Spatial Evolution in Linear Thermoelasticity

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 elasticity tensor is strongly elliptic and the conductivity tensor is positive. The motion is induced by a harmonic time-dependent displacement-temperature variation specified pointwise over the base. We establish some spatial estimates for appropriate cross-sectional measures associated with the amplitude of the corresponding harmonic vibrations that describe how the amplitude evolves with respect to the axial distance to the excited base. In fact, in the low frequency range we establish some exponential estimates describing the spatial evolution of the amplitude of vibration which confirms the observations made by Boley in related contexts.