Analyticity for Double Wall Carbon Nanotubes Modeled as Timoshenko Beams with Kelvin-Voigt and Intermediate Damping

Abstract

This manuscript studies a model of double-walled carbon nanotubes using two Timoshenko beams which are coupled by the Van der Walls force $(y-u)$. Kelvin-Voigt type dampings $(u_x-v{)}_{xt}$ and $(y_x-z{)}_{xt}$ and fractional dampings $(-{\partial }_{xx}{)}^{\alpha }{v}_t$ and $(-{\partial }_{xx}{)}^{\beta }{z}_t$ in both beams have been considered. We show that our proposed model is well established and that the semigroup associated is exponentially stable and analytical for any $(\alpha ,\beta )\in [0,1{]}^2$. As a consequence of this, a result on the analyticity of a Timoshenko System is obtained.

21 pages, 2 figures