Normal point force and point electric charge in a piezoelectric transversely isotropic functionally graded half-space

Abstract

Normal point force and point electric charge acting on surface of a transversely isotropic piezoelectric half-space with a functionally graded transversely isotropic piezoelectric coating are considered. Elastic moduli, piezoelectric constants and dielectric permeabilities of the coating vary with depth according to arbitrary functions. Analytical expressions for the elastic displacements and potential of the electrostatic field are derived for a fixed value of the depth coordinate. Asymptotical analysis of these formulas is derived for small and big values of a radial coordinate. An equilibrium of the half-space under the action of axisymmetric mechanical (normal and tangential) and electric loading is studied and a scheme of reducing the solutions of mixed boundary value problems to integral equations is obtained. As an illustration of the obtained solution, the PZT-5H piezoceramics with typical examples of functionally graded and homogeneous coatings are considered. The results include computations of the profiles of displacements and electric potential for different types of variation of electro-elastic properties in the coating.