Determination of the displacement field in an inhomogeneous coating of an elastic plate when passing through her plane sound wave

The article considers a boundary value problem for a system of linear second-order ordinary differential equations constructed for determining the displacement field in a continuously inhomogeneous elastic coating of the plate when a plane sound wave passes through.
It is believed that a homogeneous isotropic elastic plate with inhomogeneous in thickness elastic coating borders on ideal liquids.
An approximate analytical solution of the boundary value problem by the power series method is obtained. The boundary-value problem is reduced to problems with initial conditions. The solution of the boundary value problem is presented in the form of a linear combination of fundamental decisions. Found analytical solution boundary value problem is valid for a wide class of heterogeneity laws of the coating material.
The numerical calculations of the dependences of the components of the displacement vector at the boundaries of the coating from the angle of incidence of the plane wave are presented.