静电驱动微镜参数激励下的亚谐振动分析  

Analysis of subharmonic vibrations under parametric excitation of electrostatically driven micromirrors

作　　者：李徐 冯晶晶[1,2] 郝淑英[1,2] 胡文华[1,2] LI Xu;FENG Jingjing;HAO Shuying;HU Wenhua(Tianjin Key Laboratory for Advanced Mechatronic System Design and Intelligent Control,Tianjin University of Technology,Tianjin 300384,China;National Demonstration Center for Experimental Mechanical and Electrical Engineering Education,Tianjin University of Technology,Tianjin 300384,China)

机构地区：[1]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,天津300384 [2]天津理工大学机电工程国家级实验教学示范中心,天津300384

出　　处：《振动工程学报》2025年第2期242-248,共7页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(12072233,12072234);天津市自然科学基金资助项目(20JCYBJC00510)。

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影响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。Parametric vibrations are commonly observed in microelectromechanical systems(MEMS)coupled with multi-physical fields.To study the parametric resonance nonlinear dynamics problems in electrostatically 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 un-der different factors by fitting a seventh-order polynomial to the comb capacitance variation and establishing a micromirror dynamics model.The influence of changes in the micromirror’s structural parameters on the torsion angle under static conditions is investigat-ed.The multi-scale method is applied to analyze how system parameters affect the variation in resonance amplitude during the reso-nance state,and numerical verification of system parameter resonance is performed.Finally,the stability of subharmonic paramet-ric resonance in the system is analyzed and verified using the Runge-Kutta method.The results show that subharmonic parametric resonance exists in the micromirror system.Factors such as excitation voltage and capacitance fitting parameters can affect the sys-tem’s resonance amplitude.Damping can alter the system’s instability region,increase the instability threshold,and influence the occurrence of subharmonic parametric resonance in the system.

关 键 词：非线性振动 参数共振 微镜 多尺度法 数值验证 

分 类 号：O322[理学—一般力学与力学基础]