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Nonlinear dynamics and chaos in micro/nanoelectromechanical beam resonators actuated by two-sided electrodes

Author

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  • Gusso, André
  • Viana, Ricardo L.
  • Mathias, Amanda C.
  • Caldas, Iberê L.

Abstract

We investigate theoretically the nonlinear dynamics and the emergence of chaos in suspended beam micro/nanoelectromechanical (MEMS/NEMS) resonators actuated by two-sided electrodes. Through the analysis of phase diagrams we have found that the system presents a rich and complex nonlinear behavior. Multistability is observed in a significant region of the relevant parameter space, involving periodic and chaotic attractors. Complex and varied routes to chaos were also found. Basins of attraction with strongly intermingled attractors provide further evidence of multistability. The basins are analyzed in greater detail. Their fractal dimensions and uncertainty exponent are calculated using the well known box counting and uncertainty methods. The results for the uncertainty exponent are compared with those obtained with yet another approach, based on the recently proposed basin entropy method. The comparison provides a test for the new approach, which we conclude that is a reliable alternative method of calculation. Very low uncertainty exponents have been obtained, indicating that some basins have extremely intermingled attractors, what may have significant influence in the experimental investigation and practical applications of the resonators. We also conclude that the observation of chaos in this system is favored by lower frequencies of excitation and comparatively small quality factors (larger dissipation).

Suggested Citation

  • Gusso, André & Viana, Ricardo L. & Mathias, Amanda C. & Caldas, Iberê L., 2019. "Nonlinear dynamics and chaos in micro/nanoelectromechanical beam resonators actuated by two-sided electrodes," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 6-16.
    • Handle: RePEc:eee:chsofr:v:122:y:2019:i:c:p:6-16
    DOI: 10.1016/j.chaos.2019.03.004
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    References listed on IDEAS

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    1. Dario Antonio & Damián H. Zanette & Daniel López, 2012. "Frequency stabilization in nonlinear micromechanical oscillators," Nature Communications, Nature, vol. 3(1), pages 1-6, January.
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    Cited by:

    1. Gusso, André & de Mello, Leandro E., 2021. "Fractal dimension of basin boundaries calculated using the basin entropy," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    2. Ebrahimi, Reza, 2022. "Chaos in coupled lateral-longitudinal vibration of electrostatically actuated microresonators," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    3. Alneamy, Ayman M., 2024. "Dynamic snap-through motion and chaotic attractor of electrostatic shallow arch micro-beams," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    4. Luo, Shaohua & Yang, Guanci & Li, Junyang & Ouakad, Hassen M., 2022. "Dynamic analysis, circuit realization and accelerated adaptive backstepping control of the FO MEMS gyroscope," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).

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