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 - Klecha, T. (Archives of Mechanics, 1996)
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.