Separation of the Stress Equations of Motion in Nonhomogeneous Isotropic Elastic Media

Abstract

Tensorial equations of motion are considered in order to attack the problem of the separation of the stress equations of motion in nonhomogeneous isotropic elastic media. We confine ourselves to the plane equations in a medium whose elastic coefficients and density are arbitrary functions of a single Cartesian coordinate. It is shown that the stresses are expressible in terms of a single function satisfying a fourth-order ordinary differential equation. The solution obtained may be useful in studying surface waves in nonhomogeneous media.