In this study, vibration analysis of single-walled carbon nanotube (SWCNT) has been carried out by using a refined beam theory, namely one variable shear deformation beam theory. This approach has one variable lesser than a contractual shear deformation theory such as first-order shear deformation theory (FSDT) and acts like classical beam approach but with considering shear deformations. The SWCNT has been placed in an axial or longitudinal magnetic field which is also exposed to both the hygroscopic as well as thermal environments. The thermal environment is considered as nonlinear thermal stress field based on the Murnaghan’s model whereas the hygroscopic environment is assumed as a linear stress field. The size effect of the SWCNT has been captured by both the nonlocal and gradient parameters by employing the Nonlocal Strain Gradient Theory (NSGT). Governing equation of motion of the proposed model has been developed by utilizing the extended Hamilton’s principle and the non-dimensional frequency parameters have been computed by incorporating the Navier’s approach for Hinged–Hinged (HH) boundary condition. The proposed model is validated with the existing model in special cases, by comparing the non-dimensional frequency parameters, displaying an excellent agreement. Further, a parametric study has been conducted to analyze the impact of nonlocal parameter, gradient parameter, thermal environment, hygroscopic environment, and magnetic field intensity on the non-dimensional frequency parameters. Also, results for some other theories like Classical Elasticity Theory (CET), Nonlocal Elasticity Theory (NET), and Strain Gradient Theory (SGT) have been presented along with the NSGT.

中文翻译：

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基于修正梁理论和非局域应变梯度模型的非线性温度分布单壁碳纳米管的湿磁振动

在这项研究中，单壁碳纳米管（SWCNT）的振动分析采用了一种改进的梁理论，即一个可变剪切变形梁理论。这种方法比一阶剪切变形理论 (FSDT) 等合同剪切变形理论少一个变量，并且其作用类似于经典梁方法，但考虑了剪切变形。SWCNT 被放置在轴向或纵向磁场中，该磁场也暴露在吸湿和热环境中。基于Murnaghan模型，热环境被认为是非线性热应力场，而吸湿环境被认为是线性应力场。通过采用非局部应变梯度理论 (NSGT)，非局部和梯度参数都捕获了 SWCNT 的尺寸效应。所提出模型的控制运动方程是通过利用扩展的 Hamilton 原理开发的，并且通过结合 Navier 的铰链 - 铰链 (HH) 边界条件方法计算了无量纲频率参数。该模型在特殊情况下与现有模型进行了验证，通过比较无量纲频率参数，显示出良好的一致性。此外，还进行了参数研究，分析了非局部参数、梯度参数、热环境、吸湿环境和磁场强度对无量纲频率参数的影响。还，