On the propagation of plane waves in dissipative anisotropic media

Abstract

A theory for propagation of time-harmonic fields in dissipative anisotropic media is not a simple extension of the elastic theory. Firstly, one has to decide for an appropriate constitutive equation that reduces to Hooke’s law in the elastic limit. In this work, one relaxation function is assigned to the mean stress and three relaxation functions are assigned to the deviatoric stresses in order to model the quality factors along preferred directions. Secondly, in dissipative media there are two additional variables compared to elastic media: the magnitude of the attenuation vector and its angle with respect to the wave-number vector. When these vectors are colinear (homogeneous waves), phase velocity, slowness, and attenuation surfaces are simply derived from the complex velocity, although even in this case many of the elastic properties are lost. The wave fronts, defined by the energy velocities, are obtained from the energy balance equation. The attenuation factors are directly derived from the complex velocities, but the quality factors require the calculation of the potential and loss energy densities, yet resulting in a simple function of the complex velocities. [Work supported by EEC.]