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首页> 外文期刊>Journal of Sound and Vibration >Nonlinear vibrations and energy exchange of single-walled carbon nanotubes. Circumferential flexural modes
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Nonlinear vibrations and energy exchange of single-walled carbon nanotubes. Circumferential flexural modes

机译：单壁碳纳米管的非线性振动和能量交换。周向弯曲模式

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In this paper, the nonlinear vibrations and energy exchange of single -walled carbon nanotubes (SWNTs) are studied. The Sanders-Koiter theory is applied to model the nonlinear dynamics of the system in the case of finite amplitude of vibration. The SWNT deformation is described in terms of longitudinal, circumferential and radial displacement fields. Simply supported, clamped and free boundary conditions are considered. The circumferential flexural modes (CFMs) are investigated. Two different approaches based on numerical and analytical models are compared. In the numerical model, an energy method based on the Lagrange equations is used to reduce the nonlinear partial differential equations of motion to a set of nonlinear ordinary differential equations, which is solved by using the implicit Runge-Kutta numerical method. In the analytical model, a reduced form of the Sanders-Koiter theory assuming small circumferential and tangential shear deformations is used to get the nonlinear ordinary differential equations of motion, which are solved by using the multiple scales analytical method. The transition from energy beating to energy localization in the nonlinear field is studied. The effect of the aspect ratio on the analytical and numerical values of the nonlinear energy localization threshold for different boundary conditions is investigated. (C) 2016 Elsevier Ltd. All rights reserved.
机译：本文研究了单壁碳纳米管的非线性振动和能量交换。在振动幅度有限的情况下，使用Sanders-Koiter理论对系统的非线性动力学进行建模。 SWNT变形是根据纵向，圆周和径向位移场来描述的。考虑简单支持，限制和自由边界条件。研究了圆周弯曲模式（CFM）。比较了基于数值模型和分析模型的两种不同方法。在数值模型中，基于拉格朗日方程的能量方法用于将运动的非线性偏微分方程简化为一组非线性常微分方程，这可以通过使用隐式Runge-Kutta数值方法求解。在分析模型中，使用假设圆周和切向剪切变形较小的Sanders-Koiter理论的简化形式来获得非线性常微分运动方程，可使用多尺度分析方法对其进行求解。研究了非线性领域中从能量跳动到能量局部化的转变。研究了纵横比对不同边界条件下非线性能量局部化阈值的分析和数值的影响。 （C）2016 Elsevier Ltd.保留所有权利。

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