Vibrational analysis of single-walled carbon nanotubes using beam element

Vibrational analysis of single-walled carbon nanotubes (SWCNTs) is performed using a finite element method (FEM). To this end, the vibrational behavior of bridge and cantilever SWCNTs with different side lengths and diameters is modeled by three-dimensional elastic beams and point masses. The beam element elastic properties are calculated by considering mechanical characteristics of the covalent bonds between the carbon atoms in the hexagonal lattice. The mass of each beam element is assumed as point masses at nodes coinciding with the carbon atoms. Implementing the atomistic simulation approach, the natural frequencies of zigzag and armchair SWCNTs are computed. It is observed that the findings are in good agreement with the molecular structural mechanics data available in the literature. Then, the computational results are adopted to develop a predictive equation to propose a quick tool for estimating natural frequencies of the SWCNTs with different boundary conditions and geometrical parameters.