基于辛理论的载流碳纳米管能带分析  

ANALYSING THE WAVE SCATTERING IN SINGLE-WALLED CARBON NANOTUBE CONVEYING FLUID BASED ON THE SYMPLECTIC THEORY

作　　者：李渊[1] 邓子辰[1] 叶学华[1] 王艳[1] 

机构地区：[1]西北工业大学工程力学系,西安710072

出　　处：《力学学报》2016年第1期135-139,共5页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(11372252);高校博士点基金(20126102110023);中央高校基本科研业务费专项资金(310201401JCQ01001)资助项目

摘　　要：基于连续介质力学理论和辛弹性理论,将载流碳纳米管等效为铁木辛柯梁,采用哈密顿变分原理建立了载流碳纳米管的振动控制方程;引入对偶变量将振动控制方程从拉格朗日体系导入到哈密顿体系下;通过波传播方法分析了载流碳纳米管的能带结构;研究了流体密度、流速对载流碳纳米管能带结构的影响;同时计算了载流碳纳米管的散射矩阵.研究发现:管内流速以及流体密度对剪切频率和弯曲频率有着非常重要的影响.研究结果表明:载流碳纳米管的剪切频率和弯曲频率因流体的加入而减小,并随流速及流体密度的增大而减小;通过对数值结果的分析发现:载流碳纳米管由于管内流体、流速以及流体密度的作用,会使得载流碳纳米管变的更"软".其中,哈密顿体系下所得出的载流碳纳米管弯曲频率随管内流体密度的增加而变小,有别于在拉格朗日体系下非局部梁理论所得的结论.同时,数值结果表明散射矩阵是酉矩阵,辛体系下的入射波功率流与反射波功率流相等,即功率流守恒,体现了辛弹性力学理论的优越性.Based on tcontinuum mechanics theory and the symplectic theory, the single-walled carbon nanotube （SWCNT） is modelled as a Timoshenko beam. The dynamics equations of fluid-conveying SWCNT are derived from Hamilton＇s principle. By introducing the symplectic variable into the mechanics system, the governing equation of fluid-conveying SWCNT is transformed from Lagrange system into Hamilton system, then the governing equation is employed to analyse the energy band structure of the SWCNT and the wave scattering in the beam. Moreover, the scattering matrix of the nanotube is calculated by symplectic methodology. The influences of the fluid density and velocity to SWCNT＇s band structure are also analysed. The results show that the shear and flexural frequencies of SWCNT are greater than those of fluid-conveying SWCNT. The analyses indicate that the shear and flexural frequencies of fluid-conveying SWCNT decrease with the fluid velocity and density increasing, because the effect of the fluid inside makes the nanotube softer. Meanwhile, it is also found that the scattering matrix is unitary matrix, pointing the power flow of the incident wave is equal to that of the reflected wave, indicating the power flow of Hamilton system is conserved. Furthermore, the results show the superiority of the symplectic elasticity theory.

关 键 词：碳纳米管 散射 能带 辛理论 

分 类 号：O302[理学—力学]