Equipartition of energy for anisotropic elastic waves

Equipartition of Energy for Waves in Symmetric Space

Let X = G=K be an odd-dimensional semisimple Riemannian symmetric space of the noncompact type, and suppose that all Cartan subgroups of G are conjugate. Let u be a real-valued classical solution of the modiied wave equation u tt = ((+ k)u on R X, the Cauchy data of which are supported in a closed metric ball of radius a at time t = 0. Here t is the coordinate on R, is the (nonpositive deenite)...

Shear Waves Through Non Planar Interface Between Anisotropic Inhomogeneous and Visco-Elastic Half-Spaces

A problem of reflection and transmission of a plane shear wave incident at a corrugated interface between transversely isotropic inhomogeneous and visco-elastic half-spaces is investigated. Applying appropriate boundary conditions and using Rayleigh’s method of approximation expressions for reflection and transmission coefficients are obtained for the first and second order approximation of the...

Scattering of Longitudinal Elastic Waves From an Anisotropic Spherical Shell

On Group Velocity of Elastic Waves, in an Anisotropic Plate

The equivalence of the energy velocity and the group velocity is often taught in university physics. An early proof of the equivalence of the two velocities for one-dimensional water waves was given by Rayleigh [1]. In the 1950s and 1960s many studies [2}4] were done to show the equivalence of the two velocities for more general systems. Later, in the 1990s, Awati and Howes raised a question as...

Anisotropic transport and diffusion of elastic waves in random media

We discuss the influence of material anisotropy on the possible depolarization and diffusion of elastic waves in randomly heterogeneous media. Anisotropy is considered at two levels. The first one is related to the constitutive law of random materials, which may be handled by a random matrix theory for the elasticity tensor. The second level is related to the correlation structure of these rand...