Research Papers

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

[+] Author and Article Information
P. Soltani

Department of Mechanical Engineering,
Islamic Azad University,
Semnan Branch,
Semnan 35198, Iran
e-mails: p.soltani@semnaniau.ac.ir; payam.soltani@gmail.com

J. Saberian, R. Bahramian

Department of Mechanical Engineering,
Islamic Azad University,
Semnan Branch,
Semnan 35198, Iran

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received March 11, 2013; final manuscript received May 25, 2015; published online June 30, 2015. Assoc. Editor: Carmen M. Lilley.

J. Comput. Nonlinear Dynam 11(1), 011002 (Jan 01, 2016) (10 pages) Paper No: CND-13-1062; doi: 10.1115/1.4030753 History: Received March 11, 2013; Revised May 25, 2015; Online June 30, 2015

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.

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Fig. 1

Cylindrical shell representation of SWCNT

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Fig. 2

An influence of the nonlocal parameters on the vibration behavior for ξ = 1/4

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Fig. 3

Influence of nonlocal parameter on vibration frequencies ξ = 1/4

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Fig. 4

Influence of nonlocal parameter on vibration frequencies for different amplitudes ξ = 1/4

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Fig. 5

Influence of nonlocal parameter on vibration frequencies for different amplitudes ξ = 4

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Fig. 6

An influence of the nonlinear parameters on the vibration behavior of the nanotubes

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Fig. 7

An influence of the different aspect ratio on vibration behavior for (ξ = (1/2),(1/4))

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Fig. 8

An influence of the different aspect ratio on vibration behavior for (ξ = 2,4)

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Fig. 9

Influence of the length on the nonlocal theory (A¯ = 7)

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Fig. 10

An influence of the different circumferential wave numbers on the vibration behavior



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