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TRANSITION TO CHAOS IN A CURVED CARBON NANOTUBE UNDER HARMONIC EXCITATION

YIXIANG GENG

Department of Engineering Mechanics, Kunming University of Science and Technology, Kunming, Yunnan 650051, China

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and

LIXIANG ZHANG

Department of Engineering Mechanics, Kunming University of Science and Technology, Kunming, Yunnan 650051, China

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https://doi.org/10.1142/S0217979212502104Cited by:4 (Source: Crossref)

Abstract

The chaotic behavior of a carbon nanotube with waviness along its axis is investigated. The equation of motion involves a quadratic and cubic terms due to the curved geometry and the mid-plane stretching. Melnikov method is applied for the system, and Melnikov criterion for global homoclinic bifurcations is obtained analytically. The numerical solution of the system using a fourth-order-Runge–Kutta method confirms the analytical predictions and shows that the transition from regular to chaotic motion is often associated with increasing the energy of an oscillator. Moreover, a detailed numerical study of the periodic attractor in the period window is also carried out.

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