Purpose <p>This study investigates the multi-stable vibration characteristics of a buckling fixed beam actuated by fringing electrostatic fields.</p> Methods <p>A resonant signal filtering structure actuated by a fringing electrostatic field is proposed, comprising a movable beam and a stationary electrode. A governing equation is established to analyze both static and dynamic behaviors.&#xa0;The Method of Multiple Scales is employed to analyze the frequency-amplitude response of parametrically resonant electrostatically actuated buckling beams. An experiment is designed to observe the dynamic analysis of this structure.</p> Conclusion <p>Key findings reveal: (1) Negative stiffness induces multi-stable nonlinear vibration, with parameter P effectively modulating potential barrier height; (2) Excitation energy dictates vibration confinement—low energy restricts motion to single potential wells, while high energy enables inter-well transitions, facilitated by increased excitation voltage; (3) The system exhibits strong noise immunity, maintaining stable vibration amplitude/frequency under Gaussian noise. Excitation bandwidth expands with increasing energy and parameter K<sub>3</sub>, while phase-locking provides an effective method for locating maximum amplitude points. These results demonstrate significant tunability and robustness in electrostatic-actuated multi-stable systems.</p>

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Tunable Multi-Stable Vibration via Negative Stiffness Modulation in Electrostatic Buckled Beams

  • Zhichong Wang,
  • Yifeng Zhang,
  • Haorui Gu,
  • Liang Qiao,
  • Yun Hu

摘要

Purpose

This study investigates the multi-stable vibration characteristics of a buckling fixed beam actuated by fringing electrostatic fields.

Methods

A resonant signal filtering structure actuated by a fringing electrostatic field is proposed, comprising a movable beam and a stationary electrode. A governing equation is established to analyze both static and dynamic behaviors. The Method of Multiple Scales is employed to analyze the frequency-amplitude response of parametrically resonant electrostatically actuated buckling beams. An experiment is designed to observe the dynamic analysis of this structure.

Conclusion

Key findings reveal: (1) Negative stiffness induces multi-stable nonlinear vibration, with parameter P effectively modulating potential barrier height; (2) Excitation energy dictates vibration confinement—low energy restricts motion to single potential wells, while high energy enables inter-well transitions, facilitated by increased excitation voltage; (3) The system exhibits strong noise immunity, maintaining stable vibration amplitude/frequency under Gaussian noise. Excitation bandwidth expands with increasing energy and parameter K3, while phase-locking provides an effective method for locating maximum amplitude points. These results demonstrate significant tunability and robustness in electrostatic-actuated multi-stable systems.