The impact of a thermoelastic rod against a rigid heated barrier

The impact of a thermoelastic rod with a heat-insulated lateral surface against a rigid heated barrier is considered. The heat exchange between the rod and the wall occurs at one of its ends contacting with the wall, while the other end is heat-insulated and free from external forces. The behaviour of the rod during the impact process is described by the Green-Naghdy theory which allows one to take finite speed of heat propagation into account, neglecting therewith thermal relaxation. The Laplace integral transform with the subsequent expansion of the found images in terms of the natural functions of the problem is used as a method of solution, which is found in explicit exact closed form. The analytical time-dependence of displacements, stresses, and temperature at each rod particle is obtained. The emphasis is on the analysis of the contact stress, the temperature of the colliding bodies during their contact interaction, and on the detection of the duration of contact of the rod with the rigid wall. It is shown that the contact time essentially depends on the relationship between the mechanical and thermal values.