Crossover/Veering in V-Shaped MEMS Resonators

Nouha Alcheikh*, Hassen M. Ouakad, Sofiane Ben Mbarek, Mohammad I. Younis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


We investigate experimentally and theoretically mode crossing and mode veering between the first two symmetric and anti-symmetric modes of an electrothermally and electrostatically actuated in-plane V-shaped micro-beam. The micro-beam is sandwiched between four electrodes to electrostatically activate both modes of vibrations and to offer various actuation options. When tuning the electrothermal voltage, the natural frequencies of the two modes approach each other until they cross. Under an asymmetrical electrostatic actuation, it is shown experimentally that the system undergoes a transition between modes crossing to veering. In addition, an analytical study is presented based on a Galerkin-based reduced-order model of a nonlinear Euler-Bernoulli shallow arch beam equation. The analytical results are compared to experimental data showing excellent agreement. The effects of the shape profile, Cosine and Arc, and micro-beam length are theoretically investigated on the transition between the crossing and veering behavior for the first four vibration modes.

Original languageEnglish
Pages (from-to)74-86
Number of pages13
JournalJournal of Microelectromechanical Systems
Issue number1
Publication statusPublished - Feb 1 2022


  • V-
  • cosine-and arc-shaped micro-resonators
  • crossover and veering phenomenon
  • electrothermal and electrostatic actuations

ASJC Scopus subject areas

  • Mechanical Engineering
  • Electrical and Electronic Engineering


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