25. Vibration and instability analysis of fluid‑conveying nanotubes embedded in visco‑elastic medium with consideration of surface effect

Ya-Xin Zhen

School of Mathematics and Physics, North China Electric Power University, Beijing, 102206, China

E-mail: yasine_zhen@163.com

Received 12 August 2016; accepted 14 August 2016

DOI https://doi.org/10.21595/mme.2016.17553

Abstract. We establish an analytical model to investigate the surface effects on the vibration and instability of fluid-conveying nanotubes embedded in visco-elastic medium. Based on nonlocal elastic theory and Euler-Bernoulli beam theory, the vibration equation of fluid‑conveying nanotubes is established with considering three typical boundary conditions. The effects of both inner and outer surface layers on the nanotubes are taken into consideration and the Kelvin‑Voigt model is introduced. The results show that the boundary conditions of system, the damping and elastic coefficient of the surrounding medium, thickness of nanotubes and aspect ratios have significant effects on the dynamic behaviors of the nanotubes. The damping parameter of the visco‑elastic foundation causes an obvious reduction of the critical flow velocity. For smaller tube thickness, larger aspect ratio or higher elastic parameter of surrounding foundation, the stability of the nanotubes may be greatly enhanced. This article might be helpful for the design and improvement of nanotubes for fluid-conveying applications embedded in elastic medium in nanoelectromechanical systems and microelectromechanical systems.

Keywords: surface effect, fluid-conveying nanotubes, vibration, Kelvin-Voigt model.

References

[1]        Gibson R. F., Ayorinde E. O., Wen Y. F. Vibrations of carbon nanotubes and their composites: a review. Composites Science and Technology, Vol. 67, 2007, p. 1‑28.

[2]        Li C., Thostenson E. T., Chou, T.-W. Sensors and actuators based on carbon nanotubes and their composites: a review. Composites Science and Technology, Vol. 68, Issue 6, 2008, p. 1227‑1249.

[3]        Gadd G. E., Blackford M., Moricca S., Webb N., Evans P. J., et al. The world’s smallest gas cylinder. Science, Vol. 277, 1997, p. 933‑936.

[4]        Yang Z., Zhang Y., Yang Y., Sun L., Han D., et al. Pharmacological and toxicological target organelles and safe use of single-walled carbon nanotubes as drug carriers in treating Alzheimer disease. Nanomedicine‑Nanotechnology Biology and Medicne, Vol. 6, 2010, p. 427‑441.

[5]        Gao Y. H., Bando Y. Nanotechnology: Carbon nanothermometer containing gallium. Nature, Vol. 415, 2002, p. 599‑599.

[6]        Yoon J., Ru C. Q., Mioduchowski A. Vibration and instability of carbon nanotubes conveying fluid. Composites Science and Technology, Vol. 65, 2005, p. 1326‑1336.

[7]        Yoon J., Ru C. Q., Mioduchowski, A. Flow-induced flutter instability of cantilever carbon nanotubes. International Journal of Solids and Structures, Vol. 43, 2006, p. 3337‑3349.

[8]        Chang W. J., Lee H. L. Free vibration of a single-walled carbon nanotube containing a fluid flow using the Timoshenko beam model. Physical Letters A, Vol. 373, 2009, p. 982‑985.

[9]        Khosravian N., Rafii-Tabar H. Computational modeling of the flow of viscous fluids in carbon nanotubes. Journal of Physics D: Applied physics, Vol. 40, 2007, p. 7046‑7052.

[10]     Yan Y., He X. Q., Zhang L. X., Wang Q. Flow-induced instability of double-walled carbon nanotubes based on an elastic shell model. Journal of Applied Physics, Vol. 102, 2007, p. 044307.

[11]     Wang L. Dynamical behaviors of double-walled carbon nanotubes conveying fluid accounting for the role of small length scale. Computational Materials Science, Vol. 45, 2009, p. 584‑588.

[12]     Zhen Y. X., Fang, B. Thermal-mechanical and nonlocal elastic vibration of single-walled carbon nanotubes conveying fluid. Computational Materials Science, Vol. 49, 2010, p. 276‑282.

[13]     Xia W., Wang L. Vibration characteristics of fluid-conveying carbon nanotubes with curved longitudinal shape. Computational Materials Science, Vol. 49, 2010, p. 99‑103.

[14]     Ghavanloo E., Rafiei M., Daneshmand F. In-plane vibration analysis of curved carbon nanotubes conveying fluid embedded in viscoelastic medium. Physics Letters A, Vol. 375, 2011, p. 1994‑1999.

[15]     Wang Y. Z., Li F. M. Nonlinear free vibration of nanotube with small scale effects embedded in viscous matrix. Mechanics Research Communications, Vol. 60, 2014, p. 45‑51.

[16]     Zhen Y. X., Fang B. Nonlinear vibration of fluid-conveying single-walled carbon nanotubes under harmonic excitation. International Journal of Non-Linear Mechanics, Vol. 76, 2015, p. 48-55.

[17]     She H., Wang B. A geometrically nonlinear finite element model of nanomaterials with consideration of surface effects. Finite Elements in Analysis and Design, Vol. 45, 2009, p. 463‑467.

[18]     He J., Lilley C. M. Surface effect on the elastic behavior of static bending nanowires. Nano Letters, Vol. 8, Issue 7, 2008, p. 1798‑1802.

[19]     Farshi B., Assadi A., Alinia-ziazi A. Frequency analysis of nanotubes with consideration of surface effects. Applied Physics Letters, Vol. 96, 2010, p. 093105.

[20]     Gheshlaghi B., Hasheminejad S. M. Surface effects on nonlinear free vibration of nanobeams. Composites: Part B, Vol. 42, 2011, p. 934-937.

[21]     Wang L. Vibration analysis of fluid-conveying nanotubes with consideration of surface effects. Physica E, Vol. 43, 2010, p. 437‑439.

[22]     Wang L. Surface effect on buckling configuration of nanobeams containing internal flowing fluid: A nonlinear analysis. Physica E, Vol. 44, 2012, p. 808‑812.

Cite this article

Zhen Ya‑Xin Vibration and instability analysis of fluid‑conveying nanotubes embedded in visco‑elastic medium with consideration of surface effect. Mathematical Models in Engineering, Vol. 2, Issue 2, 2016, p. 108‑113.

 

Mathematical Models in Engineering. December 2016, Volume 2, Issue 2

© JVE International Ltd. ISSN Print 2351-5279, ISSN Online 2424-4627, Kaunas, Lithuania