Effect of length and thickness variations on the vibration of SWCNTs based on Flügge's shell model

Abstract

This work aims to investigate the vibration of the zigzag and chiral single-wall carbon nanotubes (SWCNTs) based on Flugge shell theory considering the clamped-simply supported, clamped-free, clamped-clamped and simply supported-simply supported end conditions. After developing the governing equation of the objective system, the wave propagation approach is implemented for the purpose of obtaining the frequency equation in the eigen form for vibration of the considered system. In addition, the applicability of this model for the analysis of vibration of carbon nanotube is examined with the effect of length and ratio of height-to-radius. To generate the fundamental natural frequencies of SWCNTs, computer software MATLAB engaged. The numerical results are validated with existing open text. Since the percentage of error is negligible, the model has been concluded as valid.