On the nonlinear resonances and dynamic pull-in of electrostatically actuated resonators
On the nonlinear resonances and dynamic pull-in of electrostatically actuated resonators
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DOI：
10.1088/0960-1317/19/4/045013
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发表时间：
2009-04-01
影响因子：
2.3
通讯作者：
Ouakad, Hassen M.
中科院分区：
文献类型：
--
作者：
Alsaleem, Fadi M.;Younis, Mohammad I.;Ouakad, Hassen M.
我们提出了建模，分析和实验研究的非线性谐振和动态吸合不稳定性的静电驱动谐振器。这些现象是由激励与非线性强迫组成的直流平行板静电负载叠加在一个交流谐波负载的微结构。从实验和理论上研究了非线性现象，包括主共振、超谐波和亚谐波共振、动态吸合和从势阱逃逸现象。作为一个案例研究，电容传感器的两个悬臂梁与附加到其尖端的检测质量。采用非线性弹簧-质量-阻尼器模型，考虑挤压膜阻尼和平行板静电力。采用有限差分法结合Floquet理论进行了长时间积分和全局动力学分析，以捕获周期轨道并分析其稳定性。数值计算频率响应曲线上数据点的吸引域（吸引盆）。计算了多佛悬崖完整性曲线，并研究了激励频率扫过主共振和动态吸合时安全吸引域的侵蚀。根据模拟的吸引盆和观察到的实验数据，提出了关于MEMS谐振器的安全性和完整性的结论。
We present modeling, analysis and experimental investigation for nonlinear resonances and the dynamic pull-in instability in electrostatically actuated resonators. These phenomena are induced by exciting a microstructure with nonlinear forcing composed of a dc parallel-plate electrostatic load superimposed on an ac harmonic load. Nonlinear phenomena are investigated experimentally and theoretically including primary resonance, superharmonic and subharmonic resonances, dynamic pull-in and the escape-from-potential-well phenomenon. As a case study, a capacitive sensor made up of two cantilever beams with a proof mass attached to their tips is studied. A nonlinear spring-mass-damper model is utilized accounting for squeeze-film damping and the parallel-plate electrostatic force. Long-time integration and a global dynamic analysis are conducted using a finite-difference method combined with the Floquet theory to capture periodic orbits and analyze their stability. The domains of attraction (basins of attraction) for data points on the frequency-response curve are calculated numerically. Dover cliff integrity curves are calculated and the erosion of the safe basin of attraction is investigated as the frequency of excitation is swept passing primary resonance and dynamic pull-in. Conclusions are presented regarding the safety and integrity of MEMS resonators based on the simulated basin of attraction and the observed experimental data.