Reflection and Transmission of Transverse waves at a corrugated interface of two functionally graded piezoelectric half-spaces

At the corrugated interface of two different functionally graded piezoelectric materials, reflection and transmission coefficients resulting from incident at the corrugated interface of plane transverse waves are considered. Both piezoelectric materials inhomogeneity is regarded as exponential. Analytically, the solutions are derived for half-spaces. The reflection coefficient and transmission coefficient for the first-order estimate of corrugation are calculated using Rayleigh’s approximation approach. Furthermore, for a specific kind of interface, the reflected coefficient and transmitted coefficient of regularly and irregularly reflected and transmitted waves are determined in closed form. For numerical interpretation of the results, a sets of piezoelectric materials such as PZT-5H ceramic and BaTiO 3 ceramic are considered. The reflection coefficient and transmission coefficient expressions show that they depend heavily on material coefficients with inhomogeneity characteristics, as well as the known wave propagation components, such as the corrugation’s wavelength, and amplitude of corrugation. Graphs representing the results were produced using Mathematica 7 to present the findings. The transmission coefficients and reflection coefficients are graphed versus the incidence angle.