Green's functions for transversely isotropic piezoelectric multilayered half-spaces

Abstract

This paper presents Green's functions for transversely isotropic piezoelectric and layered half-spaces. The surface of the half-space can be under general boundary conditions and a point source (point-force/point-charge) can be applied to the layered structure at any location. The Green's functions are obtained in terms of two systems of vector functions, combined with the propagator-matrix method. The most noticeable feature is that the homogeneous solution and propagator matrix are independent of the choice of the system of vector functions, and can therefore be treated in a unified manner. Since the physical-domain Green's functions involve improper integrals of Bessel functions, an adaptive Gauss-quadrature approach is applied to accelerate the convergence of the numerical integral. Typical numerical examples are presented for four different half-space models, and for both the spring-like and general traction-free boundary conditions. While the four half-space models are used to illustrate the effect of material stacking sequence and anisotropy, the spring-like boundary condition is chosen to show the effect of the spring constant on the Green's function solutions. In particular, it is observed that, when the spring constant is relatively large, the response curve can be completely different to that when it is small or when it is equal to zero, with the latter corresponding to the traction-free boundary condition.