Instability of single-walled carbon nanotubes conveying Jeffrey fluid* *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).

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.