Diffraction of cylindrical sound waves by an elastic cylinder with an radially inhomogeneous coating

In article the problem of the diffraction of cylindrical monochromatic sound waves by an homogeneous elastic cylinder with a radially inhomogeneous elastic covering is considered. It is believed that the body is placed in an endless space filled with ideal fluid. The analytical solution of the problem is received.
Wave fields in a containing medium and homogeneous elastic cylinder are found in the form of expansions in wave cylindrical functions. The boundary-value problem for the system of ordinary second order differential equations is constructed for determination of the displacement field in inhomogeneous coating.
Numerical calculations of angular and frequency characteristics of the scattered field for elastic cylinders with homogeneous and inhomogeneous coatings are performed. Influence of continuously inhomogeneous elastic coatings on sound-reflecting properties of elastic cylindrical bodies are revealed.