Analysis of elastic wave propagation in a hollow cylinder with two-dimensional (2D) functionally graded material (FGM) and the curved outer surface under internal moving shock loading is the subject of this study. In the proposed method, there is no restriction on the distribution of material properties, the shape of the outer surface, and the applied shock loading. They are treated with non-uniform rational B-spline (NURBS). The isogeometric approach is developed for solving the problem to ensure precise modeling of the geometry. Also, the Newmark approach is used for full discretization of the isogeometric equations. The distributions of all elastic field quantities are determined for two types of material distributions and shock loadings. The effects of shock loadings, the shape of the outer surface, and the material distribution on the elastic wave are thoroughly examined. Propagation, reflections, and propagation speed inside the hollow cylinder are investigated. It is found that the propagation speeds of elastic waves have a distribution associated with the distribution of the material properties. Also, the shape of the outer surface can affect the amplitude of the elastic wave and the locations of concentration stress. It is concluded that the sonic boom phenomenon occurs in the solids as well as in the air.
In-plane elastic wave propagation and band-gaps in layered functionally graded phononic crystals
