Dynamic stress concentrations of semi-elliptical surface notches in piezoelectric media: investigation under shear horizontal waves

Dynamic loading induces significant stress concentrations at surface notches, which are further exacerbated by piezoelectric effects. This study presents a novel semi-analytical approach to investigate the dynamic stress concentrations in semi-elliptical surface notches within piezoelectric media under the influence of shear horizontal (SH) waves. The mirror method is employed to impose traction-free and electrically insulating boundary conditions, effectively transforming the half-space problem into an equivalent full-space formulation. An elliptical coordinate system, integrated with Mathieu functions, is utilized to accurately model the semi-elliptical notch geometry. The potential function in the elliptic coordinate system is derived after decoupling, and boundary conditions are applied to establish an infinite set of linear algebraic equations. To ensure the accuracy of the solution, a truncation scheme based on the convergence properties of Mathieu functions is implemented prior to solving the system. A comprehensive parametric study is conducted based on numerical results, illustrating the sensitivity of scattered wave fields and dynamic stress concentrations to key parameters, including incident wave angle, applied wave frequency, notch depth, and piezoelectric material properties. The proposed model exhibits strong geometric generality, and the findings provide valuable theoretical insights for the design of piezoelectric components, as well as a benchmark for verifying approximate computational methods.