Mechanical vibration of single-walled carbon nanotubes at different lengths and carbon nanobelts by modal analysis method

Abstract

In this paper, we analyzed the mechanical vibration of single-walled carbon nanotubes (SWCNTs) at different lengths and carbon nanobelts formed with beam elements. We found out that the natural frequency of bending mode of SWCNTs larger than nanotube aspect ratio 30, which represents the ratio of length-to-diameter, can be represented by Bernoulli-Euler beam theory, and the numerical simulation using modal analysis method is necessary to calculate the natural frequency of SWCNTs smaller than the aspect ratio 30 accurately. In particular, the vibrational amplitudes and the natural frequency of SWCNTs larger than nanotube aspect ratio 3 were analyzed by considering that the structural damping depends on length of SWCNTs under water conditions. Furthermore, SWCNTs and carbon nanobelts smaller than the aspect ratio 1 significantly increase the static modulus, and their first vibration mode also changes from bending mode to the radial mode. These results provide a suitable modeling method and mechanical vibrational characteristics of SWCNTs at different lengths.