Nonlinear dynamics of MEMS arches assuming out-of-plane actuation arrangement

Hassen M. Ouakad*, Fehmi Najar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)


In this work, the nonlinear dynamics of a microbeam shallow arch actuated through an out-of-plane electrostatic force arrangement is investigated. A reduced order model is developed to analyze the static, free vibration, and nonlinear dynamic response of the microstructure under different direct current and alternating current load conditions. A numerical investigation is conducted by comparing the response of the arch near primary and secondary resonances using a nonparallel plates actuation scheme where the arch itself forms a moving electrode. The results show that the nonparallel excitation can be efficient for primary and secondary resonances excitation. Moreover, unlike the classical parallel plates method, where the structure is vulnerable to the dynamic pull-in instability, this nonparallel excitation arrangement can provide large amplitude motion while protecting the structure from the so-called static and dynamic pull-in instabilities. In addition to primary resonance, secondary resonances are demonstrated at twice and one-half the primary resonance frequency. The ability to actuate primary and/or secondary resonances without reaching the dynamic pull-in instability can serve various applications where large strokes increase their performance, such as for resonator-based sensitive mass sensors.

Original languageEnglish
Article number041010
JournalJournal of Vibration and Acoustics, Transactions of the ASME
Issue number4
Publication statusPublished - Aug 1 2019
Externally publishedYes


  • bistability
  • nonlinear response
  • out-of-plane electrostatic force
  • shallow arch

ASJC Scopus subject areas

  • Acoustics and Ultrasonics
  • Mechanics of Materials
  • Mechanical Engineering


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