The Green's functions for an infinite piezoelectric strip with line sources at the surfaces

Abstract

A series of the Green's functions describing 2D electro-elastic fields excited in an arbitrary infinite piezoelectric strip by the different combinations of line sources at the surfaces are derived. Four types of sources are considered: a line of forces applied to a free surface, a step of displacements on a clamped surface, a line of electric charge or a line of electric potential discontinuity on a surface. In the absence of electrical sources at the surface the latter is supposed to be adjoined to an isotropic dielectric medium with an arbitrary permittivity. The Green's functions are expressed in terms of eigenvectors and eigenvalues of the generalized Stroh problem in the form of convergent Fourier integrals. These integrals are taken for the particular cases when, due to the symmetry of the material of the strip, the eigenvalues of the 8 × 8 Stroh matrix are purely imaginary. The results of integration are presented as sums of residues at the poles determined by some equations. Finding the roots of these equations needs additional computing.