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Fabrication and Characterization of High-Q Silicon Nitride Membrane Resonators

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Nonlinear mode saturation in a U-shaped micro-resonator.

Rodrigo T Rocha¹, Mohammad I Younis^2,3

¹Physical Sciences and Engineering Division, King Abdullah University of Science and Technology-KAUST, Thuwal, 23955, Saudi Arabia.

Scientific Reports

|June 21, 2022

Summary

This study demonstrates nonlinear saturation in a micro portal frame, observing a 2:1 internal resonance between vibration modes. These findings advance understanding of saturation phenomena in microstructures.

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Area of Science:

Nonlinear Dynamics
Microelectromechanical Systems (MEMS)

Background:

The phenomenon of saturation has been observed in various physical systems since the 19th century.
Understanding nonlinear saturation is crucial for designing stable and predictable dynamic systems.

Purpose of the Study:

To demonstrate and comprehensively study nonlinear saturation in a U-shaped micro portal frame.
To investigate the activation of a 2:1 internal resonance between the first (sway) and second (symmetric) in-plane vibration modes.

Main Methods:

Fabrication of a compound micromachined structure (micro portal frame) as a multi-input/multi-output device.
Utilizing geometric nonlinearities and electrostatic softening effects to induce internal resonance.
Combining experimental data with analytical simulations to analyze the phenomenon.

Main Results:

Successful demonstration of nonlinear saturation in the micro portal frame.
Observation of a 2:1 internal (auto-parametric) resonance between the sway and symmetric vibration modes.
Experimental and simulation data confirm the internal resonance and saturation effects.

Conclusions:

The U-shaped micro portal frame exhibits nonlinear saturation due to internal resonance.
These findings offer potential for advanced microstructures and further studies on saturation in diverse systems.