Nonlinear vibration of micromachined angular vibration resonator in low pressure

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, 1100 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.