Nonlinear vibration behaviors of a micro-gyroscope system actuated by a parametric excitation

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Journal of Vibration and Shock ›› 2017, Vol. 36 ›› Issue (1) : 102-107.

SHANG Huilin1, ZHANG Tao1, WEN Yongpeng2

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Abstract

For a typical non-interdigitated combfinger actuated micro-gyroscope, a 2-DOF dynamic model with cubic nonlinear stiffness and parametric excitation was established. For the principal parametric resonance case and 1:1 internal resonance, the periodic solutions were obtained with the multi-scale method. Conditions of Hopf bifurcation of the periodic solutions were derived according to the theory of bifurcation. Then the dynamic responses of the system were simulated. Finally, the effect mechanism of the systems parameters on the modal amplitudes and bifurcation behaviors was analyzed. It was shown that the variation of the excitation frequency is easy to cause various complex dynamic behaviors of the microgyroscope vibrating system, such as, multi-stable solution, amplitude jump phenomena and quasi-periodic responses under a large angular speed of the carrier and 1:1 internal resonance.

Key words

Micro-gyroscope / electrostatic force / principal parametric resonance / multi-stability / jump phenomenon

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SHANG Huilin1, ZHANG Tao1, WEN Yongpeng2. Nonlinear vibration behaviors of a micro-gyroscope system actuated by a parametric excitation[J]. Journal of Vibration and Shock, 2017, 36(1): 102-107

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