Constitutive thermal laws and the exact solutions of Timoshenko systems

Abstract

We consider a Timoshenko-type thermoelastic beam model that is defined by a system of partial differential equations, coupled with several thermal laws of heat conduction. Namely, we consider laws that characterize the dynamics of the system where any loss of energy is due to thermal effects in the absence of mechanical dissipation. Fourier law, as a consequence of parabolicity, describes an infinite propagation speed of thermal signals. We find that it possesses advantages over Cattaneo and Green–Naghdi Type III thermal law. This advantage can be seen from symmetry classifications of the optimal system of one-dimensional subalgebras. We show that Fourier law leads to a greater number of exact solutions when compared to any other thermal law studied. Finally, the evolution of the exact solutions is graphically presented.