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Sensors 2016, 16(10), 1700;

A Stepped Frequency Sweeping Method for Nonlinearity Measurement of Microresonators

State Key Laboratory of Precision Measurement Technology and Instruments, Department of Precision Instrument, Tsinghua University, Beijing 100084, China
High-Tech Institute of Xi’an, Xi’an 710025, China
Author to whom correspondence should be addressed.
Academic Editor: Stefano Mariani
Received: 18 August 2016 / Revised: 27 September 2016 / Accepted: 10 October 2016 / Published: 13 October 2016
(This article belongs to the Section Physical Sensors)
Full-Text   |   PDF [8396 KB, uploaded 13 October 2016]   |  


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. View Full-Text
Keywords: MEMS resonators; nonlinear features; Hilbert transform; Backbone curve; singular spectrum analysis MEMS resonators; nonlinear features; Hilbert transform; Backbone curve; singular spectrum analysis

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Wei, Y.; Dong, Y.; Huang, X.; Zhang, Z. A Stepped Frequency Sweeping Method for Nonlinearity Measurement of Microresonators. Sensors 2016, 16, 1700.

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