Multiple internal resonances in MEMS arch resonators

A. Z. Hajjaj, N. Jaber, M. A.A. Hafiz, S. Ilyas, M. I. Younis*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

42 Scopus citations


Micromachined shallow arch resonant beams have attracted significant attention thanks to their rich dynamical behavior, inherent nonlinearities, and the potential to excite various internal resonances. Currently, there is a lack of comprehensive experimental studies for the various types of internal resonances in arches and particularly at the micro and nano scales. Here, we aim to investigate and identify different types of internal resonances of an initially curved beam, electrothermally actuated and electrostatically driven, by electrical characterization techniques. Upon changing the electrothermal voltage of silicon micromachined arches, the second symmetric natural frequency of an arch is adjusted to near twice, three times, and four times the fundamental natural frequency, which gives rise to 2:1, 3:1, and 4:1 autoparametric resonances between the two modes. These resonances are demonstrated experimentally. We show various frequency-response curves of the total response around the excitation frequency and highlight the contribution of each mode before, during, and after the internal resonances. Allan-deviation results are also shown indicating enhanced frequency stabilization of the arch oscillation when experiencing internal resonances. These studies motivate further research in this direction to exploit internal resonances of micromachined resonators for practical applications, such as sensors and mechanical amplifier.

Original languageEnglish (US)
Pages (from-to)3393-3398
Number of pages6
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Issue number47
StatePublished - Nov 30 2018


  • Electrothermal and electrostatic actuation
  • Internal resonance
  • Micromachined arch resonator
  • Nonlinearity

ASJC Scopus subject areas

  • General Physics and Astronomy


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