An analytical solution for vibration analysis of carbon nanotube conveying viscose fluid embedded in visco-elastic medium

Abstract

In this paper, considering a more realistic model for the carbon nanotube (CNT) conveying viscous fluid which is embedded in a visco-elastic medium, the effect of viscosity of the medium surrounding the CNT has been investigated. By taking into account the influence of the fluid viscosity and using the Navier-Stokes equations, the governing equation of motion has been derived and a new analytical technique based on the power series is presented for its vibration analysis. The frequency equation of the system is obtained by applying the boundary conditions. The influence of the medium parameters and the fluid viscosity on the natural frequencies of the CNT has been studied. The results show that the medium damping has a marked effect on the natural frequencies and the critical fluid velocity. Furthermore, by increasing the fluid viscosity, the natural frequencies and the critical fluid velocity increase. There is a good agreement between the results obtained through the proposed method and the data reported in the literature. The two main advantages of the proposed method are the applicability of the method to all kinds of the boundary conditions and its rapid convergence.