This work is based on a part of the plenary lecture I gave in the PCM-CMM-2019 conference in Krakow, Poland. It presents a new mathematical model for a thermoelastic 2D bar and proposes three problems for the processes of: (i) dynamic contact of the bar with an obstacle below it; (ii) vibrations of the right end between two stops; and (iii) debonding of two bars because of vibrations, humidity and thermal effects. The models are new and questions of existence of weak solutions, analysis of the solutions, effective numerical methods and simulations, as well as possible control, are unresolved yet.
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