Natural Frequencies of Bending Vibrations of Carbon Nanotubes

Using a molecular-dynamics model with a reduced number of degrees of freedom, the natural frequencies of bending vibrations of carbon nanotubes (CNTs) of various diameters are calculated under plane strain conditions. It is shown that the theory of thin cylindrical shells provides high accuracy in estimating the frequencies of low-amplitude natural vibrations even for relatively small CNT diameters. It is shown that, with an increase in amplitude, the frequency of natural vibrations decreases, which is consistent with the data available in the literature. The results obtained are necessary for the design of terahertz resonators based on CNTs and high-precision mass and force nanosensors based on the effect of electromechanical coupling that CNTs exhibit.