Spatial decay estimates of saint-venant type in generalized thermoelasticity

Abstract

Decay estimates of Saint-Venant type are established within the context of dynamic generalized thermoelasticity. A thermoelastic body is deformed under null body loads and initial conditions and subject to non-zero boundary data only on a plane end. The behaviour is studied for the total energy stored in that part of the body beyond a distance z from the basis. An estimate is established that describes the spatial decay of end effects. When the harmonically vibrations of a right cylinder are considered, it is shown that an exponential decay of activity holds away from the excited end provided that the exciting frequency is less than a certain critical frequency.