In this paper, the usability of the classical Harmonic Balancing method (cHB) to calculate the weakly nonlinear motion of phase- and amplitude controlled MEMS resonators is demonstrated. A polynomial mechanical stiffness description and linearized electrostatic effects are considered, which allow determining the Jacobian analytically. The effects of amplitude and phase control are taken into account by applying boundary conditions in the iteration process. With a customized cHB, it is possible to efficiently simulate the behavior of a MEMS gyroscope undergoing nonlinear resonance with higher parasitic modes. The presented results of a virtual model compare very well with solutions obtained with the Shooting method. Furthermore, we compare the measurement of a drive frequency discontinuity, taken from a different prototype, with the prediction from our linear extrapolated model and from a model with artificially fitted parameters. The cHB approach yields an order of magnitude speed-up in comparison to the transient simulation method. Besides some restrictions, customized cHB methods are interesting candidates for fast system-type simulation considering the MEMS-ASIC interface. [2021-0028]

中文翻译：

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使用谐波平衡方法确定 MEMS 陀螺仪的非线性运动


本文证明了经典谐波平衡方法 (chB) 在计算相位和幅度控制 MEMS 谐振器的弱非线性运动方面的可用性。考虑多项式机械刚度描述和线性化静电效应，这允许通过分析确定雅可比行列式。通过在迭代过程中应用边界条件来考虑幅度和相位控制的影响。通过定制的 cHB，可以有效地模拟 MEMS 陀螺仪在较高寄生模式下经历非线性谐振的行为。虚拟模型给出的结果与通过射击方法获得的解决方案非常吻合。此外，我们还将取自不同原型的驱动频率不连续性的测量结果与线性外推模型和人工拟合参数模型的预测进行比较。与瞬态仿真方法相比，chB 方法可实现一个数量级的加速。除了一些限制之外，考虑到 MEMS-ASIC 接口，定制的 cHB 方法是快速系统类型仿真的有趣候选者。 [2021-0028]