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 thermoelastic contact with a moving surface. In general, the model consists of $N$ heat equations for the temperature in each pin, subject to nonsmooth and nonlocal coupling through the conditions for contact between each pin and the moving surface. When the normalized coefficient of thermal expansion is sufficiently large, the model predicts large-amplitude oscillatory behavior in qualitative agreement with experimental observations of thermoelastic instability. We use perturbation methods to analyze the model and thus describe in detail the bifurcation behavior of the system as the relevant physical parameters are varied.