Love wave in an isotropic homogeneous elastic half-space with a functionally graded cap layer

The dispersion characteristics of Love wave in an isotropic homogeneous half-space covered with a functionally graded layer is investigated. Governing equations for the anti-plane shear wave in the graded layer are derived, and analytical solutions for the displacement and stress field in the layer are given. Moreover, the general dispersion relations of Love wave in both the half-space and the layer are analyzed. For the layer with shear modulus and mass density varying in a parabolic form, the dispersion equations are solved in terms of iteration method. The obtained dispersion curves reveal that there exists a cut-off frequency in the lowest order vibration mode.