Surface stress waves in a nonhomogeneous elastic half-space Part II. Existence of surface waves for an arbitrary variation of Poisson's ratio Approximate solution based on perturbation methods

Abstract

Two approaches to the solution of the nonlinear eigenvalue problem of propagation of surface waves in a nonhomogeneous isotropic elastic half-space are considered. In Sec. 1 the nonlinear eigenvalue problem is transformed to the equivalent integral equation, and the method of solving this equation is proposed. In Sec. 2 Friedrich's perturbation theory [6] is used to solve an eigenvalue problem describing the surface stress waves in a "weakly" nonhomogeneous isotropic elastic half-space. Two cases are discussed in detail: a) a half-space with a "weak" variation of density, b) a half-space with a "weak" variation of the shear modulus. In both cases an asymptotic solution is obtained and numerical results are given.