International Journal of Fluid Mechanics Research, 45(2):171–186 (2018) INVESTIGATION ON THE EFFECT OF AXIALLY MOVING CARBON NANOTUBE, NANOFLOW, AND KNUDSEN NUMBER ON THE VIBRATIONAL BEHAVIOR OF THE SYSTEM Soheil Oveissi, 1 Davood Toghraie, 2,* & S. Ali Eftekhari 2 1 Department of Mechanical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran 2 Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran *Address all correspondence to: Davood Toghraie, Department of Mechanical Engineering, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran; Tel./Fax: +98 3366 0011, E-mail: Toghraee@iaukhsh.ac.ir Original Manuscript Submitted: 6/31/2017; Final Draft Received: 8/8/2017 The equation of motion of the axially moving carbon nanotube conveying fluid is obtained in order to investigate the effect of the velocity of axially moving CNT and internal flowing fluid on the vibrational behavior of the system. To this end, the nonlocal continuum theory is used to consider the small-scale effect and the Knudsen number is employed to create the nanoflow as a fluid passing through the CNT. The equation of motion is obtained by using Hamilton’s principle and the Galerkin method is used to discretize and solve it. The results indicate that the small-scale parameter plays a key role in determining the critical velocity values and the occurring instabilities of the system. It is obvious that for the eigenfunction in the higher modes, the imaginary parts of the eigenvalues reach zero at a lower critical velocity in longitudinal vibration of the axially moving CNT conveying fluid. Moreover, it can be found that the stability of the system decreases when the axially moving CNT conveying fluid is considered with the constant axial movement velocity of the CNT, the constant fluid velocity, and the case in which both velocities are the same, respectively. Also, the existence of the fluid could cause an approximately 0.2% reduction in the magnitude of the system critical velocity, and then the system’s stability decreases. KEY WORDS: longitudinal vibration, axially moving CNT conveying fluid, divergence and flutter in- stabilities, Galerkin weighted residual method 1. INTRODUCTION Since carbon nanotubes, due to their amazing properties, are of interest to researchers, their physical behaviors are studied in many fields. One of the less considered subjects is the vibrational response of the dynamical CNT. Up to this time, it has been realized that the CNT in the stationary stage has various abilities that can be used, as in nanofluidic devices, nanomechanical sensors, drug delivery, biological and molecular sensors, etc. Another application of CNT that has been studied is its vibrational behavior while the fluid flow passes through it. The flowing fluid and its velocity could have an effective role in determining frequencies, stabilities, and wave prop- agation in CNT conveying fluid. For example, Yoon et al. (2005, 2006) studied the influence of internal flowing fluid on free vibration and flow-induced structural instabilities (divergence and flutter) of CNTs. They indicated that internal moving fluid has a substantial effect on vibrational frequencies, especially for suspended, longer, and larger-innermost-radius CNTs at higher flow velocity; the decaying rate of amplitude and the critical flow velocity 1064–2277/18/$35.00 © 2018 by Begell House, Inc. www.begellhouse.com 171