弹性介质中多壁碳纳米管扭转屈曲的近似分析  

Approximate Analytical Method of Torsional Buckling of Multi-Wall Carbon Nanotubes Embedded in Elastic Medium

作　　者：姚小虎[1] 韩强[1] 李兰芳[1] 

机构地区：[1]华南理工大学交通学院,广东广州510640

出　　处：《华南理工大学学报（自然科学版）》2008年第2期48-54,共7页Journal of South China University of Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10672059);广东省自然科学基金资助项目(06025689);华南理工大学优秀博士论文创新基金资助项目

摘　　要：研究了弹性介质中多壁碳纳米管的扭转屈曲,同时考虑了周边弹性介质和范德华力的影响.运用连续介质力学理论,提出了分析多壁碳纳米管扭转屈曲的多层弹性壳模型.基于这一模型,给出了用较少层的弹性壳模型代替多壁碳纳米管的近似分析方法.当N层碳纳米管的径厚比大于5时,N层碳纳米管可以近似地等效于一个单壁碳纳米管,其等效弯曲刚度和厚度分别是单壁碳纳米管的(10N-9)倍和N倍.最后,通过数值计算估计了多壁碳纳米管的临界屈曲扭矩.结果表明,该近似方法是简单、有效的.In this paper, the torsional buckling of a multi-wall carbon nanotube embedded in elastic medium is investigated by considering the effects of the surrounding elastic medium and the van der Waals force. Then, based on the theory of continuum mechanics, a multi-layer elastic shell model is presented to analyze the torsional buckling of the nanotube. Moreover, an approximate method is suggested based on the proposed model, which substitutes an elastic shell with fewer layers for the multi-wall carbon nanotube. In particular, when the radius-to-thickness ratio of a N-wall carbon nanotube is more than 5, the nanotube may be approximately equivalent to a singlewall elastic shell, and the effective bending stiffness and thickness of the N-wall nanotube are （10N- 9） and N times that of the single-wall nanotube, respectively. The critical buckling torque of the multi-wall carbon nanotube is finally estimated by numerical calculation. The results demonstrate that the proposed approximate method is simple and effective.

关 键 词：碳纳米管 屈曲 弹性介质 WINKLER模型 范德华力 

分 类 号：O33[理学—一般力学与力学基础]