Validation of the non-local elastic shell model for studying longitudinal waves in single-walled carbon nanotubes

This study deals with the dispersion of longitudinal waves in a single-walled armchair carbon nanotube, focusing on the effect of the microstructure of the carbon nanotube on the wave dispersion. To reveal the effect analytically, the carbon nanotube is modelled as a non-local elastic cylindrical shell in the study. The dynamic equation of the non-local elastic cylindrical shell is established and the corresponding dispersion relation of longitudinal waves is derived. These analytic results are verified via molecular dynamics simulations, based on the Terroff-Brenner potential, for the propagation of various longitudinal waves in three single-walled armchair carbon nanotubes. The molecular dynamics simulations indicate that the longitudinal wave dispersion predicted by the model of the non-local elastic cylindrical shell shows a good agreement with that of molecular dynamics simulations in a wide frequency range up to the terahertz region. They also show that both the microstructure of the carbon nanotube and the coupling between the longitudinal wave and the radial motion play an important role in the dispersion of longitudinal waves in a single-walled armchair carbon nanotube.