Dispersion relation for transverse waves in pre-stressed irregular single-walled carbon nanotubes

This article studies the dispersion relation of transverse waves in an initially stresses single-walled carbon nanotube (SWCNT) with surface irregularity using Flugge shell theory. Taking into account the effects of surface irregularity and initial stresses, propagation of transverse waves is studied and dispersion curves are plotted for optical transverse waves in several figures. The effects of surface irregularity and initial stresses are confirmed by comparing obtained numerical results with those in cases of uniform and initial stress-free SWCNT. Obtained results turn out that, the increase of irregularity parameter increases the phase velocity of transverse waves, while the increase of the initial stress parameter decreases the phase velocity of transverse waves propagating in SWCNTs. To the author best knowledge, effects of surface irregularity and initial stresses on transverse waves propagation, especially propagation in single-walled carbon nanotubes, have not been done before. The previous studies were devoted to the uniform and initial stresses-free carbon nanotubes. It should be emphasized that the transverse waves propagation in pre-stressed and irregular single-walled carbon nanotubes is novel, workable, and at the beginning of the path. In this manner, understanding the influences of surface irregularity as well as initial stresses on the phase velocity of transverse waves may serve as useful references for the applications and designs of nano oscillators and nanodevices, in which single-walled carbon nanotubes act as the most prevalent nanocomposite structural element.