Diffraction of a plane sound wave by an elastic sphere with an inhomogeneous transversal isotropic layer

In paper the problem of diffraction of a harmonic plane sound wave by a homogeneous isotropic elastic sphere with a continuously inhomogeneous anisotropic elastic layer is considered. It is believed that the body is placed in an infinite ideal fluid, the laws of heterogeneity of the coating material are described by continuous functions.
An analytical solution to the diffraction problem is obtained for the case when the material of the sphere layer is radially inhomogeneous and transversally isotropic.
Wave field in a containing medium and a homogeneous isotropic sphere are described by expansions in spherical 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 of sphere.
The results of numerical calculations of directional patterns for scattered acoustic field in the far zone are presented. It is shown that anisotropy of continuously inhomogeneous elastic layer one can substantially change the scattering characteristics of spherical bodies.