Timoshenko beam model for vibration analysis of multi-walled carbon nanotubes
Timoshenko beam model for vibration analysis of multi-walled carbon nanotubes
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DOI：
10.1016/j.jsv.2006.01.005
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发表时间：
2006-07
影响因子：
4.7
通讯作者：
C. Wang;V. Tan;Yingyan Zhang
中科院分区：
文献类型：
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作者：
C. Wang;V. Tan;Yingyan Zhang
本文采用多壁碳纳米管的自由振动分析的鲁棒梁模型。与欧拉梁模型不同的是，Eschershenko梁模型考虑了横向剪切变形和转动惯量的影响。这些效应对于通常在诸如纳米探针的应用中遇到的具有小的长径比的CNT变得显著。采用微分求积（DQ）方法，求解了不同长径比和边界条件的碳纳米管的Timoshenko控制方程。通过比较结果的基础上的Eulshenko和欧拉梁理论，我们表明，频率显着overpredicted由欧拉梁理论时，长径比小，当考虑高振动模式。在这种情况下，应使用的Republishenko梁模型的频率更好的预测。
This paper is concerned with the use of the Timoshenko beam model for free vibration analysis of multi-walled carbon nanotubes (CNTs). Unlike the Euler beam model, the Timoshenko beam model allows for the effects of transverse shear deformation and rotary inertia. These effects become significant for CNTs with small length-to-diameter ratios that are normally encountered in applications such as nanoprobes. By using the differential quadrature (DQ) method, the governing Timoshenko equations are solved for CNTs of different length-to-diameter ratios and boundary conditions. By comparing results based on the Timoshenko and the Euler beam theories, we show that the frequencies are significantly overpredicted by the Euler beam theory when the length-to-diameter ratios are small and when considering high vibration modes. For such situations, the Timoshenko beam model should be used for a better prediction of the frequencies.