The contact problems of the excitation of harmonic oscillations by an oscillating rigid stamp on the thermoelastic layered pre-stressed body surface are considered. The body is represented by a layer lying on half-space. At the interface, two modes of mechanical boundary conditions are assumed: rigid adhesion and the absence of friction along one of the coordinates. In addition thermal contact condition is assumed. The initial deformed state is created due to thermal and mechanical effects. To find a solution of contact problems we introduced a boundary value problems with homogeneous boundary conditions on the surface. The Green function of auxiliary problems is constructed. Using operational calculus, the system of integral equations for the stress distribution function is reduced to a one-dimensional integral equation. Its solution is constructed by using the method of fictitious absorption. As an example, the contact problems on vibrations of a half-space of magnesium oxide coated with cadmium sulfide are considered. The solution to the contact problems, the distribution of vertical displacements over the entire surface of a thermoelastic prestressed body, is calculated and presented graphically. The influence of preheating and conditions at the interface is studied on the distribution of vertical stresses and displacements over the surface of a layered half-space. It is shown that under conditions of preheating and stretching of the layer in the direction of the horizontal coordinate under the action of a hard stamp on the surface the larger vertical stresses arise in the case of hard pinching of the coating with the base than with non-ideal adhesion. On the contrary, preheating and extension of the layer affect vertical displacements outside the contact area more when imperfect coupling.
THE OSCILLATIONS ON SURFACE OF THE PRE-STRESSED THERMOELASTIC LAYERED HALF-SPACE