Vibrational analysis of an irregular single-walled carbon nanotube incorporating initial stress effects

In this work, an attempt is done to apply the eigenvalue approach as well as Donnell thin-shell theory to find out the vibrational analyses of an irregular single-walled carbon (ISWCNT) incorporating initial stress effects. The effects of surface irregularity and initial stresses on natural frequency of vibration of nano materials, especially for single-walled carbon nanotubes (SWCNTs), have not been investigated before, and most of the previous research have been carried for a regular and initial stress-free CNTs. Therefore, it must be emphasized that the vibrations of prestressed irregular SWCNT are novel and applicable for the design of nano oscillators and nanodevices, in which SWCNTs act as the most prevalent nanocomposite structural element. The surface irregularity is assumed in the parabolic form at the surface of SWCNT. A novel equation of motion and frequency equation is derived. The obtained numerical results provide a better representation of the vibration behavior of prestressed ISWCNTs. It has been observed that the presence of either surface irregularity or initial stress has notable effects on the natural frequency of vibration, particularly in the short-length SWCNTs. Numerical results show that the natural frequency of SWCNT decreases with increase in surface irregularity and initial stress parameters. To the authors’ best knowledge, the effect of surface irregularity and initial stresses on the vibration behavior of SWCNTs has not yet been studied, and the present work is an attempt to find out this effectiveness. In addition, the results of the present analysis may serve as useful references for the application and the design of nano oscillators and nanodevices, in which SWCNTs act as the most prevalent nanocomposite structural element