A nonlinear, nonstationary problem of frictional contact with inertia and heat generation taken into account

A problem of a thermo-elastic contact of a solid in the form of an elastic layer moving between two rigid walls is considered. The initial temperature is that of the natural state, however the forces of friction generate heat causing an increase in temperature and that of the layer volume due to the thermal linear expansion. In effect the gap between the walls and the moving layer decreases and consequently the motion slows down until the arrest. The arrested solid cools down, its dimensions decrease due to the heat exchange, the gap between the walls and the layer appears again, in the result the layer starts moving. We have taken into account the inertia forces and considered a dynamical model of thermo-elastic contact of the solids in relative motions.