微机械角振动谐振器在低气压下的非线性振动

Nonlinear vibration of micromachined angular vibration resonator in low pressure

本文研究气压对微机械角振动谐振器振动特性的影响。基于谐振器的梁的弹性力矩和角位移之间的3次多项式关系,建立了谐振器非线性振动方程。给出了谐振器自然频率与振幅的关系和频率响应特性与振幅关系的理论解。测试了在大气压、1100Pa和130Pa下谐振器的频率响应曲线。通过对大气压下振动频率特性的分析,得到了非线性振动方程的基本参数,将这些参数和低气压小振幅下的品质因数代入频率特性的理论解,推算出的低气压大振幅下的频率特性与实测曲线符合。随着气压的降低,谐振器振动频率响应的非线性程度增大。

An investigation into the influence of air pressure on the vibration characteristic of a micromachined angular vibration resonator is presented. Based on the cubic polynomial relationship between elastic moment and angular displacement, the nonlinear differential equation of the resonator is established. Theoretical solutions for the relationships of natural frequency as well as frequency response characteristic to vibration amplitude are presented. The frequency response curves of the resonator are tested under atmospheric pressure, 1 100 Pa and 130 Pa. Through analyzing the frequency characteristic in atmospheric pressure, the basic parameters of the nonlinear vibration equation are obtained. These parameters and the Q-factor obtained from low pressure and small amplitude cases are introduced into the theoretical solution of frequency characteristic, the frequency characteristic curves for low pressure and large amplitude are calculated. The theoretical curves agree with the tested results. The nonlinear degree of the vibration frequency response increases while the pressure decreases.