This paper investigates the responses of initially curved micro-beams subjected to an electrostatic excitation. A Euler–Bernoulli beam theory is utilized to derive the governing equation of motion. A reduced-order model was developed by discretizing the equation of motion using straight beam mode shapes as basis functions in a Galerkin expansion. The results show evidence of the superharmonic resonances of order-three and two in addition to primary resonance. The co-existence of multiple stable orbits observed around only one stable equilibrium and under excitation waveforms with RMS voltage less than the snap-back voltage. These branches are a branch of small orbits within a narrow potential well and two branches of medium-sized and large orbits within a wider potential well. The transition between them results in the characteristic of the double peaks appearing in the frequency-response curve. We also report a bubble structure along the medium-sized branch consists of a cascad...

中文翻译：

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静电驱动的弯曲梁的大振动

本文研究了初始弯曲的微束在静电激励下的响应。欧拉-伯努利梁理论被用来导出运动的控制方程。通过在Galerkin展开中使用直光束模式形状作为基础函数离散运动方程来开发降阶模型。结果表明除了初级共振外，还有三阶和二阶的超谐共振。多个稳定轨道的共存仅在一个稳定平衡附近以及在RMS电压小于骤回电压的激励波形下观察到。这些分支是狭窄势阱内小轨道的分支，而较宽势阱内是中型轨道和大轨道的两个分支。它们之间的过渡导致双峰的特征出现在频率响应曲线中。我们还报告了由级联组成的中型分支上的气泡结构。