NONLINEAR VIBRATION ANALYSIS OF SINGLE-WALLED CARBON NANOTUBES BASED ON THE NONLOCAL SHELL ELACTICITY THEORY

NONLINEAR VIBRATION ANALYSIS OF SINGLE-WALLED CARBON NANOTUBES BASED ON THE NONLOCAL SHELL ELACTICITY THEORY 

By Payam SOLTANI, Javad SABERIAN, Roja BAHRAMIAN

Abstract:

In this paper, the nonlinear vibration of a single-walled carbon nanotube (SWCNT) with simply supported ends is investigated based on the von Karman geometric nonlinearity and nonlocal shell theory. The SWCNT is described as an individual shell and the Donnell's equations of cylindrical shells are used to obtain the governing equations. The Galerkin's procedure is used to discrete partial differential equations of the motion into the ordinary differential equations. The method of averaging is applied to analyze the nonlinear vibration of (10, 0), (20, 0) and (30, 0) zigzag SWCNTs in the analytical calculations. The effects of the nonlocal parameters, nonlinear parameters, different aspect ratios, different circumferential wave numbers and longitudinal half-wave numbers are investigated. The results of the classical and the nonlocal models are compared with the different nonlocal elasticity constants . The results show that the nonlocal parameter has much influence on the vibration frequency and the nonlinear behavior of the CNTs. So that, an increment of the nonlocal parameter makes the vibration frequencies increase or decrease in line with the different aspect ratios. Also, it can change the nonlinear vibration behavior to the softening type or the hardening type. The results indicate that geometrical nonlinearity and nonlocal elasticity play important roles for an accurate vibration behavior modeling of the SWCNT.

http://computationalnonlinear.asmedigitalcollection.asme.org/article.asp...