Internal resonance of vibrational modes in single-walled carbon nanotubes

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

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

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
Volume465
Issue number2110
DOIs
StatePublished - Oct 8 2009

Fingerprint

Internal Resonance
Single-walled Carbon Nanotubes
Single-walled carbon nanotubes (SWCN)
breathing
vibration mode
carbon nanotubes
Shell Model
Continuum Model
Molecular Dynamics Simulation
Critical value
Molecular dynamics
Shell
Continuum
Diagram
continuums
Atoms
Computer simulation
assembly
diagrams
occurrences

Keywords

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

ASJC Scopus subject areas

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

Cite this

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abstract = "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",
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Internal resonance of vibrational modes in single-walled carbon nanotubes. / Shi, M. X.; Li, Q. M.; Huang, Yonggang.

In: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 465, No. 2110, 08.10.2009, p. 3069-3082.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Internal resonance of vibrational modes in single-walled carbon nanotubes

AU - Shi, M. X.

AU - Li, Q. M.

AU - Huang, Yonggang

PY - 2009/10/8

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N2 - 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

AB - 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

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KW - Internal resonance

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