A reduced-order model for electrically actuated microbeam-based MEMS

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

601 Scopus citations


We present an analytical approach and a reduced-order model (macromodel) to investigate the behavior of electrically actuated microbeam-based MEMS. The macromodel provides an effective and accurate design tool for this class of MEMS devices. The macromodel is obtained by discretizing the distributed-parameter system using a Galerkin procedure into a finite-degree-of-freedom system consisting of ordinary-differential equations in time. The macromodel accounts for moderately large deflections, dynamic loads, and the coupling between the mechanical and electrical forces. It accounts for linear and nonlinear elastic restoring forces and the nonlinear electric forces generated by the capacitors. A new technique is developed to represent the electric force in the equations of motion. The new approach allows the use of few linear-undamped mode shapes of a microbeam in its straight position as basis functions in a Galerkin procedure. The macromodel is validated by comparing its results with experimental results and finite-element solutions available in the literature. Our approach shows attractive features compared to finite-element softwares used in the literature. It is robust over the whole device operation range up to the instability limit of the device (i.e., pull-in). Moreover, it has low computational cost and allows for an easier understanding of the influence of the various design parameters. As a result, it can be of significant benefit to the development of MEMS design software.

Original languageEnglish (US)
Pages (from-to)672-680
Number of pages9
JournalJournal of Microelectromechanical Systems
Issue number5
StatePublished - Oct 2003
Externally publishedYes


  • Capacitive microswitches
  • Microelectromechanical systems (MEMS)
  • Pressure sensors
  • Pull-in time
  • Reduced-order models

ASJC Scopus subject areas

  • Mechanical Engineering
  • Electrical and Electronic Engineering


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