Thermal Effect on Elastic Waves of Anisotropic Saturated Porous Solid

S H Guo

doi:10.1155/2011/179467

Abstract

The motion equations of anisotropic media, coupled to the mass conservation and thermoequilibrium equations of fluid, are studied here based on the standard space of physical presentation for thermoelastic dynamics of anisotropic saturated porous solids. By introducing a new compressible thermo-elastic model, a set of uncoupled equations of elastic waves are deduced. The results show that the elastic waves and speeds of elastic waves are affected by both anisotropic subspaces of solids and thermal and compressive coupling coefficients between fluid and solid. Based on these laws, we discuss the propagation behaviour of elastic waves for various anisotropic solids.

Highlights

A general theory of three-dimensional propagation of elastic waves in a fluid-saturated porous solid was presented by Biot [1,2,3]
A new theory of elastic waves in a fluid-saturated porous solid subjected to thermal effects is given, in which the idea of standard spaces [6,7,8,9,10,11,12,13] is used to deal with the motion equation, thermoequilibrium equation, and the mass conservation equation
The classical Newton’s equation of motion, thermoequilibrium equation, and the mass conservation equation under the geometric presentation can be transformed into the eigen ones under the physical presentation

Summary

Introduction

A general theory of three-dimensional propagation of elastic waves in a fluid-saturated porous solid was presented by Biot [1,2,3]. A new theory of elastic waves in a fluid-saturated porous solid subjected to thermal effects is given, in which the idea of standard spaces [6,7,8,9,10,11,12,13] is used to deal with the motion equation, thermoequilibrium equation, and the mass conservation equation. By this method, the classical Newton’s equation of motion, thermoequilibrium equation, and the mass conservation equation under the geometric presentation can be transformed into the eigen ones under the physical presentation. By introducing a new compressible thermoelastic model, a set of uncoupled modal equations of elastic waves are obtained, each of which shows the existence of elastic subwaves; the propagation speed, propagation direction and space pattern of these subwaves can be completely determined by the modal equations

Constitutive Equations of Anisotropic Porous Media

Application

Conclusion