  We consider the response of a one-dimensional system with friction. S.W. Shaw
(Journal of Sound and Vibration, 1986) introduced the set up of different
coefficients for the static and dynamic phases (also called stick and slip
phases). He constructs a step by step solution, corresponding to an harmonic
forcing. In this paper, we show that the theory of variational inequalities
provides an elegant and synthetic approach to obtain the existence and
uniqueness of the solution, avoiding the step by step construction. We then
apply the theory to a real structure with real data and show that the model is
quite accurate. In our case, the forcing motion comes from dilatation, due to
temperature.
