Wave Motion


Book Description

Waves are a ubiquitous and important feature of the physical world, and throughout history it has been a major challenge to understand them. They can propagate on the surfaces of solids and of fluids; chemical waves control the beating of your heart; traffic jams move in waves down lanes crowded with vehicles. This introduction to the mathematics of wave phenomena is aimed at advanced undergraduate courses on waves for mathematicians, physicists or engineers. Some more advanced material on both linear and nonlinear waves is also included, thus making the book suitable for beginning graduate courses. The authors assume some familiarity with partial differential equations, integral transforms and asymptotic expansions as well as an acquaintance with fluid mechanics, elasticity and electromagnetism. The context and physics that underlie the mathematics is clearly explained at the beginning of each chapter. Worked examples and exercises are supplied throughout, with solutions available to teachers.




Wave Motion in Elastic Solids


Book Description

Self-contained coverage of topics ranging from elementary theory of waves and vibrations in strings to three-dimensional theory of waves in thick plates. Over 100 problems.




Wave Propagation


Book Description

An engineering-oriented introduction to wave propagation by an award-winning MIT professor, with highly accessible expositions and mathematical details—many classical but others not heretofore published. A wave is a traveling disturbance or oscillation—intentional or unintentional—that usually transfers energy without a net displacement of the medium in which the energy travels. Wave propagation is any of the means by which a wave travels. This book offers an engineering-oriented introduction to wave propagation that focuses on wave propagation in one-dimensional models that are anchored by the classical wave equation. The text is written in a style that is highly accessible to undergraduates, featuring extended and repetitive expositions and displaying and explaining mathematical and physical details—many classical but others not heretofore published. The formulations are devised to provide analytical foundations for studying more advanced topics of wave propagation. After a precalculus summary of rudimentary wave propagation and an introduction of the classical wave equation, the book presents solutions for the models of systems that are dimensionally infinite, semi-infinite, and finite. Chapters typically begin with a vignette based on some aspect of wave propagation, drawing on a diverse range of topics. The book provides more than two hundred end-of-chapter problems (supplying answers to most problems requiring a numerical result or brief analytical expression). Appendixes cover equations of motion for strings, rods, and circular shafts; shear beams; and electric transmission lines.




Waves


Book Description




Stability and Wave Motion in Porous Media


Book Description

This book describes several tractable theories for fluid flow in porous media. The important mathematical quations about structural stability and spatial decay are address. Thermal convection and stability of other flows in porous media are covered. A chapter is devoted to the problem of stability of flow in a fluid overlying a porous layer. Nonlinear wave motion in porous media is analysed. In particular, waves in an elastic body with voids are investigated while acoustic waves in porous media are also analysed in some detail. A chapter is enclosed on efficient numerical methods for solving eigenvalue problems which occur in stability problems for flows in porous media. Brian Straughan is a professor at the Department of Mathemactical Sciences at Durham University, United Kingdom.




Wave Motion in Earthquake Engineering


Book Description

This volume features invited contributions from researchers whose work has recently been the focus of attention in journals and at conferences.




Introduction to Wave Propagation in Nonlinear Fluids and Solids


Book Description

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.




Wave Fields in Real Media


Book Description

Authored by the internationally renowned José M. Carcione, Wave Fields in Real Media: Wave Propagation in Anisotropic, Anelastic, Porous and Electromagnetic Media examines the differences between an ideal and a real description of wave propagation, starting with the introduction of relevant stress-strain relations. The combination of this relation and the equations of momentum conservation lead to the equation of motion. The differential formulation is written in terms of memory variables, and Biot's theory is used to describe wave propagation in porous media. For each rheology, a plane-wave analysis is performed in order to understand the physics of wave propagation. This book contains a review of the main direct numerical methods for solving the equation of motion in the time and space domains. The emphasis is on geophysical applications for seismic exploration, but researchers in the fields of earthquake seismology, rock acoustics, and material science - including many branches of acoustics of fluids and solids - may also find this text useful. New to this edition: This new edition presents the fundamentals of wave propagation in Anisotropic, Anelastic, Porous Media while also incorporating the latest research from the past 7 years, including that of the author. The author presents all the equations and concepts necessary to understand the physics of wave propagation. These equations form the basis for modeling and inversion of seismic and electromagnetic data. Additionally, demonstrations are given, so the book can be used to teach post-graduate courses. Addition of new and revised content is approximately 30%. Examines the fundamentals of wave propagation in anisotropic, anelastic and porous media Presents all equations and concepts necessary to understand the physics of wave propagation, with examples Emphasizes geophysics, particularly, seismic exploration for hydrocarbon reservoirs, which is essential for exploration and production of oil




Wave Propagation in Structures


Book Description

This book introduces spectral analysis as a means of investigating wave propagation and transient oscillations in structures. After developing the foundations of spectral analysis and the fast Fourier transform algorithm, the book provides a thorough treatment of waves in rods, beams, and plates, and introduces a novel matrix method for analysing complex structures as a collection of waveguides. The presentation includes an introduction to higher-order structural theories, the results of many experimental studies, practical applications, and source-code listings for many programs. An extensive bibliography provides an entry to the research literature. Intended as a textbook for graduate students of aerospace or mechanical engineering, the book will also be of interest to practising engineers in these and related disciplines.




Wave Propagation in Electromagnetic Media


Book Description

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.




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