Instabilities in dynamic anti-plane sliding of an elastic layer on a dissimilar elastic half-space

The stability of dynamic anti-plane sliding at an interface between an elastic layer and an elastic half-space with dissimilar elastic properties is studied. Friction at the interface is assumed to follow a rate- and state-dependent law, with a positive instantaneous dependence on slip velocity and a rate weakening behavior in the steady state. The perturbations are of the form exp(ikx+pt), where k is the wavenumber, x is the coordinate along the interface, p is the time response to the perturbation and t is time. The results of the stability analysis are shown in Figs. 1 and 2 with the velocity weakening parameter b/a=5, shear wave speed ratio c_s^'/c_s=1.2, shear modulus ratio μ^'/μ=1.2 and non-dimensional layer thickness H=100. The normalized instability growth rate and normalized phase velocity are plotted as a function of wavenumber. Fig.1 is for a non-dimensional unperturbed slip velocity ɛ=5 (rapid sliding) while Fig. 2 is for ɛ=0.05 (slow sliding). The results show the destabilization of interfacial waves. For slow sliding, destabilization of interfacial waves is still seen, indicating that the quasi-static approximation to slow sliding is not valid. This is in agreement with the result of Ranjith (Int. J. Solids and Struct., 2009, 46, 3086-3092) who predicted an instability of long-wavelength Love waves in slow sliding.