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Nonlinear dynamical analysis of some microelectromechanical resonators with internal damping

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Abstract

In this paper, a new Kelvin-Voigt type beam model of a microelectromechanical resonator made of power-law materials taking into account internal strain-rate damping is proposed and the corresponding lumped-parameter model is derived. Analytical formulas of the lumped parameters in the model are presented. And the pull-in solution is analyzed based on the lumped-parameter model. It is demonstrated analytically and numerically that the internal damping plays an important role in the pull-in solution as well as in determination of the amplitudes and frequencies of the resonator. The hysteresis loops are provided for this model with initial conditions using numerical simulations. The approximation of the electrostatic force in the lumped-parameter model can describe the relations between amplitudes and frequencies with different values of the stiffness and damping coefficients quite well.

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Acknowledgements

This work was supported by the Nazarbayev University research, rapid response fixed astronomical telescope for gamma ray bust observation (Grant OPCRP2020002).

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Authors and Affiliations

  1. School of Sciences and Humanities, Nazarbayev University, Nur-Sultan, 010000, Kazakhstan

    Dongming Wei, Daulet Nurakhmetov & Almir Aniyarov

  2. School of Engineering, Nazarbayev University, Nur-Sultan, 010000, Kazakhstan

    Christos Spitas & Dichuan Zhang

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  1. Dongming Wei
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  2. Daulet Nurakhmetov
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Correspondence to Almir Aniyarov.

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Executive Editor:}} \communicated{\xm{Executive Editor Executive Editor: Lifeng Wang.

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Wei, D., Nurakhmetov, D., Spitas, C. et al. Nonlinear dynamical analysis of some microelectromechanical resonators with internal damping. Acta Mech. Sin. 37, 1457–1466 (2021). https://doi.org/10.1007/s10409-021-01114-x

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