静电驱动微镜参数激励下的亚谐振动分析
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天津理工大学 天津市先进机电系统设计与智能控制重点实验室

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国家自然科学基金(12072233);天津市自然科学基金(20JCYBJC00510)


Analysis of subharmonic vibrations under parametric excitation of electrostatically driven micromirrors
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    摘要:

    参数振动广泛存在于多物理场耦合的微机电系统中。为研究静电驱动微镜系统中存在的参数共振非线性动力学问题,以一类静电梳齿驱动微镜为例,通过七次多项式拟合梳齿电容变化并建立微镜动力学模型,研究不同因素下系统的参数共振响应变化。研究了静态下微镜结构参数变化对扭转角度的影响规律;应用多尺度法分析了谐振状态下系统参数对共振幅值变化的作用规律并对系统参数共振进行了数值验证;最后利用Runge-Kutta法对系统亚谐参数共振的稳定性进行了分析与验证。研究表明:微镜系统存在亚谐参数共振,激励电压、电容拟合参数等因素会影响系统共振幅值;阻尼可以改变系统不稳定区域,提高失稳阈值,影响系统亚谐参数共振发生。

    Abstract:

    Parametric vibrations are widely present in microelectromechanical systems coupled with multi-physical fields. To study the parametric resonance nonlinear dynamics problem existing in electrostatic driven micromirror systems, a class of electrostatic comb-driven micromirrors is used as an example to study the parametric resonance response variation of the system under different factors by fitting the comb capacitance variation with a seventh order polynomial and establishing a micromirror dynamics model. The law of the influence of the change of structural parameters of the micromirror on the torsion angle under static conditions was investigated; the multi-scale method is applied to analyze the action law of system parameters on the change of resonance amplitude in the resonance state and numerically verify the system parameter resonance; finally, the stability of the subharmonic parametric resonance of the system was analyzed and verified using the Runge-Kutta method. It is shown that subharmonic parametric resonance exists in the micromirror system, and factors such as excitation voltage and capacitance fitting parameters can affect the system resonance amplitude; damping can change the system instability region, raise the instability threshold, and affect the occurrence of subharmonic parametric resonance in the system.

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  • 收稿日期:2023-03-21
  • 最后修改日期:2023-05-29
  • 录用日期:2023-06-02
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