时滞位置反馈对一类双边电容型微谐振器复杂振动的控制  

Control of the complex vibration of a class of double-side capacitive microresonator via the delayed position feedback

作　　者：尚慧琳 刘海 董章辉 刘智群 SHANG Huilin;LIU Hai;DONG Zhanghui;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》2022年第6期213-221,共9页Journal of Vibration and Shock

基　　金：国家自然科学基金(11472176)。

摘　　要：以一类静电双边电容型微谐振器为研究对象,在直流电压上施加时滞位移反馈以控制微结构的复杂动力学行为,如混沌和吸合不稳定。首先,基于全局分岔理论讨论时滞位移反馈控制系统发生同宿分岔和异宿分岔的必要条件,从而分析时滞位移反馈抑制系统混沌运动和吸合不稳定的控制机理。数值和解析结果相吻合验证了该理论预测的有效性。研究发现,当反馈增益系数为正时,时滞位移反馈能够有效抑制双边电容型微谐振器系统的混沌和吸合不稳定这两类复杂动力学现象;尽管二者可归因于系统发生的全局分岔行为,但机理完全不同。该结果在保障微谐振器振动系统的动完整性以及微结构的设计方面具有潜在的应用价值。A type of electrostatic double-side capacitive micro resonator was considered,and the time-delayed position feedback on the DC voltage of its driven circuit was applied to control the complex dynamic behaviors of the microstructure,such as chaos and pull-in instability.Firstly,based on the theory of global bifurcation,the necessary conditions for homoclinic and heteroclinic bifurcation in a time-delay position feedback control system were discussed;and the control mechanism of the chaotic motion and pull-in instability was analyzed.Then the validity of the theoretical prediction was verified by the agreement between numerical results and theoretical ones.It follows that when the coefficient of the gain is positive,the delayed position feedback can be applied to effectively suppress the two complex dynamic phenomena i.e.chaos and pull-in instability.Both phenomena can be attributed to the global bifurcation but with totally different mechanism.The paper has some potential value of application in ensuring the dynamic integrity of micro-resonator vibration systems and the design of microstructures.

关 键 词：微谐振器 混沌 吸合不稳定 时滞位移反馈 全局分岔 

分 类 号：O322[理学—一般力学与力学基础] TH113.1[理学—力学]