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TECHNICAL PAPERS

# Vibration Characteristics of Multiwalled Carbon Nanotubes Embedded in Elastic Media by a Nonlocal Elastic Shell Model

[+] Author and Article Information
Renfu Li, George A. Kardomateas

Georgia Institute of Technology, Atlanta, GA 30332-0150

J. Appl. Mech 74(6), 1087-1094 (Jan 02, 2007) (8 pages) doi:10.1115/1.2722305 History: Received March 11, 2006; Revised January 02, 2007

## Abstract

In this paper, the vibrational behavior of the multiwalled carbon nanotubes (MWCNTs) embedded in elastic media is investigated by a nonlocal shell model. The nonlocal shell model is formulated by considering the small length scales effects, the interaction of van der Waals forces between two adjacent tubes and the reaction from the surrounding media, and a set of governing equations of motion for the MWCNTs are accordingly derived. In contrast to the beam models in the literature, which would only predict the resonant frequencies of bending vibrational modes by taking the MWCNT as a whole beam, the current shell model can find the resonant frequencies of three modes being classified as radial, axial, and circumferential for each nanotube of a MWCNT. Big influences from the small length scales and the van der Waals’ forces are observed. Among these, noteworthy is the reduction in the radial frequencies due to the van der Waals’ force interaction between two adjacent nanotubes. The numerical results also show that when the spring constant $k0$ of the surrounding elastic medium reaches a certain value, the lowest resonant frequency of the double walled carbon nanotube drops dramatically.

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## Figures

Figure 5

The variation of the frequencies versus (m,n)

Figure 1

A shell model of multiwalled nanotubes in an elastic medium

Figure 2

Variation of frequencies with the aspect ratio, L∕R2

Figure 3

Variation of frequencies with the ratio of thickness over distance between the nanotubes, h∕(R2−R1)

Figure 4

The influence of the internal characteristic parameter, aeo of the DWCNTs

Figure 6

The influence on the frequencies of the stiffness of the surrounding medium, k0 versus (m,n=1)

Figure 7

The influence on the frequencies of the stiffness of the surrounding medium, k0 versus (m,n=2)

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