Elliptic Boundary Layer in Shells of Revolution under Surface Shock Loading of Normal Type

In the present article, a method for solving a boundary value problem for an elliptical boundary layer occurring in thin-walled shells of revolution under normal-type impacts on the front surfaces is constructed. The elliptical boundary layer is constructed in the vicinity of a conditional front of Rayleigh surface waves and is described by elliptic equations with boundary conditions specified by hyperbolic equations. In the general case of shells of revolution, the methods for solving equations for an elliptical boundary layer developed for shells of revolution of zero Gaussian curvature cannot be used. The previously considered scheme for using the integral Laplace and Fourier transforms ceases to work since the resolving equations become equations with variable coefficients. The method for solving the equations of an elliptical boundary layer proposed in this paper is based on the use of an asymptotic representation of the images of the Laplace solution (in time) in exponential form. The paper presents a numerical calculation of the normal stress based on the obtained analytical solutions for the case of a spherical shell.