A correspondence for acceleration waves in elastic non-conductors

Abstract

It is shown that Truesdell's theorem on the existence of waves in an inhomogeneous elastic material can be readily carried over to the case of an elastic non-conductor of heat, provided that the isentropic elasticity tensor is strongly elliptic. That is, there is at least one direction in which one longitudinal wave and two transverse waves with orthogonal amplitudes may exist and propagate. Further, if one considers a situation for which the waves are necessarily plane, then one finds that the amplitudes of these waves depend on the mechanical properties of the material alone, independent of its thermal properties. In other words, one would not be able to ascertain the effects of the thermal properties of the material on the behaviour of these waves.