Analysis of Solutions for Elliptic Boundary Layer in Cylindrical Shells at Edge Shock Loading

This paper is devoted to analysis of the asymptotic solution behaviour for the elliptic boundary layer in cylindrical shells in small vicinities of the surface Rayleigh wave front under normal edge shock loading. The boundary layer is described by the elliptic equations along the thickness of shells and the hyperbolic equations which are defined boundary conditions on the faces. These boundary conditions on cylindrical faces characterise wave motion on them. The sought for solution is presented by the composite ones. The first one is theparticular solution, satisfeing only the boundary conditions on the shell edge. The boundary value problem for the second one is reduced to the problem for shock loading on the faces of the infinite cylindrical shell. This one is solved with the help of the Laplace transform on time and the Fourier transform on the longitudinal coordinate. Invertiation of the Laplace and Fourier transforms allows us represent the solution on the base of elementary function arctg of the complicated arguments. Analysis of this solution in a small quasifront vicinity by the asymptotic method defined properties of them at moving from the quasifront along the longitudinal coordinate. Numerical calculations confirmed this quality analysis of the solution.