Reflection behavior of elastic waves in the functionally graded piezoelectric microstructures

The reflection behaviors of elastic waves in the functionally graded piezoelectric (FGP) microstructures are studied based on the modified couple stress theory. The extended Legendre orthogonal polynomial method (LOPM) is employed to obtain the analytical solutions of governing equations. The LOPM does not require delamination and calculation of the displacements of each partial wave. It is more suitable for solving FGP microstructure. The solutions of the incident P wave and SH wave with the consideration of open-circuit surface and short-circuit surface electrical boundaries are illustrated, respectively. The convergence of the polynomial series method is analyzed through numerical examples. The influences of the length scale parameters, gradient shapes and different electrical boundaries on the reflection behaviors are discussed. It is found that the couple stress can increase the propagation velocity of SH waves in the microstructures, and then reduce the critical angle of the total reflection of the incident SH wave.