Thermoelastic Instability in the Quasi-Static Coupled Thermoelasticity Problem Dealt with the Sliding Contact with Frictional Heating

A quasi-static coupled contact problem of thermoelasticity that deals with a sliding frictional contact with taking into account the frictional heating is considered. Exact solutions of the problem are constructed in the form of Laplace convolutions, after calculating which the solution has been written in form of infinite series over eigenvalues of problem. The study of these eigenvalues in relation to three dimensionless parameters of the problem is carried out. Based on the analysis of the solutions obtained, it is possible to distinguish the domains of stable and unstable solutions in the space of dimensionless parameters. The properties of the obtained solutions are studied in relation to the dimensional and dimensionless parameters of the problem. Within the framework of the main research problem, partial problems of monitoring the sliding parameters as well as problems of controlling contact parameters in order to avoid thermoelastic instability are formulated and solved.