Chaos Prediction and Nonlinear Dynamic Analysis of a Dimple-Equipped Electrostatically Excited Microbeam

Ayman M. Alneamy ()
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Ayman M. Alneamy: Department of Mechanical Engineering, College of Engineering and Computer Sciences, Jazan University, Jazan 45142, Saudi Arabia

Mathematics, 2025, vol. 13, issue 18, 1-14

Abstract: As MEMS design encounters growing challenges, particularly stiction between movable and stationary electrodes, dielectric charging, pull-in instability, and multi-valued response characteristics, the integration of dimple-equipped structures has emerged as a pivotal solution to mitigate these fundamental issues. Consequently, this study investigates the dynamic behavior of an electrostatically actuated double-clamped microbeam incorporating dimples and contact pads. While the dimples enhance the beam’s travel range, they may also induce an impact mode upon contact with the landing pads, leading to complex nonlinear dynamic phenomena. A reduced-order model was developed to numerically solve the governing equation of motion. The microbeam’s response was analyzed both with and without dimples using multiple analytical techniques, including bifurcation diagrams and discrete excitation procedures near the impacting regime. The findings demonstrate that the inclusion of dimples effectively suppresses stiction, pull-in instability, and multi-valued responses. The results indicate that upon contacting the landing pads, the beam exhibits pronounced nonlinear dynamic behaviors, manifesting as higher-period oscillations such as period-3, period-4 and period-5 and then fully developed chaotic attractors. Indeed, this specifically demonstrates the potential of using the dynamic transition from a steady-state to a chaotic response to build novel MEMS sensors.

Keywords: stiction; dimples; contact pads; chaos; tapping mode (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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