Vibrational analysis of carbon nanotubes and graphene sheets using molecular structural mechanics approach

In this article, the vibrational properties of two kinds of single-layered graphene sheets and single-wall carbon nanotubes (SWCNT) are studied. The simulations are carried out for two types of zigzag carbon nanotubes (6,0), (12,0), armchair carbon nanotubes (4,4), (6,6) and zigzag and armchair graphene sheets with free-fixed and fixed–fixed end conditions.Fundamental frequency is determined by means of molecular structural mechanics approach. In this approach, carbon nanotubes (CNTs) and grapheme sheets are considered as space frames. By constructing equality between strain energies of each element in structural mechanics and potential energies of each bond, equivalent space frames can be achieved. Carbon atoms are considered as concentrated masses placed in beam joints (bond junctions).Results are presented as diagrams stating fundamental frequencies of nanotubes and graphene sheets with respect to aspect ratios. The results indicate that fundamental frequency decreases as aspect ratio increases. So it is preferred to use nanotubes and graphene sheets with lower aspect ratios for dynamic applications in order to prevent resonance and dynamic damage. Fundamental frequency of nanotubes is larger than that of graphene sheets. The results are in good agreement with results of previous researches.