Instability of single-walled carbon nanotubes conveying Jeffrey fluid

doi:10.1088/1674-1056/abcf36

Abstract We report instability of the single-walled carbon nanotubes (SWCNT) filled with non-Newtonian Jeffrey fluid. Our objective is to get the influences of relaxation time and retardation time of the Jeffrey fluid on the vibration frequency and the decaying rate of the amplitude of carbon nanotubes. An elastic Euler-Bernoulli beam model is used to describe vibrations and structural instability of the carbon nanotubes. A new vibration equation of an SWCNT conveying Jeffrey fluid is first derived by employing Euler-Bernoulli beam equation and Cauchy momentum equation taking constitutive relation of Jeffrey fluid into account. The complex vibrating frequencies of the SWCNT are computed by solving a cubic eigenvalue problem based upon differential quadrature method (DQM). It is interesting to find from computational results that retardation time has significant influences on the vibration frequency and the decaying rate of the amplitude. Especially, the vibration frequency decreases and critical velocity increases with the retardation time. That is to say, longer retardation time makes the SWCNT more stable.

Keywords: single-walled carbon nanotubes Jeffrey fluid relaxation time retardation time

Received: 08 July 2020
Revised: 12 November 2020
Accepted manuscript online: 01 December 2020

PACS:	47.61.-k	(Micro- and nano- scale flow phenomena)
	47.50.-d	(Non-Newtonian fluid flows)
	47.10.ad	(Navier-Stokes equations)
	46.70.De	(Beams, plates, and shells)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11772162), the Natural Science Foundation of Inner Mongolia Autonomous Region of China (Grant No. 2019BS01004), and the Inner Mongolia Grassland Talent, China (Grant No. 12000-12102408).

Corresponding Authors: ^†Corresponding author. E-mail: jianyj@imu.edu.cn

Cite this article:

Bei-Nan Jia(贾北楠) and Yong-Jun Jian(菅永军) Instability of single-walled carbon nanotubes conveying Jeffrey fluid 2021 Chin. Phys. B 30 044601

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