Abstract 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.

中文翻译：

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包含初始应力效应的不规则单壁碳纳米管的振动分析

摘要 在这项工作中，尝试应用特征值方法以及 Donnell 薄壳理论来找出包含初始应力效应的不规则单壁碳 (ISWCNT) 的振动分析。表面不规则和初始应力对纳米材料固有振动频率的影响，特别是单壁碳纳米管（SWCNTs），以前没有研究过，以前的大部分研究都是针对规则和初始应力进行的——免费的碳纳米管。因此，必须强调的是，预应力不规则单壁碳纳米管的振动是新颖的，适用于纳米振荡器和纳米器件的设计，其中单壁碳纳米管是最普遍的纳米复合结构元件。表面不规则性假设为 SWCNT 表面的抛物线形式。推导出一个新的运动方程和频率方程。获得的数值结果更好地表示了预应力 ISWCNTs 的振动行为。已经观察到，表面不规则或初始应力的存在对振动的固有频率有显着影响，特别是在短长度的 SWCNT 中。数值结果表明，随着表面不规则度和初始应力参数的增加，单壁碳纳米管的固有频率降低。据作者所知，表面不规则性和初始应力对单壁碳纳米管振动行为的影响尚未得到研究，目前的工作是试图找出这种有效性。此外，