Free vibration analysis of viscoelastic nanotubes under longitudinal magnetic field based on non-position strain gradient of Tymoshenko beam model

In this paper, the free vibration of viscoelastic nanotubes under longitudinal magnetic field is investigated. The governing equation is formulated using the Tymoshenko beam model and the Kelvin-Witt model based on the theory of nonlinear strain gradient. The local adaptive differential squaring (LADQM) method is used in the analysis procedure. Also, the effect of non-positional parameters, structural depreciation coefficient, material length scale parameter and longitudinal magnetic field on the natural frequencies of the system has been investigated. The results of this study may be useful in understanding the potential application of nanotubes in nano-electromechanical systems.