Energy reflection and transmission characteristics of acoustic waves in a functionally graded piezoelectric plate immersed into non-viscous fluid

In this work, the reflection and transmission coefficients characteristics of plane waves in a functionally graded (FG) piezoelectric plate immersed in non-viscous liquid (water) are investigated using the stiffness matrix method (SMM). The general solutions of the displacement and the stress are expressed in terms of the eigenvalues and eigenvectors. These are derived from a system of first-order ordinary differential equations with variable coefficients of eight ranks. The SMM is employed to find the relation between the displacements and the tractions on the upper and lower interfaces of the multilayer. Subsequently, the reflection and transmission coefficients of a plane acoustic wave propagating in the FG piezoelectric plates are derived by computing the Poynting vector of each partial wave. The convergence of the SMM is studied through several numerical examples. The effects of the wave incident angle and the gradient coefficients of FG plate on the reflection/transmission characteristics and critical angle are discussed. It is found that the critical angle of incidence is strongly affected by the variation of the linear and the exponential gradient coefficient as well, the resonance frequency shifts to the lower frequency range with the increase of the gradient coefficient.