Theoretical study of the dynamic response of a functionally graded hollow cylinder in a half space subjected to plane SH waves

An analytical solution is derived for the dynamic response of a functionally graded hollow cylinder in a half space under incident plane SH waves. The shear modulus and shear wave velocity of the functionally graded hollow cylinder are assumed to have a power-law variation with respect to radius. Based on the wave function expansion method and the image technique, the wave fields with unknown coefficients in the hollow cylinder and the half space are constructed in corresponding polar coordinates. After expressing the scattered wave fields induced by the hollow cylinder and its mirror in one coordinate system by the Graf's addition formula, the coefficients of the wave fields for both regions are obtained by taking advantage of the displacement and traction boundary conditions. Through a systemic parametric analysis, the effect of the inhomogeneity exponent and the boundary distance on the dynamic stress concentration factor of the functionally graded hollow cylinder is illustrated.