基于非局部高阶剪切梁理论的碳纳米管弯曲波研究  

Flexural Wave Propagating in Carbon Nanotubes Based on Nonlocal High-order Shear Beam Theory

作　　者：金花 张志纯 龙志林[2] 黄彬 周强 武井祥 JIN Hua;ZHANG Zhichun;LONG Zhilin;HUANG Bin;ZHOU Qiang;WU Jingxiang(College of Physics and Optoelectronic Engineering,Xiangtan University,Xiangtan,Hunan 411105,China;School of Civil Engineering and Mechanics,Xiangtan University,Xiangtan,Hunan 411105,China)

机构地区：[1]湘潭大学物理与光电工程学院,湖南湘潭411105 [2]湘潭大学土木工程与力学学院,湖南湘潭411105

出　　处：《复旦学报（自然科学版）》2020年第4期419-426,437,共9页Journal of Fudan University：Natural Science

基　　金：湖南省教育厅湘潭大学配套科研项目(KZ03030)。

摘　　要：本文提出了一种适用于圆截面纳米梁的非局部高阶剪切梁理论模型,相比Timoshenko梁,该模型不仅考虑了横截面剪切变形的影响,而且满足圆周上剪应力为零的条件,同时又不需要引入剪切修正系数的概念.将此模型用于单壁和多壁碳纳米管在自由空间及弹性介质中弯曲波的研究,采用双参数Pasternak基来模拟弹性介质.建立了碳纳米管的波动控制方程,推导了单壁和多壁碳纳米管中弯曲波的色散关系.与分子动力学结果对比,表明本文提出的非局部高阶剪切梁理论模型能够有效准确地表征碳纳米管的波动特性.A nonlocal high-order shear beam model for circular cross-section nanobeam is presented.Compared with Timoshenko beam,the effect of cross-section shear deformation is not only considered,but also the shear in circumference is met to be zero,and the concept of shear correction factor isn’t introduced.Using this model,flexural waves propagating in Single-walled Carbon Nanotubes(SWCNT)and Multi-Walled Carbon Nanotubes(MWCNT)in free space and embedded in elastic medium are investigated,elastic medium is simulated by a biparameter Pasternak substrate.Furthermore,the governing equations of the nonlocal high-order shear beam model is established to deduce the dispersion of flexural waves in SWCNT and MWCNT.Subsequently,the theoretical results have a good agreement with those from Molecular Dynamics simulation,which demonstrates that the wave behaviors of carbon nanotubes can be correctly described by the presented model.

关 键 词：碳纳米管 弯曲波 高阶剪切梁 弹性介质 

分 类 号：O343.1[理学—固体力学]