Parametric resonance and pattern selection in an array of microcantilevers interacting through fringing electrostatic fields

Nir Dick, Slava Krylov

Research output: Contribution to journalArticlepeer-review

Abstract

We investigate collective resonant dynamics of an array of microcantilevers coupled elastically, through a flexible overhang, and electrostatically, through fringing fields. Time-harmonic modulation of the effective coupling stiffness parameterized by voltage results in excitation of the parametric resonance accompanied by modal pattern switching during an actuating signal frequency sweep. Using the two-stage Galerkin projection, the equations governing the array’s dynamics are reduced to two nonlinearly coupled Mathieu–Duffing equations, which are then analyzed numerically and asymptotically. At sufficiently high actuating voltages, the regions of the parametric resonance associated with different modes of the array overlap, resulting in an abrupt switching between the modes previously observed in the experiments.

Original languageEnglish
Pages (from-to)1703-1723
Number of pages21
JournalNonlinear Dynamics
Volume107
Issue number2
DOIs
StatePublished - Jan 2022

Keywords

  • Cantilevers array
  • Electrostatic coupling
  • MEMS
  • Parametric resonance
  • Pattern selection
  • Reduced-order modeling

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