A double-side electrically-actuated arch microbeam for pressure sensing applications

In this study, we consider a pressure sensor whose main component is a clamped-clamped shallow arched microbeam. Two fixed electrodes are used to actuate the microbeam in the transverse direction. The lower electrode is powered by a combination of DC and AC voltages sources to excite the microbeam (drive mode). The upper electrode is polarized with a DC voltage and used to detect the change in the capacitance resulting from the transverse vibrations of the microbeam (sense mode). We formulate a fully-coupled multi-physics model of the electrically-actuated shallow arch microbeam combining the nonlinear Euler-Bernoulli beam theory with the nonlinear Reynolds equation governing the surrounding fluid domains (drive and sense zones). The model captures the inherent nonlinear physical aspects including the mid-plane stretching, the squeeze film damping, and fringing field effect. We validate the developed model by quantitatively comparing our nonlinear frequency-response against existing experimental results. We conduct static analysis to identify the occurrence of snap-through and pull-in instability for different initial midpoint rises. The coupled eigenvalue problem is also solved to compute the damped natural frequencies along with their corresponding beam and fluid mode shapes. The obtained natural frequencies are in good agreement with those reported in the literature. High sensitivity of the natural frequency to pressure variations is observed when decreasing the gap distance separating the microbeam from the fixed electrodes and reducing the initial midpoint rise of the curved microbeam. We also investigate the effect of breaking the symmetry of the microstructure on its dynamic response by introducing a slight perturbation in the mass distribution. The stability analysis reveals the occurrence of a new period doubling bifurcation point. Of interest, the location of this bifurcation point is observed to be sensitive to the pressure of the surrounding fluid medium. As such, we propose to exploit this nonlinear feature for design enhancement of the pressure sensor.