Transient waves in an inhomogeneous hollow infinite cylinder

Effects on transient waves of circumferential and radial inhomogeneity are studied in a plane-strain hollow cylinder. A periodic circumferential inhomogeneity modulating a constant value is analyzed adopting the Galerkin method where trial functions are chosen as the axisymmetric and asymmetric modes of the homogeneous cylinder. A periodic radial inhomogeneity is analyzed by dividing the cylinder into annular segments of constant width. A stepwise variation in modulus is assumed where modulus is constant over each segment. Adopting transfer matrices, continuity of state variables at interfaces of segments establishes the global dynamic equilibrium of the segmented cylinder. The static-dynamic superposition method is employed to solve for transient response.