Scattering of a plane sound wave by elastic a cylinder with an inhomogeneous anisotropic coating in the presence of a plane

In the article the direct and inverse problems of scattering of a harmonic plane sound wave by a homogeneous isotropic cylinder with inhomogeneous anisotropic elastic coating in the presence of the underlying flat surface are considered. It is assumed that the coating material of cylinder is radially inhomogeneous and transverse-isotropic, the inhomogeneity laws of the coating material described by continuous radial coordinate functions, the body is placed in an ideal fluid, underlying surface is perfect (absolutely hard or acoustically soft).
An analytical solution of the direct diffraction problem is obtained. The scattered acoustic field and wave fields in the cylinder and its coating are defined.
Based on the solution of the direct problem a mathematical modeling of an inhomogeneous anisotropic coating of a elastic cylinder providing the least sound reflection done.
The inhomogeneity laws of the coating material ensuring the minimum sound scattering in the given frequency range at a fixed angle of observation and also in the given angular sector of observation at a fixed frequency are obtained. The functionals expressing the average intensity of sound scattering are built. Minimization of the functionals are implemented with the help of the burnout simulation algorithm.
The results of numerical calculations of frequency dependencies of intensity of the scatter acoustic field at the optimal parabolic inhomogeneity laws are presented for different types of transverse-isotropic coatings.