A Finite Element Approach for the Vibration of Single-Walled Carbon Nanotubes

Abstract

We worked on vibrational aspects of zigzag single wall nanotubes using the finite element simulation. We modeled the nanotube and graphene sheet as 3D frame structures using beam elements. The natural frequencies of vibration and their vibration modes are obtained. The simulations are done for the zigzag nanotubes (8,0). The first five natural frequencies are obtained for aspect ratios in the range of 4 to 20. The results show that the natural frequencies decrease as the aspect ratios increase. The results also indicate similar trends with results of previous studies for CNTs using universal force field potential. We also present frequencies of nanotube versus aspect ratio of SWNT in two boundary conditions (clamped–clamped and clamped-free), and compare it with solutions taken from MD, local shell model and nonlocal shell model which still remains the same trends and are close enough.