : J. D. Achenbach
Download or read book Wave Propagation in Elastic Solids written by J. D. Achenbach and published by North-Holland. This book was released on 1973 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: The propagation of mechanical disturbances in solids is of interest in many branches of the physical scienses and engineering. This book aims to present an account of the theory of wave propagation in elastic solids. The material is arranged to present an exposition of the basic concepts of mechanical wave propagation within a one-dimensional setting and a discussion of formal aspects of elastodynamic theory in three dimensions, followed by chapters expounding on typical wave propagation phenomena, such as radiation, reflection, refraction, propagation in waveguides, and diffraction. The treatment necessarily involves considerable mathematical analysis. The pertinent mathematical techniques are, however, discussed at some length.
Book Synopsis Introduction to Elastic Wave Propagation by : A. Bedford
Download or read book Introduction to Elastic Wave Propagation written by A. Bedford and published by . This book was released on 1994-09-06 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
Author :Michael A Slawinski Publisher :World Scientific Publishing Company ISBN 13 :9813107677 Total Pages :614 pages Book Rating :4.8/5 (131 download)
Book Synopsis Waves And Rays In Elastic Continua by : Michael A Slawinski
Download or read book Waves And Rays In Elastic Continua written by Michael A Slawinski and published by World Scientific Publishing Company. This book was released on 2010-09-09 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present book — which is the second, and significantly extended, edition of the textbook originally published by Elsevier Science — emphasizes the interdependence of mathematical formulation and physical meaning in the description of seismic phenomena. Herein, we use aspects of continuum mechanics, wave theory and ray theory to explain phenomena resulting from the propagation of seismic waves.The book is divided into three main sections: Elastic Continua, Waves and Rays and Variational Formulation of Rays. There is also a fourth part, which consists of appendices.In Elastic Continua, we use continuum mechanics to describe the material through which seismic waves propagate, and to formulate a system of equations to study the behaviour of such a material. In Waves and Rays, we use these equations to identify the types of body waves propagating in elastic continua as well as to express their velocities and displacements in terms of the properties of these continua. To solve the equations of motion in anisotropic inhomogeneous continua, we invoke the concept of a ray. In Variational Formulation of Rays, we show that, in elastic continua, a ray is tantamount to a trajectory along which a seismic signal propagates in accordance with the variational principle of stationary traveltime. Consequently, many seismic problems in elastic continua can be conveniently formulated and solved using the calculus of variations. In the Appendices, we describe two mathematical concepts that are used in the book; namely, homogeneity of a function and Legendre's transformation. This section also contains a list of symbols.
Book Synopsis Parabolic Wave Equations with Applications by : Michael D. Collins
Download or read book Parabolic Wave Equations with Applications written by Michael D. Collins and published by Springer Nature. This book was released on 2019-11-04 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces parabolic wave equations, their key methods of numerical solution, and applications in seismology and ocean acoustics. The parabolic equation method provides an appealing combination of accuracy and efficiency for many nonseparable wave propagation problems in geophysics. While the parabolic equation method was pioneered in the 1940s by Leontovich and Fock who applied it to radio wave propagation in the atmosphere, it thrived in the 1970s due to its usefulness in seismology and ocean acoustics. The book covers progress made following the parabolic equation’s ascendancy in geophysics. It begins with the necessary preliminaries on the elliptic wave equation and its analysis from which the parabolic wave equation is derived and introduced. Subsequently, the authors demonstrate the use of rational approximation techniques, the Padé solution in particular, to find numerical solutions to the energy-conserving parabolic equation, three-dimensional parabolic equations, and horizontal wave equations. The rest of the book demonstrates applications to seismology, ocean acoustics, and beyond, with coverage of elastic waves, sloping interfaces and boundaries, acousto-gravity waves, and waves in poro-elastic media. Overall, it will be of use to students and researchers in wave propagation, ocean acoustics, geophysical sciences and more.
Book Synopsis Elastic wave propagation in transversely isotropic media by : R.C. Payton
Download or read book Elastic wave propagation in transversely isotropic media written by R.C. Payton and published by Springer Science & Business Media. This book was released on 1983-10-31 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this monograph I record those parts of the theory of transverse isotropic elastic wave propagation which lend themselves to an exact treatment, within the framework of linear theory. Emphasis is placed on transient wave motion problems in two- and three-dimensional unbounded and semibounded solids for which explicit results can be obtained, without resort to approximate methods of integration. The mathematical techniques used, many of which appear here in book form for the first time, will be of interest to applied mathematicians, engeneers and scientists whose specialty includes crystal acoustics, crystal optics, magnetogasdynamics, dislocation theory, seismology and fibre wound composites. My interest in the subject of anisotropic wave motion had its origin in the study of small deformations superposed on large deformations of elastic solids. By varying the initial stretch in a homogeneously deformed solid, it is possible to synthesize aniso tropic materials whose elastic parameters vary continuously. The range of the parameter variation is limited by stability considerations in the case of small deformations super posed on large deformation problems and (what is essentially the same thing) by the of hyperbolicity (solids whose parameters allow wave motion) for anisotropic notion solids. The full implication of hyperbolicity for anisotropic elastic solids has never been previously examined, and even now the constraints which it imposes on the elasticity constants have only been examined for the class of transversely isotropic (hexagonal crystals) materials.
Book Synopsis Wave Propagation and Inversion by : William Edward Fitzgibbon
Download or read book Wave Propagation and Inversion written by William Edward Fitzgibbon and published by SIAM. This book was released on 1992-01-01 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of three volumes on topics that arose from a September 1989 conference in Houston on mathematical and computational issues in geophysical fluid and solid mechanics. The nine papers include discussions of waves in partially saturated porous media, wave propagation by step marching, and optimal fi
