Stochastic SH Waves along a Frictional Interface

The reflection, refraction, and adsorption of a planar SH wave with stochastic time dependence at a frictionally bonded interface between elastic solids is considered. The incident stress wave is assumed to be a sample function from a zero-mean Gaussian random process with known power spectral density. Exact and approximate solutions are presented for the probability density functions of the transmitted and reflected stress waves and for the rate of slip at the interface. Results are also presented for the stationary and nonstationary mean-square values of these quantities, the mean energy flux partitioning between the various waves, and the mean rate of energy dissipation at the interface. It is shown that for small levels of incident stress, the interface behaves as though perfectly welded, but, for high levels, it behaves as though perfectly lubricated.