Dynamic Eshelby Inclusion Problem in a Quasiplane Transversely Isotropic Piezoelectric Medium

10.30009/CJM.200303.0003

Thomas M. Michelitsch；Hua-Jian Gao

Piezoelectric quasiplane medium ； Dynamic inclusion problem ； Dynamic Green's function ； Dynamic potential function

The Chinese Journal of Mechanics

19卷1期（2003 / 03 / 01）

113 - 118

英文

We study the dynamic response of a piezoelectric medium with transversely isotropic symmetry containing a time harmonic source distribution characterized by a continuous fiber parallel to the axis of symmetry with circular cross section. Due to its symmetry the problem is equivalent to a two-dimensional space problem with circular inclusion (quasiplane problem). The solution is derived in closed form in terms of scalar solutions of 2D Laplace and Helmholtz equations. The considered problem is the dynamic variant of the piezoelectric analogue of Eshelby-inclusion problem. The inclusion (fiber) undergoes time-harmonic uniform eigenstrain and eigenelectric field. In contrast to the static case [1], the dynamic electroelastic fields inside the inclusion are non-uniform in the space frequency representation. The derived dynamic potential function is a basic quantity for the description of the dynamic properties of micro-inhomogeneous quasiplane piezoelectric material systems (e.g., fiber reinforced piezocomposites)..