The frequency of cantilevered double-wall carbon nanotube resonators as a function of outer wall length

Analysis of vibrational characteristics of cantilevered double-walled carbon nanotube (DWCNT) resonators is carried out based on classical molecular dynamics simulation. Vibrational frequencies of DWCNTs are less than those of single-walled carbon nanotubes (SWCNTs) with the same length and the same diameter because of van der Waals intertube interaction. For DWCNTs with short outer walls, the resonance frequency initially increases with increasing outer nanotube length and then decreases after a peak, and thus the result can be modeled by a Gaussian distribution. The frequency of DWCNT resonators with short outer walls is a maximum when the length of the outer wall is about 72.5% of the length of the inner wall.