Nonlinear Dynamics

, Volume 95, Issue 2, pp 1203–1220 | Cite as

Nonlinear dynamics of micromechanical resonator arrays for mass sensing

  • S. BaguetEmail author
  • V.-N. Nguyen
  • C. Grenat
  • C.-H. Lamarque
  • R. Dufour
Original Paper


This paper investigates the mass sensing capability of an array of a few identical electrostatically actuated microbeams, as a first step toward the implementation of arrays of thousands of such resonant sensors. A reduced-order model is considered, and Taylor series are used to simplify the nonlinear electrostatic force. Then, the harmonic balance method associated with the asymptotic numerical method, as well as time integration or averaging methods, is applied to this model, and its results are compared. In this paper, two- and three-beam arrays are studied. The predicted responses exhibit complex branches of solutions with additional loops due to the influence of adjacent beams. Moreover, depending on the applied voltages, the solutions with and without added mass exhibit large differences in amplitude which can be used for detection. For symmetric configurations, the symmetry breaking induced by an added mass is exploited to improve mass sensing.


MEMS Mass sensing Resonator array Nonlinear dynamics Bifurcation Symmetry breaking Electrostatic actuation 



The authors are indebted to the Institute Carnot Ingénierie@Lyon for its support and funding of the NEMROD project.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Univ Lyon, INSA-Lyon, CNRS UMR5259, LaMCoSVilleurbanneFrance
  2. 2.Univ Lyon, ENTPE, CNRS UMR5513, LTDSVaulx-en-VelinFrance

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