Snap-Through and Pull-In Instabilities of an Arch-Shaped Beam Under an Electrostatic Loading

TLDR

Pull‑in instability limits displacement by causing collision with the electrode, and while flat‑initial beams experience only pull‑in, arch‑shaped beams can exhibit either pull‑in alone or both snap‑through and pull‑in instabilities. The study investigates the snap‑through and pull‑in instabilities of micromachined arch‑shaped beams under electrostatic loading through theoretical analysis and experiments. The authors analyze snap‑through by applying a fixed electrostatic load that induces a discontinuous displacement jump without power consumption, and compare this behavior to pull‑in instability. Snap‑through arch‑shaped beams achieve larger maximum displacement than pull‑in‑only or flat‑initial beams, can tolerate additional electrostatic loading without pull‑in, and offer power‑free operation and an expanded deflection range beneficial for MEMS design.

Abstract

The snap-through and pull-in instabilities of the micromachined arch-shaped beams under an electrostatic loading are studied both theoretically and experimentally. The pull-in instability that results in a system collision with an electrode substrate may lead to a system failure and, thus, limits the system maximum displacement. The beam/plate structure with a flat initial configuration under an electrostatic loading can only experience the pull-in instability. With the different arch configurations, the structure may experience either only the pull-in instability or the snap-through and pull-in instabilities together. As shown in our computation and experiment, those arch-shaped beams with the snap-through instability have the larger maximum displacement compared with the arch-shaped beams with only the pull-in stability and those with the flat initial configuration. The snap-through occurs by exerting a fixed load, and the structure experiences a discontinuous displacement jump without consuming power. Furthermore, after the snap-through jump, the structures are demonstrated to have the capacity to withstand further electrostatic loading without pull-in. Those properties of consuming no power and increasing the structure deflection range without pull-in is very useful in microelectromechanical systems design, which can offer better sensitivity and tuning range.