A Stepped Frequency Sweeping Method for Nonlinearity Measurement of Microresonators

Area of Science:

• Nonlinear dynamics
• Micromechanical resonators
• Vibration analysis

Background:

• Characterizing nonlinear dynamics in micromechanical resonators is crucial for device performance.
• Traditional methods like frequency sweeping can be time-consuming and may not fully capture complex nonlinear behaviors.

Purpose of the Study:

• To investigate a novel free damped oscillation method for measuring nonlinear features of micromechanical resonators.
• To develop a technique that provides distinct Backbone and frequency response function (FRF) curves for nonlinear characterization.
• To assess the anti-noise performance and experimental applicability of the proposed method.

Main Methods:

• Utilizing a stair-stepped frequency sinusoidal pulse excitation near the resonant frequency.
• Acquiring free vibration response signals to capture nonlinear dynamical characteristics.
• Employing Hilbert transform and singular spectrum analysis for instantaneous amplitude and frequency extraction.
• Performing numerical simulations on a Duffing system and experimental tests on a vibrating ring microgyroscope.

Main Results:

• The method successfully obtains distinct Backbone and FRF curves, effectively characterizing nonlinear resonator dynamics.
• Numerical simulations demonstrate superior anti-noise performance compared to the FREEVIB method.
• Experimental results for a vibrating ring microgyroscope align with traditional frequency sweeping methods.

Conclusions:

• The proposed stair-stepped frequency pulse excitation method is effective for measuring nonlinear features in micromechanical resonators.
• The technique offers robust anti-noise capabilities and experimental validation.
• This method serves as a versatile tool for characterizing the dynamic behavior of various micromechanical resonators.