Mechanical Engineering Faculty Publications

Models of Electrostatically Fringe Field Actuated MEMS Resonators: Voltage-Amplitude Response of Parametric Resonance

Document Type

Conference Proceeding

Publication Date

11-16-2025

Abstract

This paper deals with the voltage–amplitude response of parametric resonance of micro-electromechanical system (MEMS) cantilever beam resonators actuated solely by fringing electrostatic fields. The system comprises a micro cantilever beam positioned parallel to a ground plate, connected via an AC voltage source which leads to electrostatic actuation. The ground plate has a hole allowing the cantilever beam deflections larger than the gap and therefore eliminating the pull-in phenomenon. A fringing field capacitance model (based on Sakurai’s empirical formula) is used in this work and compared to a more traditional fringing field model based on Palmer’s formula. The fringing field is the electric field between the ground plate and the beam’s top and sidewalls. In both models, due to the configuration of the ground plate with a hole, the parallel-plate capacitance is removed, so only the fringe field actuation is considered. For parametric resonance, the AC voltage frequency is near the resonator’s natural frequency. A nondimensionalized partial differential equation governing the system is reduced to a single-mode Reduced Order Model (ROM), which is then analytically solved using the Method of Multiple Scales (MMS). The resulting voltage–amplitude bifurcation diagram reveals a trivial solution and two branches, one stable and one unstable, emerging from super- and subcritical bifurcation points. A two-mode ROM is also developed and solved numerically to verify these findings, and the resulting equations are implemented in AUTO-07p (a continuation and bifurcation analysis software) to obtain further voltage response data. Fringing field capacitance model predictions are compared against fringing field model based on Palmer’s formula predictions, and against the case of ground plate with no hole modeled by Palmer’s formula.

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© 2025 The Author(s), under exclusive license to Springer Nature Switzerland AG.

https://rdcu.be/e1v7i

Publication Title

Acoustics and Vibration of Mechanical Structures—AVMS-2025

DOI

10.1007/978-3-032-10786-2_2

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