Contact problem of electroelasticity for a piecewise homogeneous piezoelectric plate with an elastic coating

The problem of determining the mechanical and electric fields in a piecewise homogeneous piezoelectric medium reinforced by a finite or semi-infinite coating is considered. Applying methods from the theory of analytic functions, the problem reduces to a singular integrodifferential equation with a fixed singularity. Using an integral transformation, a boundary value problem with shift (Riemann boundary value problem) is obtained, the solutions of which are represented in explicit form. On the basis of the solution obtained, an asymptotic study of contact stresses at end points (singular points) of the coating is performed.