Wei Yumiao, Dong Yonggui, Huang Xianxiang, Zhang Zhili
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.
Sensors (Basel). 2016 Oct 13;16(10):1700. doi: 10.3390/s16101700.
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.
为了测量微机械谐振器的非线性特性，研究了一种基于阶梯频率正弦脉冲激励的自由阻尼振荡方法。在谐振频率附近，采用频率步进正弦脉冲序列作为激励信号。获得了一组包含不同程度非线性动力学特性的自由振动响应信号。从强迫振动信号中获取谐振器的幅频曲线。结合奇异谱分析算法，通过希尔伯特变换从自由振动信号中提取瞬时振幅和瞬时频率。计算得到的主曲线和频率响应函数（FRF）曲线明显不同，可用于表征谐振器的非线性动力学。以杜芬系统为例，对不同信噪比（SNR）情况下的自由振动响应信号进行了数值模拟。结果表明，该方法比FREEVIB具有更好的抗噪声性能。对振动环微陀螺仪进行了实验测试。获得的主曲线和FRF曲线与传统扫频方法获得的曲线一致。作为一种测试技术，该方法还可用于实验测试其他类型微机械谐振器的动态特性。
