Strain energy density of a circular cavity buried in a semi-infinite slab of functionally graded materials subjected to anti-plane shear waves

The paper presents a theoretical method to investigate the multiple scattering of shear waves and strain energy density in a semi-infinite slab of functionally graded materials with a circular cavity. The analytical solutions of wave fields 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 condition of the semi-infinite structure. The analytical solution of the problem is derived, and the numerical solutions of the strain energy density factors around the cavity are also graphically presented. The effects of the distances between the cavity and the boundaries of the semi-infinite slab, the wave number and the non-homogeneous parameter of materials on strain energy density factors are analyzed. Analyses show that the strain energy density around the cavity increases with increasing non-homogeneous parameter of materials and incident wave number. The boundaries of the semi-infinite slab have great effect on both the maximum strain energy density and the distribution around the circular cavity, and the effect increases with increasing incident wave number. When the distance between the semi-infinite boundary and the cavity varies, the effect of the upper and lower boundaries on the distribution of the strain energy density factors around the cavity is also examined.