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Abstract：
In this paper, we present a compressive study on the design and development of a MEMS ring resonator and its dynamic behavior under electrostatic force when supported by twin circular curve beams. Finite element analysis (FEA)-based modeling techniques are used to simulate and refine the resonator geometry and transduction. In proper FEA or analytical modeling, the explicit description and accurate values of the effective mass and stiffness of the resonator structure are needed. Therefore, here we outlined an analytical model approach to calculate those values using the first principles of kinetic and potential energy analyses. The natural frequencies of the structure were then calculated using those parameters and compared with those that were simulated using the FEA tool ANSYS. Dynamic analysis was performed to calculate the pull-in voltage, shift of resonance frequency, and harmonic analyses of the ring to understand how the ring resonator is affected by the applied voltage. Additional analysis was performed for different orientations of silicon and assessing the frequency response and frequency shifts. The prototype was fabricated using the standard silicon-on-insulator (SOI)-based MEMS fabrication process and the experimental results for resonances showed good agreement with the developed model approach. The model approach presented in this paper can be used to provide valuable insights for the optimization of MEMS resonators for various operating conditions.
摘要：
在本文中,我们对MEMS环形谐振器的设计和开发及其在双圆形曲线梁支撑下在静电力下的动态行为进行了压缩研究。基于有限元分析（FEA）的建模技术用于模拟和完善谐振器的几何形状和转换。在适当的FEA或分析模型中，需要谐振器结构的有效质量和刚度的明确描述和准确值。因此,在这里，我们概述了一个分析模型的方法来计算这些值使用第一原则的动能和势能分析。然后使用这些参数计算结构的固有频率，并与使用有限元分析工具ANSYS模拟的固有频率进行比较。进行动态分析以计算吸合电压，共振频率的偏移，和谐波分析环，以了解环形谐振器如何受到施加电压的影响。对硅的不同取向进行额外分析并评估频率响应和频移。原型是使用基于标准绝缘体上硅（SOI）的MEMS制造工艺制造的，共振的实验结果与所开发的模型方法吻合良好。本文提出的模型方法可用于为各种工作条件下的MEMS谐振器的优化提供有价值的见解。
