On an axisymmetric boundary value problem for an elastic dielectric half-space

Abstract

Hankel transforms are used to construct a closed-form solution for the axisymmetric boundary value problem of a point charge forced normal to the surface of an isotropic elastic dielectric semi-space. Exact closed form expressions are obtained for the components of displacement and polarization vectors in terms of the Bessel functions and the fundamental solutions (1/R), (e−mR/R), R being the distance from the source point. The electric potential fields are determined both inside and outside the elastic dielectric semi-space. In the absence of electric polarization effects, the problem reduces to the classical axisymmetric Boussinesq problem of a point force applied normal to the surface of an isotropic elastic semi-space. The expressions of the components of displacements derived from this particular case are found to agree with known results.