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.


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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

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