The non-uniform motion of a thin smooth rigid wedge into an elastic half-plane

A two-dimensional problem of non-uniform motion by a smooth, thin, symmetric rigid wedge into the surface of an elastic half-plane is analyzed. Both the wedge starting on the surface and from an embedded position are considered. Based on the integral transforms for a more general imposed displacement, the half-plane surface and wedge path behavior yields explicit information on the various component waves appearing in the solution. Logarithmic singularities are found at the wedge apex for subsonic speeds.