Wave processes in an elastic half-plane impacted by a blunt-nosed rigid body

Abstract

The problem of unsteady deformation of an elastic half-plane is considered whose surface is impacted, at an initial instant, by a blunt-nosed rigid body, which generates diverging unsteady elastic waves and deforms the medium. The corresponding initial-boundary-value problem is formulated whose solution is constructed for the early stage of the interaction. The integral Laplace transform in the time variable and the integral Fourier transform in the one of the spatial variables are used. The solution of the problem is obtained in terms of the transforms and a formal solution is constructed in terms of the original functions. For a body with a fixed contact region, an analytical expression of the normal stress at an arbitrary point of the half-plane as a function of time is obtained. For a body shaped as an obtuse-angled wedge, analytical expressions of the normal stress and displacement at an arbitrary point at the symmetry axis of the problem are obtained. Calculations are performed and used to analyze the characteristic features of the wave processes in the medium as functions of time, the surface distance, and the mechanical properties of the material.