Analytical solutions of surface acoustic wave propagation in functionally graded plates with the homotopy analysis method

Since the governing equations of the propagation of elastic waves in functionally graded materials (FGMs) are differential equations with variable coefficients, it is difficult to solve them with existing analytical methods. In the present paper, the homotopy analysis method is used to study the propagation of surface acoustic waves in FGM plates. The numerical results confirm early conclusions that the selection of hardening or softening of materials in the thickness direction will cause the reduction or increase of deformation on the surface, which is an phenomena worth to explore for practical engineering practices which generally prefers the change of thickness rather than material properties. While the importance of FGM in many structural and functional applications has been recognized, analytical solutions to guide the precise selection and applications have to be provided by solving the seemingly unsolvable equations.