Torsional vibrational analysis of irregular single-walled carbon nanotube with elastic-support boundary conditions

Abstract

Understanding the torsional vibration characteristics of Single-Walled Carbon Nanotubes (SWCNTs) is of great interest to ensure the reliable design of various nanodevices in which SWCNT is a common structural component. The previous studies were usually limited to uniform SWCNTs under classical boundary conditions. Motivated by this limitation, a practical, accurate solution is created for the torsional vibration of an irregular SWCNT with elastic-support boundary conditions. The torsional vibration of an irregular single-walled carbon nanotube with elastic-support boundary conditions is modeled by Flügge's principle. Unlike the uniform carbon nanotube, effects of irregularity and stiffness parameters are considered within the framework of Flügge's model. Stiffness parameters are defined as a function of complex torsional wave number, which makes all the subsequent calculations be treated precisely and efficiently. The governing equations are derived using Flügge's principle, and the wave propagation approach is applied to solve these equations. The accuracy and efficiency of the current model are then illustrated by a variety of numerical examples. The impact of various parameters, including surface irregularity, stiffness, and nanotube thickness, on the torsional vibration of irregular SWCNT, is examined. According to this study, the results indicate that the frequency calculated is influenced by the irregularity parameter compared with the case of uniform SWCNT. The effects of the parameters of irregularity, stiffness, and nanotube thickness are investigated and discussed. The results show that, an increase in irregularity's parameter leads to a decrease in the natural frequency of irregular SWCNT with elastic-support boundary conditions. In addition, an increase in nanotube's thickness leads to a notable decreasing in the natural frequency of irregular SWCNT. The finding obtained in this work may serve as valuable references for the designs of Nano-oscillators and nanodevices, where the torsional vibration of the irregular SWCNT has a remarkable effect on the functioning of these devices.

Keywords

• Torsional
• Vibration
• Irregularity's parameter
• SWCNT
• Flügge model
• Stiffness's parameter