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Nonlinear vibration and rippling instability for embedded carbon nanotubes

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Abstract

Based on the rippling deformations, a nonlinear continuum elastic model is developed to analyze the transverse vibration of single-walled carbon nanotubes (SWCNTs) embedded on a Winkler elastic foundation. The nonlinear natural frequency has been derived analytically for typical boundary conditions using the perturbation method of multi-scales. The results indicate that the nonlinear resonant frequency due to the rippling is related to the stiffness of the foundation, the boundary conditions, the excitation load-to-damping ratio, and the diameter-to-length ratio. Moreover, the rippling instability of carbon nanotubes, as a structural instability, is introduced and the influences of several effective parameters on this kind of instability are widely discussed.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Semnan Branch, Islamic Azad University, Semnan, Iran

    Payam Soltani & I. Mehdipour

  2. Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran

    A. Farshidianfar

  3. Department of Mechanical Engineering, Babol University of Technology, Babol, Iran

    D. D. Ganji

Authors
  1. Payam Soltani
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  2. D. D. Ganji
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  3. I. Mehdipour
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  4. A. Farshidianfar
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Corresponding author

Correspondence to Payam Soltani.

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Recommended by Associate Editor Cheolung Cheong

Payam Soltani received his Ph.D in mechanical engineering from Ferdowsi University of Mashhad. He works currently as a faculty member of the mechanical department at IAU — Semnan branch, Iran. His research interests include nanomechanics, nanobiotechnology, nonlinear vibrations, and computational mechanics.

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Soltani, P., Ganji, D.D., Mehdipour, I. et al. Nonlinear vibration and rippling instability for embedded carbon nanotubes. J Mech Sci Technol 26, 985–992 (2012). https://doi.org/10.1007/s12206-011-1006-7

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  • DOI: https://doi.org/10.1007/s12206-011-1006-7

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