Analysis of vibration properties of single-walled carbon nanotubes with finite element method

The nature frequencies versus the change of the geometry of the cantilever SWCNTs were investigated with the finite element method. A molecular structure model of SWCNTs was built with carbon-carbon (C-C) covalent bonds simulated by the equivalent beam elements and carbon atoms equivalent to mass points. A mass scale factor β is introduced to eliminate the numerical error. The results show that the chiral angle has no obvious effect on the nature frequency of SWCNTs with the same aspect ratio and similar diameter. The natural frequency of the SWCNTs with the same diameter decreases with the increase of the length; while the fundamental frequency changes little with the increase of length when it is long enough (Aspect ratio > 10). The first four order frequencies increase with the increase of diameter and the fifth order frequency doesn't change with the diameter; while the trend is not regular for higher order nature frequencies of SWCNTs with the same length when the diameter increases. The length has a greater impact on nature frequency than the diameter does in the lower order modes.