On a Timoshenko system with thermal coupling on both the bending moment and the shear force

Abstract

The Timoshenko system is a very well-known model for vibrations of elastic beams, which is given by the coupling of two forces acting on the system: the shear force and the bending moment. In the non-isothermal case, that is, when the model is subject to the temperature variation, we consider the thermal effect acting on the whole system, that is, we propose a new thermoelastic Timoshenko system by coupling thermal laws on both the shear force and the bending moment under the Fourier’s law. Then, we show that such a fully thermoelastic system is exponentially stable without assuming equal wave speeds and also independent of any boundary conditions.