On Some Non-Standard Problems in Linear Thermoelasticity

Abstract

In the present paper we consider a prismatic cylinder occupied by an anisotropic homogeneous compressible linear thermoelastic material that is subject to zero body force and heat supply and zero displacement-temperature variation on the lateral boundary. The motion is induced by a time-dependent displacement-temperature variation specified pointwise over the base. The motion is constrained such that the displacement-temperature variation and velocity at points in the cylinder and at a prescribed time are in given proportions to, but not identical with, their respective initial values. It is shown that certain integrals of the solution spatially evolve with respect to the axial variable. Conditions are derived that show the integrals exhibit alternative behavior and in particular for the semi-infinite cylinder that there is either at least exponential growth or at most exponential decay, provided the elasticity tensor is positive definite or satisfies a strong ellipticity condition.