Asymptotic analysis of a dynamical system arising in thermoelastic contact

We consider a simple dynamical model for a discrete system of N metal pins in frictional thermoe lastic contact with a moving surface. In general, the model consists of N heat equations for the temperature in each pin, subject to non-smooth and non-local coupling through the conditions for contact between each pin and the moving surface. When the normalised coefficient of thermal expansion is sufficiently large, the model predicts large-amplitude oscillatory behaviour in qualitative agreement with experimental observations of thermoelastic in stability. We use perturbation methods to analyse the model and thus describe in detail the bifurcation behaviour of the system as the relevant physical parameters are varied.