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Dynamic snap-through motion and chaotic attractor of electrostatic shallow arch micro-beams

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  • Alneamy, Ayman M.

Abstract

In this paper, we investigate numerically the dynamic snap-through motion of a shallow arch micro-beam that is electrostatically excited through three separated electrodes. It is excited by a dc voltage and a time-varying signal with a frequency tuned near its first in-plane frequency in both initial curvature and initial-counter curvature configurations. A reduced-order model based on the Galerkin method is utilized to discretize the governing equation of motion and to analyze the static and dynamic responses of the micro-beam. The phase portraits obtained from simulations reveal the presence of a stable response that oscillates back and forth around single and double equilibria until it eventually settles in a steady state zone near the first equilibrium point or encloses both equilibria. This can be tracked using a Long-Time Integration (LTI) and recording the time–history signal for a long period. Remarkably, this behavior can be controlled by adjusting the initial operating conditions mainly the signal frequency. We also observe the emergence of a chaotic attractor in the vicinity of the resonance frequency when the shallow arch beam is excited while it is in its initial-counter curvature. The simulated FFTs indicate the presence of the chaotic attractor in the vicinity of primary resonance due to dynamic snap-through motion or large excitation between two equilibria. We observed the existence of periodic orbits with single loop (P-1) and an full chaotic behavior around the two equilibria. The existence of this phenomenon can be attributed to the fact that the excitation voltage is positioned close to the snap-through threshold.

Suggested Citation

  • Alneamy, Ayman M., 2024. "Dynamic snap-through motion and chaotic attractor of electrostatic shallow arch micro-beams," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    • Handle: RePEc:eee:chsofr:v:182:y:2024:i:c:s0960077924003291
    DOI: 10.1016/j.chaos.2024.114777
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    References listed on IDEAS

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    1. Li, Fengyun & Luo, Shaohua & Yang, Guanci & Ouakad, Hassen M., 2023. "Dynamical analysis and accelerated adaptive backstepping funnel control for dual-mass MEMS gyroscope under event trigger," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    2. Ebrahimi, Reza, 2022. "Chaos in coupled lateral-longitudinal vibration of electrostatically actuated microresonators," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    3. 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.
    4. Polo, Manuel F. Pérez & Molina, Manuel Pérez & Chica, Javier Gil, 2009. "Chaotic dynamic and control for micro-electro-mechanical systems of massive storage with harmonic base excitation," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1356-1370.
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