Rayleigh surface waves in functionally graded materials — long-wave limit

A first-order asymptotic model for describing waves propagating along the surface of a functionally graded isotropic elastic half-space is constructed in the long-wave limit under the assumption of a finitely supported perturbation of the half-space properties. Explicit approximations for the Rayleigh waves are derived under the assumption that the semi-infinite elastic medium is slightly inhomogeneous