On Sampling Rate Limits in Bistable Microbeam Sensors

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Bifurcation-based sensors, implementing stability boundaries monitoring in bistable microstructures, may manifest higher sensitivity and robustness when compared to their statically operated counterparts. In the operation of these devices, two key questions arise: 1) how to reliably identify the critical events associated with the transition between two stable states; 2) what is the maximal sampling rate allowing to identify these critical events in a periodically actuated device. Motivated by the potential implementation as a bifurcation-based flow sensor, in this work we experimentally explore the transient snap-through (ST) and snap-back (SB) dynamics of a bistable initially curved ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$500 \,\mu \text{m}$ </tex-math></inline-formula> long and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2.5\, \mu \text{m}$ </tex-math></inline-formula> wide) electrostatically actuated single-crystal Si microbeam. We employ a threshold-based approach for the ST and SB events detection and identify two mechanisms determining the maximal sampling frequency of the device: a phase lag between the voltage signal and the mechanical response and free decaying vibrations following the buckling event. In accordance with our experimental results and consistently with the reduced-order model predictions for the bistable beam operating at atmospheric pressure, at the actuation signal frequency of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\approx 0.6$ </tex-math></inline-formula> KHz, which is still much lower than the beam’s natural frequency of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\approx 110 $ </tex-math></inline-formula> KHz, the free oscillations engendered by one critical event (ST or SB) interfere with the consecutive one, preceding its emergence. On the other hand, an inherent phase lag ultimately hinders the abrupt ST and SB transitions at these actuating frequencies. [2021-0091]