The study uses complex variable functions and conformal mapping to investigate the scattering and dynamic stress concentration phenomena of SH waves in non-circular opening magnetic–elastic materials. Elastic dynamics and piezomagnetic equations are employed to derive expressions for the scattered wave intensity and dynamic stress concentration coefficient around non-circular openings. Special attention is devoted to elliptical openings, where different incident angles and dimensionless wave numbers exhibit varying effects on the dynamic stress concentration coefficients. The numerical results indicate a positive correlation between the dynamic stress concentration coefficient and the illumination region of elliptical openings, with low wave numbers exerting a more significant influence. These findings provide a valuable theoretical foundation for studying fatigue mechanics in piezomagnetic materials. Therefore, to enhance the performance and reliability of piezomagnetic materials, it is imperative to conduct elastic dynamic analysis of non-circular defects in low-frequency environments.

The present study aims to investigate the transient response of stress concentration around a circular opening. The study focuses on the composition of the shockwave, which consists of SH waves of multiple frequencies. The wave equation, expressed by the displacement function, is transformed into the Helmholtz equation through the Fourier transform method. The spectral function can be obtained by employing analytic continuation and Fourier transform of the incident wave field. An analytical expression for the dynamic stress around the aperture can be derived using the wave function expansion method and by considering the boundary conditions. The influence of the aperture on the transient response is discussed based on the distribution of the dynamic stress concentration coefficient and stress peak coefficient under different aperture sizes. The results show that the peak of the dynamic stress concentration coefficient changes with the aperture. In contrast, the stress peak coefficient is primarily concentrated in the early stages of the transient response. Furthermore, it is observed that larger radii can induce alternating stress in the material, which may lead to fatigue failure. This strategy provides a solution for addressing similar challenges.

This paper presents a targeted study on the dynamic stress concentration (DSC) in piezoelectric materials induced by SH waves, focusing on the impact of elliptical openings. By using the elliptic cylindrical coordinate system and Mathieu functions, the wave fields are decomposed into functional series. Through the establishment of a set of infinite equations with mode coefficients based on the boundary conditions, the distribution of the dynamic stress concentration coefficient is visualized via numerical simulation. Furthermore, the impact of incident wave frequency, incident angle, and elliptic eccentricity on the stress concentration coefficient is analyzed. The results demonstrate a strong correlation between these parameters and the dynamic stress concentration coefficient. These findings hold significant implications for enhancing the strength and fatigue life of piezo-electric materials, as well as for selecting appropriate nondestructive testing methods.