Natural Frequencies and Modes of Electrostatically Actuated Curved Bell-Shaped Microplates

Asaf Asher, Rivka Gilat, Slava Krylov

Research output: Contribution to journalArticlepeer-review


Configuration-dependent spectral behavior of initially curved circular microplates loaded by a distributed nonlinear electrostatic force is investigated. The structures under consideration are distinguished by two interesting features. The first is that the plates are initially bell-shaped, rather than flat or spherical, and therefore have regions of both positive and negative curvature. Second, the plates are sufficiently curved to exhibit snap-through buckling and bistability. The structure is described in the framework of the nonlinear Föppl von Kármán shallow plate theory. The influence of the initial curvature and loading on the free vibrations around unloaded and deformed equilibria is investigated. The results of the Galerkin model backed by the finite elements analysis show that the modes of even slightly curved bell-shaped unloaded plates differ significantly from those of the initially flat plates. As a result, when the natural modes of a curved plate are used as the base functions, a significantly better convergence of the RO model is achieved. In the vicinity of the critical snap-through and snap-back configurations, the sensitivity of the natural frequencies to the plate deflection is much higher than in the unloaded state. This high tunability opens new opportunities for the design of better resonant sensors with enhanced performance.

Original languageEnglish
Article number2704
JournalApplied Sciences (Switzerland)
Issue number5
StatePublished - 1 Mar 2022


  • Bistability
  • Curved micro-plate
  • Frequency tunability
  • MEMS
  • Reducedorder modeling
  • Snap-through


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