Torsional vibration of irregular single-walled carbon nanotube incorporating compressive initial stress effects

Abstract

Abstract This study is an attempt to show the impacts of surface irregularity and compressive initial stresses on the torsional vibration of a single-walled carbon nanotube (SWCNT). The governing equation and corresponding closed-form solutions were derived with the aid of Hamilton's principle. Then, the natural frequencies were obtained analytically and the influences of surface irregularity and compressive initial stresses on the torsional vibration were studied in detail. Numerical results analyzing the torsional vibration incorporating compressive initial stress effects were discussed and presented graphically. The effects of surface irregularity on the natural frequency of torsional vibrations of nanomaterials, especially for SWCNTs, have not been investigated before, and most of the previous research works have been carried for a regular carbon nanotube. Therefore, it must be emphasized that the torsional vibrations of irregular SWCNTs are novel and applicable for the design of nano-oscillators and nanodevices, in which SWCNTs act as the most prevalent nanocomposite structural element. The analytical solutions and numerical results revealed that the surface irregularity and compressive initial stress have notable effects on the natural frequency of torsional vibrations. It has been observed that, as the surface irregularity and compressive initial stress parameters increase, the torsional natural frequency of vibrations of SWCNTs also increases. Since SWCNTs have very small size, they are always subject to initial stresses from different resources; therefore, understanding the influences of compressive initial stresses on the torsional frequency of nanotubes helps the engineers and researchers to design proper nanodevices for different applications with irregular shapes.