Dynamic analysis of piezoelectric materials with an elliptical hole under the action of shear horizontal waves

The dynamic mechanical properties of piezoelectric materials are of interest because of their brittle nature. Previous studies have mainly focused on cylindrical cavities or cracks. However, these are specific forms of elliptical cylindrical cavities. This study aims to develop a semi-analytical approach for analyzing the anti-plane dynamics of piezoelectric materials containing elliptical cavities by exploiting the geometrical generality of ellipses. The Helmholtz and Laplace equations were identified as governing equations by decoupling the displacement and electric potential functions. The wave function expansion method was employed to express the displacement and electric potential functions in the form of a Mathieu function series containing unknown coefficients in the elliptical coordinate system. The unknown coefficients were determined using the traction-free boundary and electric displacement continuous condition. Although the method of intercepting a finite-term series was used, the solutions are reliable because the wave function exhibits convergence. In addition, a parametric study was conducted. The results demonstrated the importance of using large axial ratios, small wave numbers, and large piezoelectric characteristic parameters in the dynamic analysis of piezoelectric materials with elliptical defects.