Free vibration analysis of viscoelastic nanotubes under longitudinal magnetic field based on nonlocal strain gradient Timoshenko beam model

In this paper, the free vibration of viscoelastic nanotube under longitudinal magnetic field is investigated. The governing equation is formulated by utilizing Timoshenko beam model and Kelvin-Voigt model based on the nonlocal strain gradient theory. The local adaptive differential quadrature method (LADQM) is applied in the analyzing procedure. We also investigated the influences of the nonlocal parameter, structural damping coefficient, material length scale parameter and the longitudinal magnetic field on the natural frequencies of the system. The results of this research may be helpful for understanding the potential applications of nanotubes in Nano-Electromechanical System.