一类双边电容型微谐振器吸合不稳定及其时滞速度反馈控制  

Pull in instability and time delay velocity feedback control for a class of bilateral capacitive micro-resonators

作　　者：尚慧琳 董章辉 刘海 刘智群 SHANG Huilin;DONG Zhanghui;LIU Hai;LIU Zhiqun(School of Mechanical Engineering,Shanghai Institute of Technology,Shanghai 201418,China)

机构地区：[1]上海应用技术大学机械工程学院,上海201418

出　　处：《振动与冲击》2021年第7期237-243,共7页Journal of Vibration and Shock

基　　金：国家自然科学基金面上项目(11472176)。

摘　　要：以一类典型的静电驱动双边电容型微谐振器为研究对象,基于全局分岔理论,研究微结构吸合不稳定的机理;在此基础上,在系统直流偏置电压上引入线性时滞速度反馈,对系统复杂动力学行为实施控制。通过引入独立参数,得出系统异宿轨道的精确解析表达,进而利用Melnikov方法预测微结构的异宿分岔条件,从而获得引起微结构吸合不稳定的交流电压阈值。数值算例与理论解析结果的吻合验证了时滞速度反馈控制能有效抑制该类双边电容型微结构吸合不稳定以及混沌等复杂动力学行为,该研究在优化控制微谐振器性能方面具有潜在的应用价值。Based on the global bifurcation theory,the mechanism of pull-in instability of a typical electrostatic driven bilateral capacitive micro-resonator was studied.Then,a linear time-delay velocity feedback was introduced into the system’s DC bias voltage to control complex dynamic behavior of the system.By introducing independent parameters,the exact analytical expression of the system’s heteroclinic orbit was obtained.Furthermore,Melnikov method was used to predict heteroclinic bifurcation conditions of the microstructure to obtain its AC voltage threshold causing its pull-in instability.It was shown that the numerical results agree well with the theoretical analytical ones to verify the time-delay velocity feedback control being able to effectively suppress pull-in instability,chaos and other complex dynamic behaviors of this kind of bilateral capacitive micro structures;the study results have potential application value for optimal controlling the performance of micro resonators.

关 键 词：微谐振器 吸合不稳定 时滞速度反馈控制 异宿分岔 安全盆 

分 类 号：TH212[机械工程—机械制造及自动化] TH213.3