Vibrational analysis of armchair phosphorene nanotubes by a DFT-based finite element model

A finite element model based upon the density functional theory is developed to investigate the vibrational characteristics of armchair phosphorene nanotubes. To this end, the PP bonds are simulated by beam elements whose elastic properties are obtained from the analogy of molecular and structural mechanics. The effects of nanotube length, diameter and boundary conditions on the frequencies of armchair phosphorene nanotubes are evaluated. It is shown that the effect of nanotube radius on its natural frequency is weakened by increasing the nanotube aspect ratio. Comparing the first ten frequencies of armchair phosphorene nanotubes with different diameters, it is observed that the effect of diameter on the vibrational behavior of phosphorene nanotubes is more pronounced at higher modes.