Research of Natural Frequency of Single-walled Carbon Nanotube

The modied molecular structural mechanics method (MMSMM) is extended to analyze the dynamic characteristics of single-walled carbon nanotubes (SWCNTs). In MMSMM, the deformation potential of SWCNT is decomposed and it can be easily expressed as the function of the positions of carbon atoms in molecular mechanics, and so the sti?ness matrix of SWCNT can be obtained. The elemental mass matrix is a diagonal one, so the natural frequency and vibration mode of SWCNT can be calculated e?ectively. In this work, the form of cantilevered nanotubes is analyzed. The natural frequencies of SWCNT computed by this algorithm are discussed. The frequency dependence on the tube diameter and length of SWCNT is conˉrmed and, it is shown that when the diameter of tube is small the frequency can reach the the GHz level. The frequency results and the vibration modes are comparable with those of other researchers. Furthermore, a new FEM continuum-model is proposed to analyze the dynamic character of SWCNT to compare with these results by MMSMM.