Nonlinear analysis of MEMS electrostatic microactuators: Primary and secondary resonances of the first mode

F. Najar, A. H. Nayfeh, E. M. Abdel-Rahman, S. Choura, Sami El-Borgi

Research output: Contribution to journalArticle

49 Citations (Scopus)


We use a discretization technique that combines the differential quadrature method (DQM) and the finite difference method (FDM) for the space and time, respectively, to study the dynamic behavior of a microbeam-based electrostatic microactuator. The adopted mathematical model based on the Eulerĝ€ " Bernoulli beam theory accounts for the system nonlinearities due to mid-plane stretching and electrostatic force. The nonlinear algebraic system obtained by the DQMĝ€"FDM is used to investigate the limit-cycle solutions of the microactuator. The stability of these solutions is ascertained using Floquet theory and/or long-time integration. The method is applied for large excitation amplitudes and large quality factors for primary and secondary resonances of the first mode in case of hardening-type and softening-type behaviors. We show that the combined DQMĝ€"FDM technique improves convergence of the dynamic solutions. We identify primary, subharmonic, and superharmonic resonances of the microactuator. We observe the occurrence of dynamic pull-in due to subharmonic and superharmonic resonances as the excitation amplitude is increased. Simultaneous resonances of the first and higher modes are identified for large orbits in both primary and secondary resonances.

Original languageEnglish
Pages (from-to)1321-1349
Number of pages29
JournalJVC/Journal of Vibration and Control
Issue number9
Publication statusPublished - Aug 2010
Externally publishedYes



  • Differential quadrature method
  • Finite difference method
  • Microactuator
  • Microelectromechanical systems
  • Secondary resonance
  • Simultaneous resonance

ASJC Scopus subject areas

  • Materials Science(all)
  • Automotive Engineering
  • Aerospace Engineering
  • Mechanics of Materials
  • Mechanical Engineering

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