A Stepped Frequency Sweeping Method for Nonlinearity Measurement of Microresonators.

Yumiao Wei,Zhili Zhang,Xianxiang Huang,Yonggui Dong

doi:10.3390/s16101700

Abstract

In order to measure the nonlinear features of micromechanical resonators, a free damped oscillation method based on stair-stepped frequency sinusoidal pulse excitation is investigated. In the vicinity of the resonant frequency, a frequency stepping sinusoidal pulse sequence is employed as the excitation signal. A set of free vibration response signals, containing different degrees of nonlinear dynamical characteristics, are obtained. The amplitude-frequency curves of the resonator are acquired from the forced vibration signals. Together with a singular spectrum analysis algorithm, the instantaneous amplitudes and instantaneous frequencies are extracted by a Hilbert transform from the free vibration signals. The calculated Backbone curves, and frequency response function (FRF) curves are distinct and can be used to characterize the nonlinear dynamics of the resonator. Taking a Duffing system as an example, numerical simulations are carried out for free vibration response signals in cases of different signal-to-noise ratios (SNRs). The results show that this method displays better anti-noise performance than FREEVIB. A vibrating ring microgyroscope is experimentally tested. The obtained Backbone and FRF curves agree with those obtained by the traditional frequency sweeping method. As a test technique, the proposed method can also be used to for experimentally testing the dynamic characteristics of other types of micromechanical resonators.

Highlights

Micromechanical resonators have been widely used as the key sensing elements in diverse sensors such as micromechanical inertial sensors, resonant pressure sensors, etc
In the vicinity of the resonant frequency, a frequency stepping sinusoidal pulse sequence is used as the excitation signal
In order to further suppress the fluctuations of instantaneous frequency (IF) and extract the frequency change trend

Summary

Introduction

Micromechanical resonators have been widely used as the key sensing elements in diverse sensors such as micromechanical inertial sensors, resonant pressure sensors, etc. Compared with conventional macroscopic-sized resonators, micromechanical resonators are more liable to present nonlinear dynamic features [1,2]. Since the resonators are small in size, they are generally driven close to or even into nonlinear regimes in order to achieve higher vibration amplitudes and sufficiently higher sensitivity and signal-to-noise ratios (SNRs). When the vibration amplitude is close to or even located in the nonlinear region, instability caused by nonlinear effects will emerge and the overall sensor performance will be decreased [3,4]. Studies on the nonlinear dynamics of microresonators have been a research hot spot in recent years [5,6,7,8]. Obtaining the nonlinear dynamics by experimental methods will benefit in operating circuit configuration for the manufactured microsensors, and provide guidance for future resonator design optimization

Results

Discussion

Conclusion