Torsional vibration of the porous nanotube with an arbitrary cross-section based on couple stress theory under magnetic field

This article presented a solution for torsion vibration a nanotube made of pores material. Based on the porosity distribution, the material properties are assumed to vary according to a function along radius of nanotube. Moreover, the cross-section area of nanotube varied in the longitudinal direction by nonlinear function. As for the torque effect of the axial magnetic field, the well-known Maxwell's relation is used. Couple stress theory is employed to study the influence of small-scale on torsional vibration of nanotube. The Navier equation and boundary conditions of the size-dependent porous nanotube were derived by the Hamilton principle. These equations were solved by employing the generalized differential quadrature method. Comparison between the results of the present work with the other paper reveals the accuracy of this study. To the best of authors' knowledge, so far all previous torsional vibration of nanotube address the case of ignoring porosity. The novelty of this work is to present a solution by taking into account the existence of porosity. Finally, numerical results are presented to study the small scale effect and porosity on the frequency of the porous nanotube.