Reflection and transmission of plane elastic waves at the boundary between piezoelectric materials and water

Reflection and transmission coefficients for plane elastic waves obliquely incident on the boundary between two isotropic materials have been known for some time. The solution for anisotropic materials, however, has not been fully treated in the literature. Here we derive these coefficients for the case of a piezoelectric ceramic in contact with water. This problem is of significant practical interest, since in a variety of applications, piezoelectric ceramics, which are inherently anisotropic, are used as transducers to radiate acoustic energy into water. Due to the anisotropy, velocities of both compressional and shear waves are functions of the angle of incidence. Piezoelectric equations are solved to find the variations of compressional and shear wave velocities with the angle of incidence. Reflection and transmission coefficients are then obtained and numerical results are presented for four piezoelectric ceramics.