Dependence of the elastic band structure of a helical medium on thermal dilatation

Abstract

We consider an elastic helical medium formed by uniformly rotating a triclinic crystal around a given axis to constitute a helical medium giving rise to a material whose tensor stiffness rotates uniformly and varies along the helix axis. A detailed analysis of its elastic properties has been done previously. Here, we are concerned in analyzing the role of thermal coupling with heat ow through the dilatation tensor. Starting from a general dynamic description of the thermoelastic phenomena which takes into account the nite speed of propagation of thermal waves, we establish a set of equations for the strains, stresses, temperature and heat ow. These equations allow to calculate the band structure and the logarithmic ratio between longitudinal and transverse strains. We express our results for different values of the thermoelastic coupling and period of the helix which show remarkable modi cations when compared with the case in which no thermoelastic coupling is present.