基于辛理论的载流碳纳米管能带分析

李渊; 邓子辰; 叶学华; 王艳

doi:10.6052/0459-1879-15-164

基于辛理论的载流碳纳米管能带分析

doi: 10.6052/0459-1879-15-164

西北工业大学工程力学系, 西安 710072

基金项目: 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.

详细信息

通讯作者:
邓子辰,教授,主要研究方向:物理波在材料和结构中的传播.E-mail:dweifan@nwpu.edu.cn

中图分类号: O302
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出版历程
- 收稿日期: 2015-05-07
- 修回日期: 2015-07-27
- 刊出日期: 2016-01-18

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

Department of Engineering Mechanics, Northwestern Polytechnical University, Xi'an 710072, China

摘要

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.
- 碳纳米管 /
- 散射 /
- 能带 /
- 辛理论
Abstract: 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 e ect 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.
- carbon nanotube /
- wave scattering /
- energy band /
- symplectic theory

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参考文献(28)

1 白春礼. 纳米科技及其发展前景. 科学通报, 2001, (02): 89-92 (Bai Chunli. Nano science and technology and its development prospect. Chinese Science Bulletin, 2001, (02): 89-92 (in Chinese))

2 Craighead HG. Nanoelectromechanical systems. Science, 2000,290(5496): 1532-1535

3 郑泉水, 徐志平, 王立峰. 碳纳米管的力学. 力学进展, 2004, 34(1):97-138 (Zheng Quanshui, Xu Zhiping, Wang Lifeng. Mechanics of carbon nanotubes. Advances in Mechanics, 2004, 34(1): 97-138 (in Chinese))

4 Liu JZ, Zheng Q, Jiang Q. E ect of a rippling mode on resonances of carbon nanotubes. Physical Review Letters, 2001, 86(21): 4843-4846

5 Zheng Q, Jiang Q. Multiwalled carbon nanotubes as gigahertz oscillators. Physical Review Letters, 2002, 88(4): 045503

6 Guo W, Guo Y, Gao H, et al. Energy dissipation in gigahertz oscillators from multiwalled carbon nanotubes. Physical Review Letters,2003, 91(12): 125501

7 Wang L. Flutter instability of supported pipes conveying fluid subjected to distributed follower forces. Acta Mechanica Solida Sinica,2012, 25(1): 46-52

8 Xia W, Wang L. Vibration characteristics of fluid-conveying carbon nanotubes with curved longitudinal shape. Computational Materials Science, 2010, 49(1): 99-103

9 Wang L, Hu H. Flexural wave propagation in single-walled carbon nanotubes. Physical Review B, 2005, 71(19): 195412

10 Wang L, Ni Q, Li M, et al. The thermal e ect on vibration and instability of carbon nanotubes conveying fluid. Physica E: Lowdimensional Systems and Nanostructures, 2008, 40(10): 3179-3182

11 王立峰. 一维纳米结构的若干力学问题. [博士论文]. 南京:南京航空航天大学, 2005 (Wang Lifeng. On some mechanics problems in one dimensional nanostructures. [PhD Thesis]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2005 (in Chinese))

12 Gibson RF, Ayorinde EO, Wen YF. Vibrations of carbon nanotubes and their composites: A review. Composites Science and Technology,2007, 67(1): 1-28

13 Zhang Y, Liu G, Han X. Transverse vibrations of double-walled carbon nanotubes under compressive axial load. Physics Letters A,2005, 340(1-4): 258-66

14 Yoon J, Ru CQ, Mioduchowski A. Timoshenko-beam e ects on transverse wave propagation in carbon nanotubes. Composites Part B: Engineering, 2004, 35(2): 87-93

15 Yoon J, Ru CQ, Mioduchowski A. Vibration and instability of carbon nanotubes conveying fluid. Composites Science and Technology,2005, 65(9): 1326-1336

16 Wang Q, Varadan VK. Wave characteristics of carbon nanotubes. International Journal of Solids and Structures, 2006, 43(2): 254-65

17 Chang TP. Thermal-mechanical vibration and instability of a fluid conveying single-walled carbon nanotube embedded in an elastic medium based on nonlocal elasticity theory. Applied Mathematical Modelling, 2012, 36(5): 1964-1973

18 Soltani P, Farshidianfar A. Periodic solution for nonlinear vibration of a fluid-conveying carbon nanotube, based on the nonlocal continuum theory by energy balance method. Applied Mathematical Modelling, 2012, 36(8): 3712-3724

19 Soltani P, Kassaei A, Taherian M, et al. Vibration of wavy singlewalled carbon nanotubes based on nonlocal Euler Bernoulli and Timoshenko models. International Journal of Advanced Structural Engineering, 2012, 4(1): 1-10

20 Kiani K. Transverse wave propagation in elastically confined singlewalled carbon nanotubes subjected to longitudinal magnetic fields using nonlocal elasticity models. Physica E: Low-dimensional Systems and Nanostructures, 2012, 45: 86-96

21 Li BH, Gao HS, Liu YS, et al. Free vibration analysis of micropipe conveying fluid by wave method. Results in Physics, 2012, 2: 104-109

22 Zhang HW, Yao Z, Wang JB, et al. Phonon dispersion analysis of carbon nanotubes based on inter-belt model and symplectic solution method. International Journal of Solids and Structures, 2007,44(20): 6428-6449

23 钟万勰. 应用力学的辛数学方法. 北京:高等教育出版社, 2006 (Zhong Wanxie. Symplectic Method in Applied Mechanics. Beijing: Higher Education Press, 2006 ( in Chinese))

24 Li W, Deng Z, Zhang S. Numerical algorithms for highly oscillatory dynamic system based on commutator-free method. Journal of Sound and Vibration, 2007, 302(1-2): 39-49

25 吴锋,徐小明,高强等. 基于辛理论的Timoshenko 梁波散射分析. 应用数学和力学, 2013, 34(12): 1225-35 (Wu Feng, Xu Xiaoming, Gao Qiang, et al. Analyzing the wave scattering in Timoshenko beam based on the symplectic theory. Applied Mathematics and Mechanics,2013, 34(12): 1225-35 (in Chinese))

26 姚伟岸,钟万勰. 辛弹性力学. 北京:高等教育出版社, 2002 (Yao Weian, Zhong Wanxie. Symplectic Elasticity. Beijing: Higher Education Press, 2002 (in Chinese))

27 Wang B, Deng Z, Ouyang H, et al. Wave characteristics of single-walled fluid-conveying carbon nanotubes subjected to multiphysical fields. Physica E: Low-dimensional Systems and Nanostructures,2013, 52: 97-105

28 Narendar S, Gopalakrishnan S. Terahertz wave characteristics of a single walled carbon nanotube containing a fluid flow using the nonlocal Timoshenko beam model. Physica E: Low-dimensional Systems and Nanostructures, 2010, 42(5): 1706-12

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