Scattering of a plane sound waves by an elastic cylinder with an non-uniform coating situated near to a flat surface

In article the problem of the scattering of an obliquely incident plane monochromatic sound wave by an elastic cylinder with a radially non-uniform elastic coating in presence of a flat surface (absolutely rigid and acoustically soft) is considered. The analytical solution of the problem by the method of imaginary sources using addition theorems for cylindrical wave functions 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 fields in inhomogeneous coatings.
Numerical calculations of frequency and angular characteristics of the scattered field for elastic homogeneous cylinders with and without coating located near the underlying plane are performed. Influence of continuously inhomogeneous elastic coatings on sound-reflecting properties of elastic cylindrical bodies are revealed.