Calibration of nonlocal strain gradient shell model for vibration analysis of a CNT conveying viscous fluid using molecular dynamics simulation

Abstract

In this article, a nonlocal strain gradient cylindrical shell model is developed to study vibration analysis and instability of a single-walled carbon nanotube conveying viscous fluid. The fluid flow is modeled by modified Navier-Stokes equation considering slip boundary condition and Knudsen number. The obtained governing equations of motion and corresponding boundary conditions are discretized using generalized differential quadrature method. Simplifying the nonlocal strain gradient theory, the results of this theory are compared to those of classical, strain gradient, and nonlocal theories. The effects of material length scale and nonlocal parameters on natural frequency and critical flow velocity are further investigated. Also, for the first time, the effect of fluid flow on vibration behavior of the carbon nanotube is studied by molecular dynamics simulation. In the simulations, TIP4P/2005 water model is used, which accurately considers thermo-physical properties of water such as viscosity. Moreover, in order to apply carbon–carbon interaction, modified Tersoff potential is used, with Lennard-Jones potential being employed for other interactions. In this study, size-dependent parameters of nonlocal strain gradient theory are calibrated and variation of calibrated values under the effect of flow velocity is explored.