Analysis of the dynamic anti-plane response characteristics in a layered piezoelectric medium with an embedded circular lining

In this study the scattering behaviour of Shear Horizontal (SH) waves by a circular lining embedded within a layered piezoelectric material was comprehensively investigated. The methods including the wave function expansion approach, the repetitive superposition of the mirror-image technique, and the complex-variable function method were employed. The boundaries of the layered structure were assumed to satisfy stress-free and electrically insulating conditions. Based on the boundary conditions imposed on the circular lining, a system of definite-integral equations for the solution was constructed. And then the numerical computations were carried out to precisely determine the dynamic stress and electric-field strength of the piezoelectric material in the vicinity of the lining. The impacts of key parameters such as the incident wave number, the thickness of the lining, and the thickness of the layers on the lining were meticulously explored. The results revealed that upon the incidence of SH waves into the interior of the structure, the stress concentrations induced by the electromechanical coupling effect at the inner and outer boundaries of the lining exhibited opposite trends. Specifically, the dynamic stress concentration coefficient at the inner boundary of the lining was notably higher than that at the outer boundary, whereas the pattern of the electric-field-strength concentration coefficient was reversed. Moreover, under high-frequency wave incidence the stress variation of the defect region was found to be more sensitive. Significantly, it is demonstrated that the damage resulting from the electromechanical coupling effect can be effectively mitigated by appropriately adjusting the thickness of the lining and the thickness of the layers.