In the present paper, the non-conservative instability of a cantilever single-walled carbon nanotube (SWCNT) through nonlocal theory is investigated. The nanotube is modeled as clamped-free beam carrying a concentrated mass, located at a generic position, or in the presence of crack, and subjected to a compressive axial load, at the free end. Nonlocal Euler–Bernoulli beam theory is used in the formulation and the governing equations of motion and the corresponding boundary conditions are derived using an extended Hamilton’s variational principle. The governing equations are solved analytically. In order to show the sensitivity of the SWCNT to the values of an added mass, or crack and the influence of the nonlocal parameter and nondimensional crack severity coefficient on the fundamental frequencies values, some numerical examples have been performed and discussed. Also, the validity and the accuracy of the proposed analysis have been confirmed by comparing the results with those obtained from the literature.

本文通过非局部理论研究了悬臂式单壁碳纳米管（SWCNT）的非保守不稳定性。纳米管的模型为自由夹持的束，该束在集中位置或存在裂纹的情况下在集中端承载集中的质量，并在自由端承受轴向压缩载荷。公式中使用了非局部Euler–Bernoulli梁理论，并使用扩展的汉密尔顿变分原理推导了运动控制方程和相应的边界条件。控制方程通过解析求解。为了显示SWCNT对附加质量或裂纹值的敏感性，以及非局部参数和无量纲裂纹严重性系数对基频值的影响，进行了一些数值示例并进行了讨论。而且，通过将结果与从文献中获得的结果进行比较，已经证实了所提出分析的有效性和准确性。