Comparison between two different analytical solutions and a horizontal shear wave propagating in a functionally graded piezoelectric-layered structure

We study the horizontal shear (SH) wave problem propagating in a functionally graded piezoelectric material (FGPM) layered structure to compare the Wentzel-Kramers-Brillouin (WKB) method with the power series method. We establish coupled governing equations on the basis of elastodynamics theory. Both the WKB and power series methods are employed to solve the second-order variation coefficient equations. The dispersive curves of the SH wave in an FGPM layered structure are illustrated. Different modes, including the surface damage model and artificial FGPM model, are considered. Analytical and numerical results show that the artificial FGPM model can be solved by both the WKB and power series methods, whereas the surface damage model can be solved by the power series technique only. The WKB method can obtain only several points and not the complete curves in the surface damage model.