Abstract 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.

中文翻译：

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用于压力传感应用的双侧电动拱形微梁

摘要 在本研究中，我们考虑了一种压力传感器，其主要部件是夹夹式浅拱形微梁。两个固定电极用于在横向上驱动微束。下电极由直流和交流电压源的组合供电以激发微束（驱动模式）。上电极用直流电压极化，用于检测微束横向振动引起的电容变化（感测模式）。我们将非线性 Euler-Bernoulli 梁理论与控制周围流体域（驱动和传感区）的非线性雷诺方程相结合，制定了电驱动浅拱微梁的全耦合多物理场模型。该模型捕获了固有的非线性物理方面，包括中平面拉伸、挤压膜阻尼和边缘场效应。我们通过将我们的非线性频率响应与现有实验结果进行定量比较来验证开发的模型。我们进行静态分析，以识别不同初始中点上升的快速通过和拉入不稳定的发生。耦合特征值问题也得到解决，以计算阻尼固有频率及其相应的梁和流体模式形状。获得的固有频率与文献中报道的那些非常一致。当减小将微束与固定电极分开的间隙距离并减小弯曲微束的初始中点上升时，观察到自然频率对压力变化的高灵敏度。我们还研究了通过在质量分布中引入轻微扰动来破坏微观结构对称性对其动态响应的影响。稳定性分析揭示了一个新的周期倍增分岔点的出现。有趣的是，观察到这个分叉点的位置对周围流体介质的压力很敏感。因此，我们建议利用这种非线性特征来增强压力传感器的设计。