Solution of the problem of thermoelasticity about sliding frictional contact of a rigid halfplane with the surface of an elastic coating, when lower boundary of the latter is perfectly bonded to a rigid foundation and the thermal flux generated by friction is directed to the coating, is cosntructed using the Laplace integral transform and is obtained in form of contour integrals. After investigation and determination of poles of integrands in a complex plane and calculation of contour quadratures, temperature, displacements and stresses distributions are obtained in the form of infinite series over eigenfunctions. Development of instability of obtained solutions for any sliding speed of the half-plane over the surface of the coating.

Keywords: thermoelastodynamic instability, sliding frictional contact, coating, sliding friction, dynamics, thermoelasticity, poles, mathematical modeling, parametric study, instability analysis