Wave Propagation in Inhomogeneous Elastic Media with (N + l)-Dimensional Spherical Symmetry

1974 ◽  
Vol 52 (14) ◽  
pp. 1246-1252 ◽  
Author(s):  
D. L. Clements ◽  
C. Rogers
Keyword(s):  
Wave Equation ◽  
Elastic Solid ◽  
Initial Boundary ◽  
Spherically Symmetric ◽  
Initial Boundary Value Problems ◽  
Governing Equations ◽  
Elastic Parameters ◽  
Uniform Loading ◽  
Inhomogeneous Elastic Media ◽  
Initial Boundary Value

Uniform loading of an (N + 1)-dimensional spherically symmetric inhomogeneous elastic solid is investigated. The governing equations are represented in a matrix form and reduction to the conventional wave equation is sought. Such reduction may be achieved for multiparameter forms of a certain function involving the density and elastic parameters of the material. The reduction to the wave equation allows certain initial/boundary value problems to be readily solved.

Thermoelasticity with Second Sound: A Review

1986 ◽  
Vol 39 (3) ◽  
pp. 355-376 ◽  
Author(s):  
D. S. Chandrasekharaiah
Keyword(s):  
Heat Transport ◽  
Relevant Literature ◽  
Initial Boundary ◽  
Second Sound ◽  
Initial Boundary Value Problems ◽  
Governing Equations ◽  
The Past ◽  
Heat Transport Equation ◽  
Characteristic Features ◽  
Initial Boundary Value

Thermoelasticity theories predicting a finite speed for the propagation of thermal signals have come into existence during the past 20 years. In contrast to the conventional thermoelasticity theory, these nonclassical theories involve a hyperbolic-type heat transport equation, and are motivated by experiments exhibiting the actual occurrence of wave-type heat transport (second sound). Several authors have formulated these theories on different grounds, and a wide variety of problems revealing characteristic features of the theories has been investigated. This article presents a fairly self-contained bibliographical review of the relevant literature. Novelties involved in the formulations of the theories are emphasized, and concise derivations of the governing equations presented. Results concerned with solutions of initial-boundary value problems are summarized, and salient aspects of the theories illustrated. The list of references is exhaustive and up-to-date.

scholarly journals The pulsating orb: solving the wave equation outside a ball

2016 ◽  
Vol 472 (2189) ◽  
pp. 20160037 ◽  
Author(s):  
P. A. Martin
Keyword(s):  
Wave Equation ◽  
Laplace Transform ◽  
Continuum Mechanics ◽  
Weak Solutions ◽  
Acoustic Waves ◽  
Initial Boundary ◽  
Initial Boundary Value Problems ◽  
Compatibility Conditions ◽  
The Laplace Transform ◽  
Initial Boundary Value

Transient acoustic waves are generated by the oscillations of an object or are scattered by the object. This leads to initial-boundary value problems (IBVPs) for the wave equation. Basic properties of this equation are reviewed, with emphasis on characteristics, wavefronts and compatibility conditions. IBVPs are formulated and their properties reviewed, with emphasis on weak solutions and the constraints imposed by the underlying continuum mechanics. The use of the Laplace transform to treat the IBVPs is also reviewed, with emphasis on situations where the solution is discontinuous across wavefronts. All these notions are made explicit by solving simple IBVPs for a sphere in some detail.

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