Abstract
We investigate the potential of electrostatic initially curved microbeams to serve as bifurcation gas sensors. Toward that end, we develop static and dynamic reduced-order models of those beams and investigate their nonlinear response. Unlike many models, ours takes into account naturally occurring asymmetries present in fabricated microbeams. We conduct a detailed analysis of the nonlinear dynamics of arch beams focused on their exploitation for inertial sensing applications. The static response reveals that accounting for asymmetry replaces the saddle-node bifurcation, where snap-back occurs, with a symmetry-breaking bifurcation and reduced the voltage range for bistability. The dynamic analysis shows that a symmetry-breaking bifurcation precludes dynamic snap-through in the vicinity of superharmonic resonance, thereby significantly reducing the amplitude of those oscillations. It also shows evidence of a period-doubling bifurcation route to chaos in the vicinity of primary resonance. Based on these findings, we present a novel phase-based bifurcation gas sensor. The proposed detection mechanism allows, for the first time, the use of transition from regular periodic to chaotic motions in inertial sensing of gases. The sensor operation point is set close to the cyclic-fold bifurcation in the vicinity of primary resonance. When mass added by gas immobilization on the detector layer exceeds a threshold, the sensor oscillations abruptly transition from regular periodic motions to chaotic motions. This change can be detected by monitoring the response phase angle as it undergoes a major shift from slow variation within a limited range to fast variation over the full range due to the stretching and folding of the chaotic attractor. The proposed detection mechanism allows the sensor to operate in binary (digital) and analog modes. This is achieved by evaluating the RMS of the response phase angle (phi) over bar and using it to either detect a gas concentration in excess of a safe threshold as an abrupt jump in (phi) over bar over bar or via a calibration curve relating (phi) over bar to the gas concentration. The minimum detectable mass of the sensor is found to be 120 pg.