磁场环境下输流碳纳米管的热振动与稳定性分析
Thermal-Mechanical Vibration and Stability Analysis of Fluid-Conveying Carbon Nanotubes under Magnetic Field

作者: 甄亚欣 :华北电力大学数理学院,北京;

关键词: 热效应非局部弹性理论磁场稳定性Thermal Effect Nonlocal Elasticity Theory Magnetic Field Stability

摘要:
本文基于非局部弹性理论和欧拉梁理论,研究了磁场和温度场耦合作用下输流碳纳米管的动力学特性。采用微分求积法进行求解,详细讨论了常温环境下温度变化量和磁通量等对系统的振动频率和临界流速的影响。结果表明随着温度变化量的增大,系统的振动频率和临界流速都增大。随着磁通量的增大,系统的振动频率和临界流速明显增大,增强磁场能够显著提高系统的稳定性。

Abstract: In this paper, based on nonlocal elasticity theory and Euler-Bernoulli beam theory, we investigate the dynamical characteristics of carbon nanotubes conveying fluid under longitudinal magnetic field with considering thermal effect. Differential quadrature method is used to do the simulation. The influence of temperature changes under normal atmospheric temperature and magnetic flux on the natural frequency and critical flow velocity are discussed in detail. The results show that the natural frequencies and critical flow velocity increase as the temperature changes increase. As the magnetic flux increases, the natural frequency and critical flow velocity increase distinctly, which demonstrate that increase the magnetic flux can obviously improve the stability of the fluid- conveying system.

文章引用: 甄亚欣 (2016) 磁场环境下输流碳纳米管的热振动与稳定性分析。 声学与振动, 4, 11-18. doi: 10.12677/OJAV.2016.42002

参考文献

[1] Iijima, S. (1991) Helical Microtubules of Graphitic Carbon. Nature, 354, 56-58. http://dx.doi.org/10.1038/354056a0

[2] 甄亚欣. 输流碳纳米管的动力学行为研究[D]: [博士学位论文]. 哈尔滨: 哈尔滨工业大学, 2012.

[3] 陈彦霖, 王晋宝, 周卫, 等. 碳纳米管的振动研究进展[J]. 浙江海洋学院学学报, 2011, 30(3): 243-248.

[4] Govindjee, C.F. and Sackman, J.L. (1999) On the Use of Continuum Mechanics to Estimate the Properties of Nanotubes. Solid State Communications, 110, 227-230. http://dx.doi.org/10.1016/S0038-1098(98)00626-7

[5] Sohlberg, K.., Sumpter, B.G., Tuzun, R.E., et al. (1998) Continuum Methods of Mechanics as a Simplified Approach to Structural Engineering of Nanostructures. Nanotechnology, 9, 30-36. http://dx.doi.org/10.1088/0957-4484/9/1/004

[6] Yoon, J., Ru, C.Q. and Mioduchowski, A. (2005) Vibration and Instability of Carbon Nanotubes Conveying Fluid. Composites Science and Technology, 65, 1326-1336. http://dx.doi.org/10.1016/j.compscitech.2004.12.002

[7] Wang, X.Y., Wang, X. and Sheng, G.G. (2007) The Coupling Vibration of Fluid-Filled Carbon Nanotubes. Journal of Physics D: Applied Physics, 40, 2563-2572. http://dx.doi.org/10.1088/0022-3727/40/8/022

[8] Khosravian, N. and Rafii-Tabar, H. (2007) Computational Modeling of the Flow of Viscous Fluids in Carbon Nanotubes. Journal of Physics D: Applied Physics, 40, 7046-7052. http://dx.doi.org/10.1088/0022-3727/40/22/027

[9] Peddieson, J., Buchanan, R. and Mcnitt, R.P. (2003) Application of Nonlocal Continuum Models to Nanotechnology. International Journal of Engineering Science, 41, 305-312. http://dx.doi.org/10.1016/S0020-7225(02)00210-0

[10] Lee, H.L. and Chang, W.J. (2008) Free Transverse Vibration of the Fluid-Conveying Single-Walled Carbon Nanotube Using Nonlocal Elastic Theory. Journal of Applied Physics, 103, 024302.

[11] Zhen, Y.X. and Fang, B. (2010) Thermal-Mechanical and Nonlocal Elastic Vibration of Single-Walled Carbon Nanotubes Conveying Fluid. Computational Materials Science, 49, 276-282. http://dx.doi.org/10.1016/j.commatsci.2010.05.007

[12] Kiani, K. (2014) Longitudinally Varying Magnetic Field Influenced Transverse Vibration of Embedded Double- Walled Carbon Nanotubes. International Journal of Mechanical Sciences, 87, 179-199. http://dx.doi.org/10.1016/j.ijmecsci.2014.04.018

[13] Eringen, A.C. (1972) Nonlocal Polar Elastic Continua. International Journal of Engineering Science, 10, 1-16. http://dx.doi.org/10.1016/0020-7225(72)90070-5

[14] Eringen, A.C. and Edelen, D.G.B. (1972) On Nonlocal Elasticity. International Journal of Engineering Science, 10, 233-248. http://dx.doi.org/10.1016/0020-7225(72)90039-0

[15] Narendar, S., Gupta, S.S. and Gopalakrishnan, S. (2012) Wave Propagation in Single-Walled Carbon Nanotube under Longitudinal Magnetic Field Using Nonlocal Euler-Bernoulli Beam Theory. Applied Mathematical Modelling, 36, 4529-4538. http://dx.doi.org/10.1016/j.apm.2011.11.073

[16] Wang, L., Ni, Q., Li, M., et al. (2008) The Thermal Effect on Vibration and Instability of Carbon Nanotubes Conveying Fluid. Physica E, 40, 3179-3182. http://dx.doi.org/10.1016/j.physe.2008.05.009

[17] Wang, Q. (2005) Wave Propagation in Carbon Nanotubes via Nonlocal Continuum Mechanics. Journal of Applied Physics, 98, 124301.

分享
Top