Dynamic potentials and Green's functions of a quasi-plane piezoelectric medium with inclusion

The dynamic potentials of a two-dimensional (2D) quasi-plane piezoelectric infinite medium of transversely isotropic symmetry containing an inclusion of arbitrary shape is derived in terms of scalar solutions of the 2D Laplace and Helmholtz equations. Closed-form expressions for the space-frequency representation of this dynamic potential are obtained for the case when the spatial source distribution is characterized by a region occupied by a circular inclusion embedded in a quasi-plane transversely isotropic matrix. The results are used to solve the dynamic Eshelby problem of a circular inclusion (plane region with the same material characteristics as the matrix) undergoing uniform eigenstrain and eigenelectric field. In contrast to the static case, the dynamic electroelastic fields inside the circular inclusion are non-uniform in the space-frequency representation. The derived dynamic piezoelectric potentials are basic quantities for the description of the dynamic properties of micro-inhomogeneous quasi-plane piezoelectric material systems (e.g. fibre-reinforced piezocomposites).