Displacements of the surface of a piezoelectric half-space with functionally-graded coating and circle electrode on the surface

A mathematical model describing the deformation of a material caused by reverse piezoelectric effect is proposed. The based on an axisymmetric problem electroelasticity for half-space with functionally-graded coating. An electric potential difference applied across circle area surface (an electrode whose thickness and elastic properties are neglected) infinity boundary half-space. Arbitrary independent variation all electroelastic in depth coating considered. assumed to be perfectly bonded substrate. solved using bilateral asymptotic method approximated analytical form effective any value relative Approximated expressions containing finite quadratures obtained distribution radial normal displacements under outside it. Numerical calculations provided two typical examples coatings wide range values Convergence results those homogeneous non-coated small large thickness. Special attention paid comparison redistribution electromechanical characteristics presence most noticeably observed near especially thin intermediate (in size electrode).