Dynamics and global stability of beam-based electrostatic microactuators

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

Research output: Contribution to journalArticle

46 Citations (Scopus)

Abstract

We investigate the dynamics and global stability of a beam-based electrostatic microactuator, which is modeled as a first-order approximation of a reduced-order model (ROM) derived using the differential quadrature method (DQM). We show that the ROM dynamics is qualitatively similar to that of a higher-order approximation. We simulate the occurrence of dynamic pull-in for excitations near the first primary resonance using the finite difference method (FDM) and long-time integration. Limit-cycle solutions are obtained using the FDM, the generated frequency- and force-response curves exhibit cyclic-fold, saddle-node, and period-doubling bifurcations. We verify that symmetry breaking is not likely to occur because the orbit is already asymmetric. We identify the basin of attraction of bounded motions using various approximation levels. The simulations reveal that the erosion of the basin of attraction depends heavily on the amplitude and frequency of the AC voltage. We show that smoothness of the boundary of the basin of attraction can be lost and replaced by fractal tongues, which dramatically increase the sensitivity of the microbeam to initial conditions. According to these simulations, the locations of the two fixed points are likely to be disturbed.

Original languageEnglish
Pages (from-to)721-748
Number of pages28
JournalJVC/Journal of Vibration and Control
Volume16
Issue number5
DOIs
Publication statusPublished - Apr 2010
Externally publishedYes

Fingerprint

Microactuators
Finite difference method
Electrostatics
Fractals
Erosion
Dynamic models
Orbits
Electric potential

Keywords

  • Bifurcation
  • Chaos
  • Global stability
  • Microactuator
  • Microelectromechanical systems

ASJC Scopus subject areas

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

Cite this

Dynamics and global stability of beam-based electrostatic microactuators. / Najar, F.; Nayfeh, A. H.; Abdel-Rahman, E. M.; Choura, S.; El-Borgi, Sami.

In: JVC/Journal of Vibration and Control, Vol. 16, No. 5, 04.2010, p. 721-748.

Research output: Contribution to journalArticle

Najar, F. ; Nayfeh, A. H. ; Abdel-Rahman, E. M. ; Choura, S. ; El-Borgi, Sami. / Dynamics and global stability of beam-based electrostatic microactuators. In: JVC/Journal of Vibration and Control. 2010 ; Vol. 16, No. 5. pp. 721-748.
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