静电驱动微梁谐振器的厚度形态误差特性分析
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国家自然科学基金资助项目(11602169,11702192), 天津市自然科学基金资助项目(16JCQNJC04700),天津市高等学校自然科学研究计划一般项目(2017KJ262)


Characteristic analysis of thickness shape error on electrostatic actuation microbeam resonator
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    摘要:

    本文研究了一类双极板静电驱动两端固支微梁谐振器.考虑中性面拉伸和厚度形态误差,建立了微谐振器连续体模型.厚度形态误差通过设置参数方程实现,方程中包含误差参数λ,用于调整误差影响程度.利用伽辽金法和NewtonCotes法将系统化简为单自由度模型.首先,通过COMSOL Multiphysics有限元软件对理论求得的静电力进行了仿真验证.然后,推导了不考虑厚度形态误差时系统的吸合情况,发现系统在特定情况下可以出现二次吸合现象.通过改变误差参数,分析了厚度形态误差对吸合情况的影响.最后,利用多尺度法求出系统小幅振动下的响应,研究了厚度形态误差对等效固有频率和系统软硬特性的影响.

    Abstract:

    A class of bipolar plate electrostatically actuation microbeam resonator with both clamped ends was studied. The continuum model was established by considering the influences of neutral surface tension and thickness shape error. The thickness shape error was described by a parameter equation with an error parameter, which was used to adjust the degree of shape error. The Galerkin method and NewtonCotes method were used to simplify the system into a singledegreeoffreedom model. The electrostatic force was simulated and verified by the multiphysics finite element software COMSOL. Then, the pullin condition of the system was deduced without thickness shape error. It was found that secondary pullin appears in the system in certain situations. Furthermore, the influence of thickness shape error on pullin condition was analyzed by adjusting the error parameter. The method of multiple scales was applied to obtain the response of smallamplitude vibrations. The influence of thickness shape error on equivalent natural frequencies as well as softening and hardening characteristics of the system were also studied.

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刘成,冯晶晶,郝淑英,张伟.静电驱动微梁谐振器的厚度形态误差特性分析[J].动力学与控制学报,2020,18(2):35~41; Liu Cheng, Feng Jingjing, Hao Shuying, Zhang Wei. Characteristic analysis of thickness shape error on electrostatic actuation microbeam resonator[J]. Journal of Dynamics and Control,2020,18(2):35-41.

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  • 收稿日期:2018-12-26
  • 最后修改日期:2019-01-14
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  • 在线发布日期: 2020-05-07
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