Nonlinear Vibration Analysis of Single-Walled Carbon Nanotube With Shell Model Based on the Nonlocal Elasticity Theory

P. Soltani, J. Saberian, R. Bahramian

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


In this paper, nonlinear vibration of a single-walled carbon nanotube (SWCNT) with simply supported ends is investigated based on von Karman's geometric nonlinearity and nonlocal shell theory. The SWCNT is designated as an individual shell, and the Donnell's formulations of a cylindrical shell are used to obtain the governing equations. The Galerkin's procedure is used to discretized partial differential equations (PDEs) into the ordinary differential equations (ODEs) of motion, and the method of averaging is applied to obtain an analytical solution of the nonlinear vibration of (10,0), (20,0), and (30,0) zigzag SWCNTs. The effects of the nonlocal parameters, nonlinear parameters, different aspect ratios, and different circumferential wave numbers are investigated. The results of the classical and the nonlocal models are compared with different nonlocal elasticity constants (e0a). It is shown that the nonlocal parameter predicts different resonant frequencies in comparison to the local models. The softening and/or hardening nonlinear behaviors of the CNTs may change against the nonlocal parameters. Hence, considering the geometrical nonlinearity and the nonlocal elasticity effects, the dynamical models of the SWCNTs predict their vibration behaviors accurately and should not be ignored during theoretical modeling.

Original languageEnglish
Article number011002
Number of pages10
JournalJournal of Computational and Nonlinear Dynamics
Issue number1
Early online date30 Jun 2015
Publication statusPublished - Jan 2016
Externally publishedYes


  • averaging method
  • carbon nanotubes
  • nonlinear vibration
  • nonlocal elasticity theory

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Mechanical Engineering
  • Applied Mathematics


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