Wave stability for nearly-constrained materials in anisotropic generalized thermoelasticity

Abstract

En
In generalized thermoelasticity Fourier’s law of heat conduction in classical thermoleasticity is modified by introducing a relaxation time associated with the heat flux. Secular equations are derived for plane harmonic body waves propagating through anisotropic generalized thermoelastic materials subject to a thermomechanical near-constraint of an arbitrary nature connecting deformation with either temperature or entropy. The near-constraints are defined in such a way that as a certain parameter becomes infinite the constraint holds exactly.Therefore a nearly-constrained material is an unconstrained material. In an unconstrained material four stable thermoelastic waves may propagate in any direction but in a deformation temperature constrained material one of these becomes unstable. The nature of this instability is explored in the passage to the limit of the constraint holding exactly. On the other hand, in a deformation-entropy constrained material only three waves may propagate in any direction but all are stable. The passage to the constrained limit illustrates this. Expansions are given for the wave speeds in terms of the relaxation time, constraint parameter and frequency. The two types of constraint are certainly not equivalent and yet a connection is demonstrated between the two near-constraints.