Dynamic stress from a subsurface cavity in a semi-infinite functionally graded piezoelectric/piezomagnetic material

Abstract In this paper, an analytical method is applied to investigate the multiple scattering of anti-plane shear waves and dynamic stress around a subsurface cavity in a semi-infinite functionally graded piezoelectric/piezomagnetic composite. The analytical solutions of wave field, electric field and magnetic field are expressed by employing wave function expansion method and the expanded mode coefficients are determined by satisfying the boundary conditions of the cavity. Image method is used to satisfy the free boundary conditions of the semi-infinite structure. According to the analytical expressions of this problem, the numerical solutions of the dynamic stress concentration factor around the cavity are presented. The effects of the piezoelectric and piezomagnetic properties, the buried depth of the cavity, the incident wave number and the nonhomogeneous parameter of materials on the dynamic stress around the cavity are graphically illustrated. Analyses show that the piezoelectric and piezomagnetic properties have great effect on the dynamic stress in the region of intermediate frequency and the effect increases with increasing nonhomogeneous parameter. The effects of the nonhomogeneous parameter of materials on the dynamic stress and electric field are examined. Comparisons with other existing models are also presented.