A dynamic contact problem for a thermoelastic prestressed layer

A dynamic problem concerning the harmonic vibrations of a rigid punch on the surface of a prestressed thermoelastic layer is considered. Outside the contact area, the surface is free from mechanical stresses and thermally insulated. In its natural state, the layer material is a material of class 6 mm hexagonal syngony with an axis of symmetry perpendicular to the surface of the medium and the initial stress state is assumed to be homogeneous. The problem is reduced to an integral matrix equation, a method of solving it is proposed and the effect of the initial stresses and preheating on the dispersion characteristics of the problem is studied. A mixed problem on the vibrations of the layer under the action of a given thermal load on the surface of the medium that simulates the action of a frequency-modulated laser beam is considered as an example. The effect of the initial stresses and preheating on the heat flux distribution in the reaction region is investigated.