Evolution of solutions for dipolar bodies in Thermoelasticity without energy dissipation

Abstract

The aim of our paper is the study of the spatial evolution of vibrations in the context of Thermoelasticity without energy dissipation for dipolar bodies. Once we get an a priori estimate for the amplitude of the vibration, which are assumed being harmonic in time, it is possible to predict some spatial decay or growth properties for the amplitude, provided the frequency of vibration is greater than a certain critical value.

Harmonic vibrations in thermoelastic dynamics with double porosity structure

“…In this paper a double porous thermoelastic material with a boundary final value problem, such that the final data are assigned at the moment t = 0, is considered. This study represents a continuation of the work of M Marin who studied the spatial evolution of the amplitude in the context of thermoelasticity without energy dissipation for dipolar and micropolar bodies [25,26].…”

“…Some spatial decay estimates were obtained by Flavin et al [22,23] for a right cylindrical body where the base is subjected to an excitation which is harmonic in time. The spatial behaviour of the harmonic in time vibrations in classical linear thermoelasticity has been studied by Chirita in [24]; the spatial evolution of vibrations in the context of thermoelasticity without energy dissipation for dipolar bodies has been studied by Marin and Abbas in [25]; and the evolution of the amplitude in the case of the harmonic vibrations of micropolar bodies has been studied by Marin and Baleanu in [26]. Spatial behaviour in thermoelastodynamics with a double porosity structure from the point of view of the impossibility of time localization of solutions and of a Phragmén-Lindelöf alternative for a semi-infinite cylinder was studied by Florea [27].…”