针对两端扭转弹簧约束下简支单层碳纳米管（SWCNT），将非局部弹性理论引入经典欧拉-伯努利梁模型，应用哈密顿原理建立了其振动控制方程以及边界条件，并依靠微分变换法（DTM法）对此高阶偏微分方程进行求解。数值计算研究了扭转弹簧弹性系数、碳纳米管小尺度效应和粘弹性性质对该系统前四阶无量纲固有频率的影响。结论表明小尺度参数、管道粘弹性阻尼参数的增加将会降低系统的各阶固有频率，而且上述两类变化情况均是高阶模态的变化显著于低阶模态；而扭转约束弹性刚度的增加则会提升纳米管的固有频率，并且这一提升效果低阶模态显著于高阶模态。

This paper investigated the free vibration of simply supported single-walled carbon nanotubes (SWCNTs) with both ends restrained elastically. The material property of CNT was simulated by Kelvin-Voigt viscoelastic constitutive relation. Based upon nonlocal Euler-Bernoulli beam theory, the governing partial differential equations of motion and associated boundary conditions were derived by Hamilton's principle. Employed the differential transformation method (DTM) to solve the equation of motion, the influences of the nonlocal parameter, the viscoelastic CNT parameter and restraining elastic coefficient on the dynamic behaviors of the SWCNT were analyzed. It can be concluded that the nonlocal small-scale parameter and the viscoelastic CNT parameter make the SWCNT natural frequency decrease. More importantly, the results show that it will be a convenient and effective way to increase the natural frequency SWCNT system through additional elastic restraining with proper coefficient on two ends while their values are low．

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