Effects of a small length scale on vibrations of anembedded double-walled carbon nanotube

H. Dalir, S. Sh Amin, A. Farshidianfar

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Extensive continuum analyses are carried out to estimate the influence of matrix stiffness, a small length scale, and intertubular radial displacements on free vibrations of an individual double-walled carbon nanotybe. The analyses are based on both local and classical Euler-Bernoulli and Timoshenko elasticity theories with concentricity and nonconcentricity assumptions. The effect of a small length scale is incorporated in the formulations. New intertubular resonant frequencies are calculated based on these theories. Detailed results are demonstrated for the resonant frequencies as functions of matrix stiffness and the small length scale. The results in dicate that the internal radial dis placement and the stiffness of the surrounding matrix cangreatly affect the resonant frequencies, especially at higher frequencies, and thus the latter does not keep the otherwise concentric structure at ultrahigh frequencies. Moreover, at high frequencies and small aspect ratios, the effect of the small length scale becomes more significant.

Original languageEnglish (US)
Pages (from-to)557-566
Number of pages10
JournalMechanics of Composite Materials
Issue number6
StatePublished - Nov 2009


  • Double-walled carbon nanotube
  • Matrix stiffness
  • Nonlocal continuum models
  • Radial displacement
  • Small length scale

ASJC Scopus subject areas

  • Ceramics and Composites
  • Biomaterials
  • General Mathematics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Polymers and Plastics


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