In this article, vibration characteristics of three different types of Single-Walled Carbon Nanotubes (SWCNTs) such as armchair, chiral, and zigzag carbon nanotubes have been investigated considering the effects of surface energy and surface residual stresses. The nanotubes are embedded in the elastic substrate of the Winkler type and are also exposed to low and high-temperature environments. A new refined beam theory namely, one-variable shear deformation beam theory has been combined with Hamilton’s principle to develop the governing equations of the proposed model. The size-dependent behavior of the SWCNTs is addressed by Eringen’s nonlocal elasticity theory whereas the model is investigated analytically by employing Navier’s technique. Also, a parametric study has been conducted to analyze the effects of various scaling parameters such as small scale parameter, temperature change, thermal environments, Winkler modulus, and length of the beam. The results are also validated with previously published articles in special cases witnessing robust agreement.

在本文中，考虑了表面能和表面残余应力的影响，研究了三种不同类型的单壁碳纳米管（SWCNT）的振动特性，例如扶手椅，手性和之字形碳纳米管。纳米管嵌入Winkler型弹性基底中，并且也暴露于低温和高温环境中。结合汉密尔顿原理，提出了一种新的细化梁理论，即一变量剪切变形梁理论，建立了该模型的控制方程。艾琳根的非局部弹性理论解决了单壁碳纳米管的尺寸依赖性行为，而采用纳维耶技术对模型进行了分析性研究。也，已经进行了参数研究，以分析各种缩放参数的影响，例如小缩放参数，温度变化，热环境，Winkler模量和光束长度。在特殊情况下，也可以使用先前发表的文章验证结果，这些文章见证了强有力的共识。