Free vibration of in-plane-aligned membranes of single-walled carbon nanotubes in the presence of in-plane-unidirectional magnetic fields

Abstract

Free in-plane and out-of-plane vibrations of two-dimensional magnetically affected ensembles of single-walled carbon nanotubes (MAESWCNTs) are of concern. Using Maxwell’s equations, nonlocal Rayleigh, Timoshenko, and higher-order beam theories, and Hamilton’s principle, the discrete equations of motion of both in-plane and out-of-plane vibrations for the proposed models are constructed. When the number of single-walled carbon nanotubes (SWCNTs) within the ensemble is large enough, evaluation of the frequencies of the nanostructure would not be an easy task. To overcome such a dilemma, some useful nonlocal continuous models are proposed. Through various numerical studies, the accuracy of such models is validated. The obtained results display that the in-plane and out-of-plane frequencies rely on the strength of the longitudinal magnetic field, small-scale parameter, number of SWCNTs with the ensemble, intertube distance, and the geometrical properties of the constitutive SWCNTs of the ensemble. The roles of these crucial factors in the fundamental frequencies of the MAESWCNTs are comprehensively examined via many numerical studies. The capabilities of the proposed nonlocal continuous models in predicting the bending frequencies are also discussed.