Section: New Results

Travelling waves in a spring-block chain sliding down a slope

Participants : Guillaume James, Jose Eduardo Morales Morales, Arnaud Tonnelier.

In this work we study the dynamics of an infinite chain of identical blocks sliding on a slope under the effet of gravity. Each block is coupled to its nearest neighbour through linear springs and is subjected to a nonlinear friction force. For a piecewise-linear spinodal friction law, a closed-form expression of front waves is derived. Pulse waves are obtained as the matching of two travelling fronts with identical wave speeds. Explicit formulas are obtained for the wavespeed and the wave form in the anti-continuum limit. The link with propagating phenomena in the Burridge-Knopoff model is briefly discussed. These results have been reported in [44].