On nonclassical behaviour of the temperature in coupled and dynamic thermoelasticity (Q1819969)

The problem of steady vibrations in the linear theory of the coupled thermoelastodynamics is considered. The behavior of the temperature in an isotropic slab, which occupies the region \(a\leq x\leq b\), is studied. The result is compared with the corresponding result within the theory of the heat conduction in rigid conductors. It is shown that for a rigid slab, when the temperature is trigonometric, the mean square temperature attains its global maximum at one of the end points \(x=a\) or \(x=b\). In the linear thermoelastodynamics, the author proves that if the temperature and the displacement are trigonometric, then the mean square temperature attains a local maximum at an endpoint. An example in which the mean square temperature fails to attain its global maximum at an endpoint is presented. This is an interesting paper.