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Analysis of dynamic pull-in voltage and response time for a micro-electro-mechanical oscillator made of power-law materials

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Abstract

Analysis of dynamic pull-in voltage for a micro-electro-mechanical oscillator of platform type is performed. The lumped mass model for the actuated micro-cantilever beam made of power-law material is established and the bifurcation is investigated with respect to the dimensionless voltage parameter using simple phase plane analysis. The necessary and sufficient conditions for the existence of periodic solutions to the lumped mass model equation are derived and proved analytically. The pull-in conditions on the strength coefficient, power-law exponent, and voltage are determined. Moreover, the response time is analyzed and approximate periodic solutions are derived. The established analytical results are illustrated numerically.

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Acknowledgements

The research was supported by the Nazarbayev University ORAU grant “Modeling and Simulation of Nonlinear Material Structures for Mechanical Pressure Sensing and Actuation Applications.” Dr. Eduard G. Kostsov, Dr. Alexei A. Sokolov, and Dr. Piotr Skrzypacz are grateful to Dr. Stanislav I. Fadeev for sharing his pearls of wisdom during the course of the research on MEMS.

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Authors and Affiliations

  1. School of Sciences and Humanities, Nazarbayev University, 53 Kabanbay Batyr Ave., Nur-Sultan, 010000, Kazakhstan

    Piotr Skrzypacz, Dongming Wei & Daulet Nurakhmetov

  2. Institute of Automation and Electrometry, Siberian Branch of Russian Academy of Sciences, pr. Akademika Koptyuga 1, Novosibirsk, 630090, Russia

    Eduard G. Kostsov & Alexei A. Sokolov

  3. King’s College, Strand, London, WC2R 2LS, UK

    Madi Begzhigitov

  4. School of Engineering and Digital Sciences, Nazarbayev University, 53 Kabanbay Batyr Ave., Nur-Sultan, 010000, Kazakhstan

    Grant Ellis

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  1. Piotr Skrzypacz
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Skrzypacz, P., Wei, D., Nurakhmetov, D. et al. Analysis of dynamic pull-in voltage and response time for a micro-electro-mechanical oscillator made of power-law materials. Nonlinear Dyn 105, 227–240 (2021). https://doi.org/10.1007/s11071-021-06653-3

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