A mathematical model of torsional vibrations of SWCNTs incorporating surface irregularity effects

The aim of the present work is to investigate the surface irregularity effects on torsional vibrations of single-walled carbon nanotubes (SWCNTs). Equation of motion and corresponding closed form solutions were derived based Hamilton's model. The equations of motion are solved analytically and the influence of surface irregularity on the natural frequency of torsional vibrations of SWCNTs is studied in detail. Numerical caculations were performed for chiral graphene SWCNT of (12, 6) and the results of torsional vibrations were discussed and presented graphically. The obtained numerical results reveal that, the surface irregularity has notable effects on the natural frequency of torsional vibrations of SWCNTs. The impacts of surface irregularities on the natural frequency of nano materials, especially for the natural frequancies of torsional vibration of SWCNTs, have not been studied and most of previous studied were carried out for regular carbon nanotubes. In this sense, the present study is novel, and it is expected that the results obtained will be useful in the design and analysis of the torsional vibration of carbon nanotubes (CNTs) and nanostructures.