Dynamic response of slacked single-walled carbon nanotube resonators

Hassen M. Ouakad, Mohammad I. Younis*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

46 Scopus citations


This paper presents an investigation of the dynamics of electrically actuated single-walled carbon nanotube (CNT) resonators including the effect of their initial curvature due to fabrication (slack). A nonlinear shallow arch model is utilized. A perturbation method, the method of multiple scales, is used to obtain analytically the forced vibration response due to DC and small AC loads for various slacked CNTs of higher and lower aspect ratio. Results of the perturbation method are verified with those obtained by numerically integrating the equations of a multi-mode reduced-order model based on the Galerkin procedure. The effective nonlinearity of the CNT is calculated as a function of the slack level and the DC load. To handle computational problems associated with CNTs of small radiuses, results based on a nonlinear cable model are also demonstrated. The results have indicated that the quadratic nonlinearity due to slack has dominant effect on the dynamic behavior of the CNT.

Original languageEnglish (US)
Pages (from-to)1419-1436
Number of pages18
JournalNonlinear Dynamics
Issue number2
StatePublished - Jan 2012
Externally publishedYes


  • Arch
  • Carbon nanotube
  • Effective nonlinearity
  • Hardening
  • NEMS
  • Resonator
  • Softening

ASJC Scopus subject areas

  • Mechanical Engineering
  • Aerospace Engineering
  • Ocean Engineering
  • Applied Mathematics
  • Electrical and Electronic Engineering
  • Control and Systems Engineering


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