Double-wall carbon nanotubes model with nonlinear localized damping: Asymptotic stability

Abstract

We consider the one-dimensional equations for the double-wall carbon nanotubes modeled by coupled Timoshenko elastic beam system with nonlinear arbitrary localized damping. We prove that the damping placed on an arbitrary small support, unquantized at the origin, leads to uniform decay rates (asymptotic in time) for the energy function. This study generalizes and improves previous literature outcomes.