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Chaotic behavior of a curved carbon nanotube under harmonic excitation

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  • Mayoof, Fathi N.
  • Hawwa, Muhammad A.

Abstract

Nonlinear vibration of a carbon nanotube with waviness along its axis is investigated. The carbon nanotube having a single wall and that is doubly clamped at a source and a drain is used to represent a single-mode resonator. The problem is formulated on the basis of the elastic continuum mechanics theory, where the carbon nanotube is modeled as a harmonically excited beam under a transverse force. The equation of motion involves a quadratic and cubic terms due to the curved geometry and the mid-plane stretching. The dynamics response of the resonator is analyzed in the context of the bifurcation theory. Noteworthy is the nonlinear effect of period doubling turning to chaos.

Suggested Citation

  • Mayoof, Fathi N. & Hawwa, Muhammad A., 2009. "Chaotic behavior of a curved carbon nanotube under harmonic excitation," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1860-1867.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:3:p:1860-1867
    DOI: 10.1016/j.chaos.2009.03.104
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    References listed on IDEAS

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    1. Vera Sazonova & Yuval Yaish & Hande Üstünel & David Roundy & Tomás A. Arias & Paul L. McEuen, 2004. "A tunable carbon nanotube electromechanical oscillator," Nature, Nature, vol. 431(7006), pages 284-287, September.
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    Cited by:

    1. Wang, Zhen & Hu, Weipeng, 2021. "Resonance analysis of a single-walled carbon nanotube," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Zhang, Shenghai & Luo, Shaohua & He, Shaobo & Ouakad, Hassen M., 2022. "Analog circuit implementation and adaptive neural backstepping control of a network of four Duffing-type MEMS resonators with mechanical and electrostatic coupling," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).

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