Internal resonance of vibrational modes in single-walled carbon nanotubes

M. X. Shi, Q. M. Li, Y. Huang

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We show, by molecular dynamics simulations, that 2 :1 internal resonance may occur between a radial breathing mode (RBM) and a circumferential flexural mode (CFM) in single-walled carbon nanotubes (SWCNTs). When the RBM vibration amplitude is greater than a critical value, automatic transformations between the RBM and CFM with approximately half RBM-frequency are observed. This discovery in the discrete SWCNT atom assembly is similar to the 2 :1 internal resonance mechanism observed in continuum shells. A non-local continuum shell model is employed to determine the critical conditions for the occurrence of observed 2 :1 internal resonance between the RBM and CFMs based on two non-dimensional parameters and the Mathieu stability diagram. This journal is

Original languageEnglish (US)
Pages (from-to)3069-3082
Number of pages14
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2110
StatePublished - Oct 8 2009


  • Carbon nanotube
  • Circumferential flexural mode
  • Internal resonance
  • Molecular dynamics
  • Radial breathing mode

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)
  • Physics and Astronomy(all)

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