Linear dynamical stability in constrained thermoelasticity II. Deformation-entropy constraints

The theory of infinitesimal disturbances of a uniform reference configuration Be of a constrained heat-conducting elastic body, developed in part I, is adapted here to the situation in which the constraint links the deformation and the entropy. There are now only three modes of plane-harmonic-wave propagation and, in contrast to the findings of part I, they all turn out to be linearly stable under conditions of a conventional kind on the material constants in Be. An a priori case is thereby established for the acceptability in thermomechanics of this type of constraint. The properties of the modes are investigated in some detail and compared with the corresponding solutions in the absence of a constraint. A limiting procedure is formulated which yields, as extreme cases, the secular equations for the constrained and unconstrained bodies.