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Exact solution for free vibrations of spinning nanotube based on nonlocal first order shear deformation shell theory

机译：基于非局部一阶剪切变形壳理论的旋转纳米管自由振动的精确解

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Spinning nanotubes are the main part of power transmission units in nano-machines. So, having proper information about the dynamic behavior of them are very important. So, as the basis of each dynamics problem free vibration of spinning nanotube is analyzed in this paper. For this purpose, Sanders first order shear deformation shell theory is combined with nonlocal elasticity and equations of motion are found. For the first time, equations are exactly solved for all classical combinations of boundary conditions. Validity and accuracy of present method are checked with literature in different tables and figures. As benchmark analysis, effects of changing geometrical parameters, spinning speed, nonlocal parameter, and boundary conditions on natural frequencies and critical speeds of nanotube is studied which will be helpful for future investigations. (C) 2016 Elsevier Ltd. All rights reserved.
机译：旋转纳米管是纳米机器中动力传输单元的主要部分。因此，掌握有关它们动态行为的适当信息非常重要。因此，本文以纺丝纳米管的自由振动作为每个动力学问题的基础。为此，将Sanders一阶剪切变形壳理论与非局部弹性相结合，找到了运动方程。对于边界条件的所有经典组合，方程式首次得到精确求解。本方法的有效性和准确性通过不同表和图中的文献进行了检验。作为基准分析，研究了改变几何参数，纺丝速度，非局部参数和边界条件对纳米管的固有频率和临界速度的影响，这将有助于将来的研究。 （C）2016 Elsevier Ltd.保留所有权利。

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