The Normal Impact of an Elastic Rod-Mass System on a Viscoelastic Half Space

The normal impact of a one-dimensional elastic rod, with a lumped mass on the trailing end, onto a viscoelastic half space is considered and the problem is solved for the time dependent interface stress and displacement. The problem is reduced to an integral equation, whose two-part kernel consists of solutions of two simpler problems. One part pertains to the half space only and the other is for the rod-mass system. The half-space portion of the kernel is obtained through a numerical inversion of the Laplace transformed solution. Given the half-space kernel contribution, which depends only on the two viscoelastic parameters and Poisson’s ratio, the integral equation is solved numerically for two families of half space materials. The viscoelastic effects on the half space are quite pronounced. Certain combinations of the parameters cause a large hysteresis in the impact, and softer half spaces require longer contact times before the rod leaves the surface.