Complex nonlinear oscillations in electrostatically actuated microstructures

Sudipto K. De, N. R. Aluru

Research output: Contribution to journalArticlepeer-review


In this paper, new nonlinear dynamic properties of electrostatically actuated microstructures [referred to as electrostatic microelectromechanical systems (MEMS)] observed under superharmonic excitations are presented using numerical simulations. Application of a large dc bias (close to the pull-in voltage of the device) is found to bring the device to a nonlinear state. This nonlinear state (referred to as "dc-symmetry breaking") can be clearly observed from the characteristic change in the phase-plot of the device. Once a steady nonlinear state is reached, application of an ac signal at the Mth superharmonic frequency with an amplitude around "ac-symmetry breaking" gives rise to M oscillations per period or M-cycles in the MEM device. "ac-symmetry breaking" can also be observed by a characteristic change in the phase-plot of the device. On further increasing the ac voltage, a period doubling sequence takes place resulting in the formation of 2n M-cycles in the system at the Mth superharmonic frequency. An interesting chaotic transition (banded chaos) is observed during the period doubling bifurcations. The nonlinear nature of the electrostatic force acting on the MEM device is found to be responsible for the reported observations. The significance of the mechanical and the fluidic nonlinearities is also studied.

Original languageEnglish (US)
Pages (from-to)355-369
Number of pages15
JournalJournal of Microelectromechanical Systems
Issue number2
StatePublished - Apr 2006
Externally publishedYes


  • Chaos
  • Complex oscillations
  • Microelectromechanical systems (MEMS)
  • Nonlinear dynamics
  • Period doubling
  • Superharmonic excitation

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Mechanical Engineering


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