Modal analysis of carbon nanotubes and nanocones using FEM

Modal analysis of single-walled carbon nanotubes (SWCNTs) and nanocones (SWCNCs) was performed using a finite element method (FEM) with ANSYS. The vibrational behaviors of fixed beam and cantilever SWCNTs with different section types of a circle and an ellipse were modeled using three-dimensional elastic beams of carbon bonds and point masses. Also, the vibrational behaviors of fixed beam and cantilever SWCNCs with different disclination angles of 120°, 180°, and 240° were modeled using the same method. The beam element natural frequencies were calculated by considering the mechanical characteristics of the covalent bonds between the carbon atoms in the hexagonal lattice. Each mass element of the carbon atoms was assigned as a point mass at the nodes of the FEM elements. The natural frequencies of zigzag and armchair SWCNTs and SWCNCs were also computed. There were some differences between the findings obtained in this study and the molecular structural mechanics data available in the literature. The natural frequencies of SWCNCs were estimated depending on the geometrical type and disclination angle with different boundary conditions. The natural frequencies of the SWCNCs with disclination angles of 120°, 180°, and 240° increased significantly at higher modes of vibration.