Reflection and transmission of cylindrical sound wave through an elastic plate with an inhomogeneous coating

In paper the problem of harmonic cylindrical sound waves reflection and transmission through a homogeneous isotropic elastic plate with a continuously inhomogeneous in thickness elastic coating is considered. It is believed that the plate is placed in an infinite ideal fluid, the laws of heterogeneity of the coating material are described by continuous functions.
An analytical solution of the posed problem is obtained on the basis of the known solution of the problem about the passage of plane sound waves through plate with a continuously inhomogeneous coating and using integral representation of a cylindrical wave in the form of an expansion on flat waves.
Finding the displacement field in an inhomogeneous layer is reduced to solving boundary value problem for a system of ordinary differential equations of the second order.
The results of numerical calculations of frequency characteristics are presented for reflected and transmitted acoustic fields. Shown strong difference of frequency dependencies for different laws of inhomogeneity coating material.