APPROXIMATED ANALYTICAL SOLUTION OF THE PROBLEM ABOUT AN ELECTRODE ON THE PIEZOELECTROELASTIC HALF-PLACE WITH PIEZOELECTROELASTIC FUNCTIONALLY GRADED COATING

The paper addresses to the plane contact problem on an electrode on the surface of a functionally graded piezoelectric coating glued with no friction with a homogeneous piezoelectric half-plane. The coating and the substrate are assumed to be transversely isotropic, the axis of isotropy coincides with the axis of polarization and normal to the surface of the coating. Arbitrary independent variation of the electroelastic properties of the coating in depth is considered. Plane electrode is placed on the surface of the coating and potential difference is applied which leads to an el ectroelastic deformation of the coating and substrate. Using the integral transformation technique, the problem is reduced to the solution of the dual integral equation. This equation is solved by the bilateral asymptotic method, based on an idea of using Pade approximation of the kernel transform of the integral equation. An approximated dual integral equation is solved in a closed analytical form. Approximated analytical expressions for electric induction and potential, vertical and horizontal displacements on the surface of the coating are constructed. These expressions are asymptotically exact both for big and small values of the relative coating thickness (relation of the coating thickness to electrode half-width).