Transient response in a one-dimensional model of thermoelastic contact

We consider two layers of different materials with the initial gap between them in the field of temperature with imperfect boundary conditions in Barber's sense. The model we discuss is that of two contacting rods (Barber and Zhang, 1988) which in the case of a single rod was devised and discussed by Dundurs and Comninou, (1976, 1979). In this paper we try to make a step further in the investigation of the essentially nonlinear problem. Though we consider a system of the linear equations of thermoelasticity the nonlinearity is induced by the boundary conditions dependent on the solution. We present an algorithm for solving the system of equations based on Laplace's transform technique. The method of solution can be used also in the dynamical problems with inertial terms taken into account. The numerical results have been obtained by a kind of computational simulation.