Love waves in a graded half-space with a homogeneous layer

The dispersion problem of Love waves is investigated in a functionally graded half-space covered with an isotropic homogeneous layer. In the functionally graded half-space, the governing equation of the antiplane shear wave is solved, the analytical solutions of displacement and stress are obtained, and the corresponding general form of Love wave dispersion equation is deduced. Two cases of the functionally graded materials with exponentially and paraboliclly varying shearing modulus and mass density along the depth are evaluated, and the dispersion curves are presented. It shows that the cut-off frequency arises in the dispersion curve of the lowest order vibration model. This work can provide theoretical basis for functionally graded materials optimization design, performance evaluation, nondestructive testing, and inverse problem analysis.