Well-posedness and stability result for carbon nanotubes Timoshenko beams with second sound

Abstract

This article presents a comprehensive study of the well-posedness and stability results for double-wall carbon nanotubes (DWCNTs) modeled as Timoshenko beams, incorporating the thermoelasticity of the second sound type and frictional damping. We establish the well-posedness of the system using the semigroup technique. Additionally, we demonstrate that the combined effects of thermal dissipation, governed by Cattaneo's law, and frictional damping lead to exponential stability of the system without imposing any restrictions on the system's parameters. The stability result is demonstrated using the multiplier method. Our result is novel and significantly improves existing results in the literature regarding the stability of DWCNTs.