Frequency and damping trimming of a microresonator via delayed feedback signals

HAN Jianxin; ZHANG Qichang; WANG Wei

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Frequency and damping trimming of a microresonator via delayed feedback signals

HAN Jianxin #,ZHANG Qichang,WANG Wei *

Department of Mechanics, School of Mechanical Engineering, Tianjin University, Tianjin 300350

*Correspondence author

#Submitted by

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Funding: National Natural Science Foundation of China （No.No. 11372210, 11102127), Research Fund for the Doctoral Program of Higher Education of China）

Opened online: 4 November 2015

Accepted by: none

Citation: HAN Jianxin,ZHANG Qichang,WANG Wei.Frequency and damping trimming of a microresonator via delayed feedback signals[OL]. [ 4 November 2015] http://en.paper.edu.cn/en_releasepaper/content/4659192

A study on an electrically actuated microresonator is carried out to investigate its dynamic characteristic with delayed displacement and velocity feedback signals. The amplitude of AC voltage is relatively smaller than that of DC voltage in real cases, which yields a small amplitude vibration around its equilibrium position. For delayed stability purpose, delay-independent region based on the linearized equation is analytically derived and then numerically verified. Then, the method of multiple scales is used to determine the frequency response equation under primary resonance of the system. Explicit expressions of the effective natural angular frequency and damping ratio are deduced, respectively. Results show that these two types of delayed feedback signals can induce frequency and damping trimming of the system. An ideal situation, when one type of signal can only tune one vibration property, is discussed in detail. Four cases of delay conditions are defined to decouple the two trimming phenomena. Finally, both the perturbation solution and numerical results are used to verify the correctness of our analysis.

Keywords:MEMS; Resonator; Frequency and damping trimming; Delayed feedback; Multiple scales

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