Instability of sliding contact with coating on elastic substrate under friction and frictional heating

A nonstationary dynamic contact thermoelasticity problem on sliding with friction and frictional heating of the rigid half-elastic coating surface bonded to an elastic substrate made of another material is considered. The solution to the formulated initial boundary value problem is obtained in the form of contour integrals of the inverse Laplace transform. The investigation of the isolated singularities of the subintegral functions in the complex plane of the integration variable is carried out, and then the problem solution is constructed in the form of infinite series over the poles of integrands with the addition of the integrals over the banks of cut. Boundaries of the stable and unstable problem solutions are determined on its dimensionless parameter set. The influence of the compliance of the substrate on the instability boundary, and also on the development of temperature and pressure at the thermoelastic frictional sliding contact is investigated.