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Fabrication and Characterization of High-Q Silicon Nitride Membrane Resonators

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Driven, autoresonant three-oscillator interactions.

O Yaakobi¹, L Friedland, Z Henis

¹Soreq NRC, Yavne 81800, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|October 13, 2007

Summary

This summary is machine-generated.

This study introduces an efficient control scheme for three-oscillator systems using chirped frequency drives. The novel autoresonance technique enables controlled amplitude growth, independent of chirp rate sign.

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Area of Science:

Nonlinear dynamics
Resonant systems
Control theory

Background:

Controlling complex resonant systems is challenging.
Phase-locking phenomena are crucial for energy transfer in oscillators.
Autoresonance offers a method for amplitude amplification.

Purpose of the Study:

To propose an efficient control scheme for resonant three-oscillator interactions.
To investigate the formation and stability of a double phase-locked (autoresonant) state.
To analyze the influence of system parameters on autoresonance behavior.

Main Methods:

Utilizing an external chirped frequency drive.
Analyzing the formation of a double phase-locked state.
Investigating system stability, dissipation, and frequency mismatch effects.

Main Results:

Demonstrated an efficient control scheme for three-oscillator interactions.
Observed amplitude growth proportional to driving frequency deviation from resonance.
Analyzed stability and identified an autoresonance threshold phenomenon.
Found excitation independence from the driving frequency chirp rate sign.

Conclusions:

The proposed autoresonance control scheme is efficient for three-oscillator systems.
The system exhibits stable, controlled amplitude growth.
The findings are robust against dissipation and initial frequency mismatches.