Transient scattering of a piezoelectric wave from a crack

Abstract

The problem of the scattering of transient antiplane shear electroelastic waves from a crack in a piezoelectric medium possessing 6-mm symmetry is solved by determining the electric dipole density induced on the crack by the incident wave. An integral equation satisfied by the Laplace-transformed dipole distribution is derived by appealing to the piezoelectric reciprocity relation. The solution of the integral equation is accomplished by expanding the dipole distribution in a series of first-order spline functions with unknown coefficients and then applying the method of moments to transform the problem to a vector-matrix one, which is readily handled by a computer. Inversion back into the time domain is effected by an efficient numerical method of inverting Laplace transforms. Results are given for the cases of normal and oblique incidence of the wave onto the crack.