On vibrations in thermoelasticity without energy dissipation for micropolar bodies

Abstract

We consider a micropolar thermoelastic body occupying a prismatic cylinder that is free of loads on lateral surface (no body force, no body couple, and no heat supply). On the base of the cylinder are prescribed a time-dependent displacement, a microrotation, and a thermal displacement, which are harmonic in time, and collaborate to induce the motion of the considered body. With the help of a measure associated with the corresponding steady-state vibration and by assuming that the exciting frequency is lower than a certain critical frequency, we will obtain a spatial decay estimate.