On the Harmonic Vibrations in Linear Thermoelasticity Without Energy Dissipation

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 and thermal displacement on the lateral boundary. The motion is induced by a harmonic time–dependent displacement and thermal displacement specified pointwise over the base. We establish some spatial estimates for an appropriate cross–sectional measure associated with the amplitude of the corresponding harmonic vibration in the high frequency range that describe how the amplitude evolves with respect to the axial distance to the excited base. In fact, in the high frequency range we establish certain algebraical estimates that predict decay or growth slower than that for the low frequency range