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Research Papers

Effects of Axial Load and Elastic Matrix on Flexural Wave Propagation in Nanotube With Nonlocal Timoshenko Beam Model

[+] Author and Article Information
Yi-Ze Wang1

 School of Astronautics, Harbin Institute of Technology, Harbin 150001, P. O. Box 137, P R China;Department of Mechanical Sciences and Engineering,  Tokyo Institute of Technology, 2-12-1, O-okayama, Meguro-ku, Tokyo 152-8552, Japan e-mail: wangyize@gmail.com

Feng-Ming Li1

 School of Astronautics,  Harbin Institute of Technology, Harbin 150001, P. O. Box 137, P R China.e-mail: fmli@hit.edu.cn

Kikuo Kishimoto

Department of Mechanical Sciences and Engineering,  Tokyo Institute of Technology, 2-12-1, O-okayama, Meguro-ku, Tokyo 152-8552, Japan

1

Corresponding authors.

J. Vib. Acoust 134(3), 031011 (Apr 24, 2012) (7 pages) doi:10.1115/1.4005832 History: Received December 13, 2010; Revised September 27, 2011; Published April 23, 2012; Online April 24, 2012

In this paper, the effects of the axial load and the elastic matrix on the flexural wave in the carbon nanotube are studied. Based on the nonlocal continuum theory and the Timoshenko beam model, the equation of the flexural wave motion is derived. The dispersion relation between the frequency and the wave number is illustrated. The characteristics of the flexural wave propagation in the carbon nanotube embedded in the elastic matrix with the axial load are analyzed. The wave frequency and the phase velocity are presented with different wave numbers. Furthermore, the small scale effects on the wave properties are discussed.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 6

Frequency (f) versus scale coefficient (e0 a) under different initial loads for the wave number k = 7 × 108 1/m. (a) Tension load and (b) compression load.

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Figure 7

Phase velocity (cp ) versus scale coefficient (e0 a) under different initial loads for the wave number k = 7 × 108 1/m. (a) Tension load and (b) compression load.

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Figure 8

Influence of the elastic matrix on wave characteristics in the carbon nanotube with the initial load for the wave number k = 3 × 108 1/m. (a) Influence of the elastic matrix on the frequency (f) and (b) influence of the elastic matrix on the phase velocity (cp ).

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Figure 1

Flexural wave propagation in the carbon nanotube embedded in elastic matrix with the axial load.

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Figure 2

Dispersion relation for the flexural wave in the carbon nanotube embedded in the elastic matrix with the axial load. Both the classical Timoshenko and Euler-Bernoulli beam models are considered.

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Figure 3

Dispersion relation for the flexural wave in the carbon nanotube embedded in the elastic matrix with the initial load and different scale coefficients.

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Figure 4

Frequency (f) versus scale coefficient (e0 a) with different wave numbers by the nonlocal Timoshenko beam model.

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Figure 5

Phase velocity (cp ) versus scale coefficient (e0 a) with different wave numbers by the nonlocal Timoshenko beam model.

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