Love-type wave fields due to the effect of traction-free and rigid boundary surfaces on the piezoelectric-dispersive layer

Abstract

This paper investigates a quantitative comparison of the Love wave propagation due to traction-free and rigid boundary surfaces on the piezoelectric-dispersive layer over a non-dispersive initially stressed half-space. The model is considered (a) transversely isotropic piezoelectric material in the upper layer, (b) exponentially increasing dispersive (non-homogeneous) layer in the intermediate, and (c) initially stressed non-dispersive (homogeneous) medium in the lower half-space. Electrical potential fields in the piezoelectric layer are defined in terms of electrical potential function with open and short circuit piezoelectricity using the quasi-static Maxwell’s equation. We have derived analytical dispersion relations for two cases of boundary conditions: (i) free surface with zero tractions and (ii) rigid boundary, in both the open and short circuit cases. The validities of the dispersion relations are shown by deriving some particular cases and compared with the classical dispersion relation of the Love wave. A novel numerical representation of changes in displacement amplitude with depth and comparative effect of various piezoelectric materials such as PZT-4, PZT-5A, PZT-7A, and BaTiO₃ are shown using MATLAB software. The rigid boundary surface case is more effective than traction-free boundary surfaces in terms of electromechanical coupling factor. It is also identified that there are significant effects on the dispersion of the Love-type waves due to different boundary conditions on the upper surface of the model. These comparative studies highlight the present work and may be helpful in the fields of solid mechanics and material fabrication processes.