Nonlinear vibration and bending instability of a single-walled carbon nanotube using nonlocal elastic beam theory

I Mehdipour, Payam Soltani, DD Ganji, Anoshirvan Farshidianfar

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Due to the nonlocal Euler–Bernoulli elastic beam theory, the effects of rippling deformation on the bending modulus and the structural bending instability of a single-walled carbon nanotube (SWCNT) are investigated. The nonlinear vibrational model of a cantilevered SWCNT is solved using the perturbation method of multiscales. The nonlinear resonant frequency and the associated effective bending modulus of the carbon nanotube (CNT) are derived analytically. The effects of the nonlocal parameter, the external harmonic force, and the diameter-to-length ratio on the effective bending modulus are discussed widely. Moreover, the model can predict special kind of structural instability due to the rippling deformation called rippling instability. The results show that the nonlocal theory forecasts larger values for the effective bending modulus compared with the classical beam theory, especially for the stubby CNTs. Meanwhile, the rippling instability threshold will move to the higher values of the diameter-to-length ratio based on the nonlocal beam theory comparing with the local ones.
Original languageEnglish
Pages (from-to)447-453
Number of pages7
JournalInternational Journal of Nanoscience
Volume10
Issue number03
DOIs
Publication statusPublished - 2011

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carbon nanotubes
vibration
forecasting
resonant frequencies
harmonics
perturbation
thresholds

Keywords

  • Carbon nanotubes
  • nonlinear vibration
  • rippling deformation
  • bending instability

Cite this

Nonlinear vibration and bending instability of a single-walled carbon nanotube using nonlocal elastic beam theory. / Mehdipour, I; Soltani, Payam; Ganji, DD; Farshidianfar, Anoshirvan.

In: International Journal of Nanoscience, Vol. 10, No. 03, 2011, p. 447-453.

Research output: Contribution to journalArticle

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AU - Soltani, Payam

AU - Ganji, DD

AU - Farshidianfar, Anoshirvan

PY - 2011

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AB - Due to the nonlocal Euler–Bernoulli elastic beam theory, the effects of rippling deformation on the bending modulus and the structural bending instability of a single-walled carbon nanotube (SWCNT) are investigated. The nonlinear vibrational model of a cantilevered SWCNT is solved using the perturbation method of multiscales. The nonlinear resonant frequency and the associated effective bending modulus of the carbon nanotube (CNT) are derived analytically. The effects of the nonlocal parameter, the external harmonic force, and the diameter-to-length ratio on the effective bending modulus are discussed widely. Moreover, the model can predict special kind of structural instability due to the rippling deformation called rippling instability. The results show that the nonlocal theory forecasts larger values for the effective bending modulus compared with the classical beam theory, especially for the stubby CNTs. Meanwhile, the rippling instability threshold will move to the higher values of the diameter-to-length ratio based on the nonlocal beam theory comparing with the local ones.

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