Investigation of the dynamics of a clamped–clamped microbeam near symmetric higher order modes using partial electrodes

Karim M. Masri*, Mohammad I. Younis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We present an investigation of the dynamics of a clamped–clamped microbeam excited electrostatically near its third and fifth natural frequencies. We study the effect of partial electrodes on the static and dynamic response of the beam. Different lower electrode configurations are utilized. A new concept of the divided lower electrode and its actuation with voltage sources of various phase shifts is introduced. A multi-mode Galerkin method is used to develop a reduced order model of the beam. Shooting and longtime integration methods are used to find the periodic motion and to generate frequency response curves. The curves show hardening behavior and dynamic pull-in. We show that the dynamic amplitude of the divided lower electrode, actuated with two voltage sources with phase shift, is higher than actuating the full electrode with one voltage source. These results are promising for the use of higher-order modes for mass detection and for ultra-sensitive resonant sensors.

Original languageEnglish (US)
Pages (from-to)173-182
Number of pages10
JournalInternational Journal of Dynamics and Control
Issue number2
StatePublished - Jun 1 2015

Bibliographical note

Publisher Copyright:
© 2015, Springer-Verlag Berlin Heidelberg.


  • Electrostatic forces
  • Higher order modes
  • Nonlinear dynamics
  • Partial electrodes
  • Resonators

ASJC Scopus subject areas

  • Mechanical Engineering
  • Control and Optimization
  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Civil and Structural Engineering
  • Modeling and Simulation


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