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Electrostatic nonlinear dispersive parametric mode interaction

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Abstract

Understanding and controlling the nonlinear coupling in micro/nanomechanical resonators are of great importance to the exploitation of advanced devices. The recently observed electrostatic nonlinear parametric coupling is a very interesting topic. However, the theoretical model of the electrostatic parametric coupling remains unclear. This paper explicitly derives the model and the electrostatically induced dispersive parametric coupling which reveals the ability to tune the bifurcation topology of capacitive resonators is analyzed based on the multiple-time-scale method. A novel displacement-to-frequency transduction scheme based on this electrostatic dispersive parametric coupling effect is proposed. The transduction sensitivity is theoretically given, which indicates that this electrostatic dispersive transduction scheme can provide even more design freedoms than the existing displacement-to-frequency transduction scheme based on tension modulation. In addition, a bifurcation reversal effect is predicted in the strong actuated states of the dispersive parametric coupled system, which reveals the ability to tune the bifurcation topology of capacitive resonators.

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Data availability

The datasets analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

We would like to thank Prof. Ashwin Seshia from the University of Cambridge for guidance.

Funding

This research was funded by the National Natural Science Foundation of China (grant number 51905539 and U21A20505), the Young Elite Scientist Sponsorship Program by CAST (grant number YESS20200127), and the Natural Science Foundation of Hunan Province for Excellent Young Scientists (grant number 2021JJ20049).

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Authors and Affiliations

  1. College of Intelligence Science and Technology, National University of Defense Technology, Changsha, 410073, China

    Xiaopeng Sun, Xin Zhou, Xingjing Ren, Lan Li, Tongqiao Miao, Kuo Lu, Xuezhong Wu & Dingbang Xiao

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  1. Xiaopeng Sun
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  3. Xingjing Ren
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Correspondence to Xin Zhou.

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Sun, X., Zhou, X., Ren, X. et al. Electrostatic nonlinear dispersive parametric mode interaction. Nonlinear Dyn 111, 3081–3097 (2023). https://doi.org/10.1007/s11071-022-08007-z

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