Modeling the inhomogeneous anisotropic coating of an elastic cylinder that provides minimal sound reflection

The article deals with the mathematical modeling of an inhomogeneous anisotropic coating of the elastic cylinder, providing the least reflection upon diffraction of a harmonic cylindrical sound wave. It is assumed that the elastic cylinder is homogeneous and isotropic, the coating material is radially inhomogeneous and transversely isotropic, the laws inhomogeneities of the coating material are described by continuous functions, the body is placed in a boundless ideal fluid.
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.
Wave fields in a containing medium and a homogeneous isotropic cylinder are described by expansions in cylindrical wave functions. A boundary value problem is constructed for a system of ordinary differential equations of the second order for finding displacement fields in an inhomogeneous anisotropic layer.
An analytical solution of the inverse problem of the diffraction about the determination of the inhomogeneity laws of the coating material, ensuring the minimum sound scattering in the specified frequency range at a fixed angle of observation and also at a given observation sector at a fixed frequency is obtained. The functionals expressing the average intensity of sound scattering in given frequency range and angular sector of observation are built. Minimization of the functionals are implemented with the help of the burnout simulation algorithm.
The results of numerical calculations of frequency and angular dependencies of the intensity of the scatter acoustic field in the far zone at the optimal parabolic inhomogeneity laws are presented.