On the Boundary Value Problems of Circular Loading for Transversely Isotropic Piezoelectric Half Space.

Abstract

This paper utilizes the potential function method to analyze the problem of circular uniform or linear variation of pressure and electric displacement on the surface of piezoelectric half space. The half space is taken as transversely isotropic piezoelectric, where the planes of isotropy are parallel to the free surface. Considering the variation of the boundary conditions, the solutions presented here actually comprise six different boundary value problems. The Green’s functions for a point normal force and charge are first used to obtain the potential functions in the form of double integrals. Using the Hankel transform, these integrals are eveluated by converting them into single infinite integrals containing product of the Bessel functions. It is shown that the integrals appearing in the potential functions have been previously evaluated in terms of complete elliptic integrals. Hence the potential functions and the electroelastic fields are presently written in terms of these integrals. Numerical results are presented to illustrate both qualitative and quantitative behavior of the induced electroelastic fields.