The elastic motion of a transversely isotropic, piezoelectric solid caused by impulsive loading

Abstract.

Based on a monograph by Payton on the wave propagation in transversely isotropic media, some new results for piezoelectric solids are presented here. The dynamic Green's tensors for the displacement fields along the symmetry axis for two- and three-dimensions concerning some piezoelectric solids of the crystal class 6mm are discussed. The central result of this paper is to show that the set of differential equations for linear, quasi-electrostatic piezoelectricity is, when eliminating e.g. the electric potential in a transformed domain, quasi-hyperbolic in the sense defined by Gal'pern. Only when specific constraints are attended, one obtains a hyperbolic operator, guaranteeing the well-posedness and solvability of the Cauchy problem.