Wave propagation in a functionally graded piezoelectric coating on a cylinder

In this paper, the wave propagation in a functionally graded piezoelectric coating on a cylinder is studied. Considering the piezoelectricity of the coating with an orthotropic symmetry, the wave equations and system matrices for state vector are obtained for SH and P-SV waves propagating along both the axial and circumferential directions. It is found that the wave propagation of the SH wave along the axial direction and the P-SV wave along the circumferential direction is not coupled to the electric field, i.e., their corresponding dispersion patterns are same as that for a functionally graded coating without piezoelectricity. However, the wave propagation of the P-SV wave along the axial direction and the SH wave along the circumferential direction is coupled to the electric field, i.e., their corresponding dispersion patterns depend on the applied electric field, their dispersion curves are different under the open or close electric boundary conditions.