Inhomogeneous Waves In Solids And Fluids

The book may be viewed as an introduction to time-harmonic waves in dissipative bodies, notably viscoelastic solids and fluids. The inhomogeneity of the waves, which is due to the fact that planes of constant phase are not parallel to planes of constant amplitude, is shown to be strictly related to the dissipativity of the medium. A preliminary analysis is performed on the propagation of inhomogeneous waves in unbounded media and of reflection and refraction at plane interfaces. Then emphasis is given to those features that are of significance for applications. In essence, they regard surface waves, scattering by (curved) obstacles, wave propagation in layered heterogeneous media, and ray methods. The pertinent mathematical techniques are discussed so as to make the book reasonably self-contained. Contents:Inhomogeneous WavesModelling of Dissipative MediaInhomogeneous Waves in Unbounded MediaReflection and RefractionSurface WavesWave Propagation in Multilayered MediaScattering by ObstaclesPerturbation Methods in Heterogeneous MediaRay Method for Heterogeneous Dissipative Media Readership: Graduate students in mechanics, mathematical physics, applied mathematics, engineers, mathematicians, physicists and geologists. keywords:Inhomogenous Waves;Reflection and Refraction;Surface Waves;Scattering;Ray Method;Waves in Multilayers;Waves in Heterogeneous Media“The book offers a well planned, systematic development of the theory of propagation of inhomogeneous waves in dissipative and prestressed media. The importance of thermodynamic conditions to the propagation characteristics has been emphasized. Readers will find a wealth of information on advanced research materials in the book due to its inclusions of many applications from various applied disciplines e.g., seismology, NDE, and ocean acoustics.”Mathematics Abstracts “…. timely and useful. Indeed, as far as I know, this is the first book on inhomogeneous plane waves in solids and fluids.”Mathematical Reviews

The book may be viewed as an introduction to time-harmonic waves in dissipative bodies, notably viscoelastic solids and fluids. The inhomogeneity of the waves, which is due to the fact that planes of constant phase are not parallel to planes of constant amplitude, is shown to be strictly related to the dissipativity of the medium. A preliminary analysis is performed on the propagation of inhomogeneous waves in unbounded media and of reflection and refraction at plane interfaces. Then emphasis is given to those features that are of significance for applications. In essence, they regard surface waves, scattering by (curved) obstacles, wave propagation in layered heterogeneous media, and ray methods. The pertinent mathematical techniques are discussed so as to make the book reasonably self-contained.

The content of the volume is constituted by four articles. The first concerns the theory of propagation of plane waves in elastic media. The second treats theoretically the linear, weakly non-linear, and non-linear stability of flows of a viscous incompressible fluid in a diverging channel. The third lecture investigates the mathematical properties of the equations governing the motion of a viscous incompressible second-grade fluid, such as existence, uniqueness of classical solutions and stability of steady-state flows. The last lecture provides some basic results on wave propagation in continuum models. The objective of this book is to emphasize and to compare the various aspects of interest which include the necessary mathematical background, constitutive theories for material of differential type, polarized and shock waves, and second sound in solids at low temperatures.

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.

Unabridged Ph.D. Thesis with thesis defense photos and presentation at the end.

This volume presents an up-to-date overview of some of the most important topics in waves and stability in continuous media. The topics are: Discontinuity and Shock Waves; Linear and Non-Linear Stability in Fluid Dynamics; Kinetic Theories and Comparison with Continuum Models; Propagation and Non-Equilibrium Thermodynamics; and Numerical Applications.

Elastic Wave Propagation in Structures and Materials initiates with a brief introduction to wave propagation, different wave equations, integral transforms including fundamentals of Fourier Transform, Wavelet Transform, Laplace Transform and their numerical implementation. Concept of spectral analysis and procedure to compute the wave parameters, wave propagation in 1-D isotropic waveguides, wave dispersion in 2-D waveguides is explained. Wave propagation in different media such as laminated composites, functionally graded structures, granular soils including non-local elasticity models is addressed. The entire book is written in modular form and analysis is performed in frequency domain. Features: Brings out idea of wave dispersion and its utility in the dynamic responses. Introduces concepts as Negative Group Speeds, Einstein’s Causality and escape frequencies using solid mathematical framework. Discusses the propagation of waves in materials such as laminated composites and functionally graded materials. Proposes spectral finite element as analysis tool for wave propagation. Each concept/chapter supported by homework problems and MATLAB/FORTRAN codes. This book aims at Senior Undergraduates and Advanced Graduates in all streams of engineering especially Mechanical and Aerospace Engineering.

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