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

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 Flu center dot gge's principle. Unlike the uniform carbon nanotube, effects of irregularity and stiffness pa-rameters are considered within the framework of Flu center dot gge'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 Flu center dot gge'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 nu-merical examples. The impact of various parameters, including surface irregularity, stiff-ness, 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 dis-cussed. 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 valuableUnderstanding 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 Flu center dot gge's principle. Unlike the uniform carbon nanotube, effects of irregularity and stiffness pa-rameters are considered within the framework of Flu center dot gge'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 Flu center dot gge'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 nu-merical examples. The impact of various parameters, including surface irregularity, stiff-ness, 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 dis-cussed. 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 vi-bration of the irregular SWCNT has a remarkable effect on the functioning of these devices.(c) 2023 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

Understanding the torsional vibration characteristics of Single-Walled Carbon Nanotubes (SWCNTs) is crucial for the reliable design of nanodevices. This study presents a practical and accurate solution for the torsional vibration of irregular SWCNTs with elastic-support boundary conditions. The effects of irregularity and stiffness parameters on the torsional vibration are considered within the framework of Flu center dot gge's model. The results demonstrate the impact of various parameters, such as surface irregularity and nanotube thickness, on the natural frequency of irregular SWCNT.