19. Elliptic Boundary Layer in Shells of Revolution Under Normal Edge Shock Loading

The present paper is aimed to construction the asymptotic theory of the elliptic boundary layer in shells of revolution under normal edge shock loading. Asymptotic equations of this boundary layer are derived in the small vicinity of the surface Rayleigh wave front. First of all the problem for normal edge shock loading is reduced to the problem for surface shock loading by constructing the particular solution, satisfying only the boundary conditions on the shell edge. Asymptotic solution of the governing equations for addition problem is obtained by using the Lourye symbolic approach and the front asymptotic near the surface Rayleigh wave front. The symbolic solution allows us to derive governing equations of the boundary layer. The behaviour of this boundary layer along the thickness is defined by elliptic equations and the boundary conditions on the faces are defined by hyperbolic equations, characterized wave motion on these faces. Considered component together with early constructed ones allows describe solution for transient waves in all parts of the phase plane.