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.