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总览 评价 柯燎亮 * （ 北京交通大学力学系，北京 100044； ） 摘要： 基于修正偶应力理论和铁木辛柯梁理论，本文研究了输流单臂碳纳米管的振动和失稳问题的解析解。该非经典Timoshenko梁模型结合了泊松比的影响，包含一个尺度参数并能考虑尺度效应。利用哈
柯燎亮*
（
北京交通大学力学系，北京 100044； ）
摘要：
基于修正偶应力理论和铁木辛柯梁理论，本文研究了输流单臂碳纳米管的振动和失稳问题的解析解。该非经典Timoshenko梁模型结合了泊松比的影响，包含一个尺度参数并能考虑尺度效应。利用哈密尔顿原理推导出高阶控制方程和边界条件。详细地讨论了尺度参数、泊松比、流速和边界条件对输流纳米管的振动和稳定特性的影响。结果显示输流碳纳米管的实频和临界流速随着尺度参数的增加而增加。
关键词：
单壁碳纳米管；尺度效应；失稳；振动；偶应力理论；Timoshenko梁理论
KE Liaoliang*
（
Institute of Engineering Mechanics, Beijing Jiaotong University, Beijing 100044； ）
Abstract：
This paper presents an analytical solution to the vibration and instability of fluid-conveying single-walled carbon nanotubes (SWCNTs) based on the modified couple stress theory and Timoshenko beam theory. This non-classical Timoshenko beam model, which incorporates the Poisson's ratio effect, contains a material length scale parameter and can capture the size effect. The higher-order governing equations and boundary conditions are derived by using the Hamilton's principle. A detailed parametric study is conducted to study the influences of length scale parameter, Poisson's ratio, aspect ratio of the SWCNTs, velocity of the fluid and end supports on the vibration and flow-induced instability of SWCNTs. Results show that increasing the length scale parameter increases the real component of the frequency and the critical flow velocity of the fluid-conveying SWCNTs.
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