Abstract:A typical electrostatically driven comb-tooth micro-gyroscope was considered. To begin with, its 2-DOF vibrating system was established, which was simplified by considering the actual situation of the micro structure. Then, the prediction and stability of the periodic solutions under the primary resonance were obtained by applying the multi-scale method. Combining with the numerical simulation for the dynamical responses of this system, the mechanism of the effect of the system parameters on the amplitude and bifurcation behaviors in the driving direction and detecting one were revealed. The results showed that it would be easy for variation of excitation frequency to induce the multi-stable attractors and other complex dynamic behaviors such as safe jump. In addition, by introducing new parameters, the heteroclinic orbits of the undisturbed system was expressed analytically; thus the necessary conditions of heteroclinic bifurcation for variation system were predicted via Melnikov's method so as to obtain the critical value of the amplitude of AC voltage which could induce pull-in instability of the structure. It was found that the delayed position feedback can be used to suppress the complex dynamic phenomenon of the micro-gyroscope structure, such as safe jump and pull-in instability. The results have potential values in the design and optimal control of Microinertia sensors.
Key words: micro-gyroscope; safe jump; pull-in instability; heteroclinic bifurcation; delayed feedback control; safe basin
尚慧琳,蒋慧敏,秦波. 时滞位置反馈对一类梳齿型微陀螺振动系统复杂动力学行为的控制[J]. 振动与冲击, 2022, 41(20): 18-27.
SHANG Huilin,JIANG Huimin,QIN Bo. Control of complex dynamical behaviours of the vibrating system of a type of comb-tooth micro-gyroscope via delayed position feedback. JOURNAL OF VIBRATION AND SHOCK, 2022, 41(20): 18-27.
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