Static and dynamic behavior of an electrically excited resonant microbeam

Mohammad I. Younis, Eihab M. Abdel-Rahman, Ali H. Nayfeh*

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

33 Scopus citations


We present a nonlinear model of electrically actuated resonators accounting for the electrostatic forcing of the air gap capacitor, the restoring force, and the axial load applied to the microbeam. The boundary-value problem describing the static deflection of the microbeam under the electrostatic loading is solved numerically. The eigenvalue problem describing the vibration of the microbeam around its statically deflected position is solved numerically for the natural frequencies and mode shapes. Comparison of results generated by our model to the experimental results show excellent agreement, thus verifying the model. Our results show that failure to account for mid-plane stretching in the microbeam restoring force leads to an underestimation of the stability limits. They also show that the ratio of the width of the air gap to the microbeam thickness can be tuned to extend the domain of the linear relationship between the DC polarization voltage and the fundamental natural frequency. This fact and the ability of the nonlinear model to predict the natural frequencies accurately for any DC polarization voltage allow designers to use a wider range of DC polarization voltages in resonators.

Original languageEnglish (US)
Pages (from-to)822-830
Number of pages9
JournalCollection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference
StatePublished - 2002
Externally publishedYes
Event43rd Structures, Structural Dynamics and Materials Conference - Denver, CO, United States
Duration: Apr 22 2002Apr 25 2002


  • Electrostatic actuation
  • Microbeam
  • Mid-plane stretching
  • Resonator dynamics

ASJC Scopus subject areas

  • Architecture
  • General Materials Science
  • Aerospace Engineering
  • Mechanics of Materials
  • Mechanical Engineering


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