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.

中文翻译：

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在Timoshenko系统上，同时在弯矩和剪切力上进行热耦合

Timoshenko系统是弹性梁振动的非常著名的模型，它是由作用在系统上的两个力（剪力和弯矩）的耦合给出的。在非等温情况下，即当模型受温度变化的影响时，我们考虑作用在整个系统上的热效应，也就是说，我们通过将热定律耦合到两个剪力上，提出了一个新的热弹性Timoshenko系统以及傅立叶定律下的弯矩 然后，我们证明了这种完全热弹性的系统在不假设相等波速的情况下也是指数稳定的，并且与任何边界条件无关。