# Parametric Resonance of Electrostatically Actuated MEMS Angled Uniform Cantilever Resonators: Amplitude-Frequency Response

## Document Type

Conference Proceeding

## Publication Date

4-11-2024

## Abstract

This paper deals with amplitude-frequency response of parametric resonance of electrostatically actuated microelectromechanical system (MEMS) uniform cantilever resonators. The model consists of an elastic cantilever beam positioned at an angle relative to a ground plate. They are not parallel. There is an initial gap distance between the beam and the plate. Alternating current (AC) at frequency near natural frequency of the MEMS resonator produces an electrostatic force that leads to parametric resonance. The electrostatic force, which includes the fringe effect, is nonlinear, while the viscous damping force is linear. The amplitude-frequency response consists of two bifurcations, namely subcritical and supercritical. The effect of the angle between the beam and the ground plate, and the effect of the ratio of the beam length to the gap length, on the amplitude-frequency response of the system are investigated. A comparison, amplitude-frequency response of parallel beam versus amplitude-frequency response of angled beam, is reported. Two methods, the Method of Multiple Scales (MMS) and Reduced Order Model (ROM), are used in this work. For small amplitudes, the predictions of the two methods are in agreement. However, MMS is only accurate for small amplitudes, while ROM, given a sufficient number of terms, is accurate for all amplitudes. The results show that as the angle between the MEMS cantilever beam and ground plate increases, the amplitude-frequency response is shifted to higher frequencies and amplitudes. A sufficiently large angle results in the disappearance of the subcritical and supercritical bifurcation points, and the appearance of a saddle-node bifurcation. A larger length-to-gap ratio amplifies the effect of the angle on the response.

## Recommended Citation

Caruntu, D.I., Huerta, B.M. (2024). Parametric Resonance of Electrostatically Actuated MEMS Angled Uniform Cantilever Resonators: Amplitude-Frequency Response. In: Herisanu, N., Marinca, V. (eds) Acoustics and Vibration of Mechanical Structures—AVMS-2023. AVMS 2023. Springer Proceedings in Physics, vol 302. Springer, Cham. https://doi.org/10.1007/978-3-031-48087-4_1

## Publication Title

Springer Proceedings in Physics, vol 302

## DOI

10.1007/978-3-031-48087-4_1

## Comments

© 2024 The Author(s), under exclusive license to Springer Nature Switzerland AG.

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