剪力非局部因子对双壁碳纳米管中弯曲波频散特性的影响

王碧蓉; 邓子辰; 徐晓建; 王艳

doi:10.3879/j.issn.1000-0887.2014.05.002

剪力非局部因子对双壁碳纳米管中弯曲波频散特性的影响

doi: 10.3879/j.issn.1000-0887.2014.05.002

¹西北工业大学工程力学系, 西安 710129;²大连理工大学工业装备结构分析国家重点实验室, 辽宁大连 116024

基金项目: 国家重点基础研究发展计划（973计划）(2011CB610300)；111引智计划项目（B07050）；国家自然科学基金(11372252；11172239)；大连理工大学工业装备结构分析国家重点实验室开放基金(GZ0802)；高校博士点基金(20126102110023)

详细信息

作者简介:
王碧蓉（1989—），女，陕西人，硕士生(E-mail: wangbirong@mail.nwpu.edu.cn)

中图分类号: TB383;O348.9
计量
- 文章访问数: 1352
- HTML全文浏览量: 136
- PDF下载量: 872
- 被引次数: 0
出版历程
- 收稿日期: 2013-12-19
- 修回日期: 2014-02-18
- 刊出日期: 2014-05-15

Effects of Nonlocal Shear Factor on Flexural Wave Dispersion in Double-Walled Carbon Nanotubes

¹Department of Engineering Mechanics, Northwestern Polytechnical University,Xi’an 710129, P.R.China;²State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, Liaoning 116024,P.R.China

Funds: The National Basic Research Program of China(973 Program)(2011CB610300)；The National Natural Science Foundation of China(11372252；11172239)

摘要

摘要: 基于应力梯度理论修正的Timoshenko(铁木辛柯)梁模型，结合管间Van der Waals(范德华)力，研究了非局部效应对双壁碳纳米管中弹性波各阶模态的相速度、频率、临界频率、内外管振幅比等频散特性的影响.数值模拟结果表明：在应力梯度理论修正模型下，对应同一波数，4阶模态的相速度、频率均随剪力非局部因子的增大而减小，且随着剪力非局部因子的等幅增加，相速度、频率的减小并没有明显的等幅规律；值得注意的是，3、4阶模态的内外管振幅比并不是随着剪力非局部因子的增加依次减小；在波数较高阶段，剪力非局部因子对双壁碳纳米管中波的相速度、频率、渐近频率、内外管振幅比等频散特性均有显著影响.
- 双壁碳纳米管 /
- 弯曲波传播 /
- 应力梯度理论 /
- 频散关系
Abstract: The effects of nonlocal factors on the wave dispersion in the doublewalled carbon nanotube(DWCNT) were analyzed with the modified Timoshenko beam model modified based on the stress gradient theory. Coupling with Van der Waals force, the dispersion characteristics, such as phase velocity, frequency, critical frequency and amplitude ratio of outer tube to inner tube, were studied. The results show that: for a given wave number, both the first 4 modes’phase velocities and frequencies of the DWCNT decrease with rise of the nonlocal shear factor, in which no obvious linear law is found. It is notable that for the 3rd and 4th modes the amplitude ratios do not decrease with the rise of the nonlocal shear factor. Meanwhile, the nonlocal shear factor has prominent effects on the wave dispersion characteristics of the DWCNT especially at relatively higher wave numbers.
- double-walled carbon nanotubes /
- wave propagation /
- stress gradient theory /
- dispersion relation

HTML全文

参考文献(16)

[1]	Wang L, Hu H. Flexural wave propagation in single-walled carbon nanotubes[J].Physical Review B,2005,71(19): 195412.
[2]	Wang Q, Varadan V K. Wave characteristics of carbon nanotubes[J].International Journal of Solids and Structures,2006,43(2): 254-265.
[3]	Yoon J, Ru C Q, Mioduchowski A. Timoshenko-beam effects on transverse wave propagation in carbon nanotubes[J].Composites Part B: Engineering,2004,35(2): 87-93.
[4]	Peddieson J, Buchanan G R, Mcnitt R P. Application of nonlocal continuum models to nanotechnology[J].International Journal of Engineering Science,2003,41(3/5): 305-312.
[5]	Lu P, Lee H P, Lu C, Zhang P Q. Dynamic properties of flexural beams using a nonlocal elasticity model[J].Journal of Applied Physics,2006,99(7): 073510-9.
[6]	Zhang Y Q, Liu G R, Xie X Y. Free transverse vibrations of double-walled carbon nanotubes using a theory of nonlocal elasticity[J].Physical Review B,2005,71(19): 195404.
[7]	Wang Q, Wang C M. The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes[J].Nanotechnology,2007,18(7): 075702.
[8]	Zhang Y Q, Liu G R, Wang J S. Small-scale effects on buckling of multiwalled carbon nanotubes under axial compression[J].Physical Review B,2004,70(20): 205430.
[9]	Ece M C, Aydogdu M. Nonlocal elasticity effect on vibration of in-plane loaded double-walled carbon nano-tubes[J].Acta Mechanica,2007,190(1/4): 185-195.
[10]	Wang C M, Zhang Y Y, He X Q. Vibration of nonlocal Timoshenko beams[J].Nanotechnology,2007,18(10): 105401.
[11]	Sudak L J. Column buckling of multiwalled carbon nanotubes using nonlocal continuum mechanics[J].Journal of Applied Physics,2003,94(11): 7281-7287.
[12]	Eringen A C. On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves[J].Journal of Applied Physics,1983,54(9): 4703-4710.
[13]	方同，薛璞. 振动理论及应用[M]. 西安：西北工业大学出版社， 1998.(FANG Tong, XUE Pu.Theory of Vibration With Applications [M]. Xi’an：Northwestern Polytechnical University Press, 1998.(in Chinese))
[14]	王碧蓉，邓子辰，徐晓建. 基于梯度理论的碳纳米管弯曲波传播规律的研究[J].西北工业大学学报, 2013,31(5): 774-778.(WANG Bi-rong, DENG Zi-chen, XU Xiao-jian. Modified Timoshenko beam models for flexural wave dispersion in carbon nanotubes with shear deformation considered[J].Journal of Northwestern Polytechnical University,2013,31(5): 774-778.(in Chinese))
[15]	Lu P, Lee H P, Lu C, Zhang P Q. Application of nonlocal beam models for carbon nanotubes[J].International Journal of Solids and Structures,2007,44(16): 5289-5300.
[16]	Wang Q, Zhou G Y, Lin K C. Scale effect on wave propagation of double-walled carbon nanotubes[J].International Journal of Solids and Structures,2006,43(20): 6071-6084.