The scattering of acoustic waves by a cylinder with a non-uniform elastic coating

The problem of the scattering of a plane acoustic wave by a solid cylinder with a radially non-uniform elastic coating is considered. An analytical expression describing the scattered acoustic field is obtained. The equations of motion of the non-uniform elastic cylindrical layer are reduced to a system of ordinary differential equations, the boundary-value problem for which is solved by the power-series method. The results of calculations of the directional pattern of the scattered field are presented.