Axisymmetric vibration of SWCNTs in water with arbitrary chirality based on nonlocal anisotropic shell model

The axisymmetric vibration of three kinds of zigzag, armchair and chiral single-walled carbon nanotubes (SWCNTs) in water is studied in the paper based on the nonlocal anisotropic shell model. The present model is justified compared with the existing experimental observation and available data in literature. It is shown that for the tubes with the same diameter, the radial breathing frequencies from lower to upper limits are zigzag, chiral and armchair tubes, respectively. However, the difference in frequency diminishes with the increase of diameter. Furthermore, we found that the axisymmetric radial, longitudinal and torsional vibrational frequencies of SWCNTs are mainly sensitive to the values of radius and the scale coefficient, but cannot be substantially changed by their atomic structure. Moreover, we can get that the local shell model for CNT analysis would lead to an overprediction of the vibrational frequencies of almost all modes. So the nonlocal isotropic continuum models are practical in analyzing CNTs of large geometric sizes. Finally, the results show that the effects of fluid motion surrounding CNTs can be ignored for the large wave numbers.