第一作者张琪昌男，博士，教授，1959年生

通信作者王炜男，博士，讲师，1980年8月生

压膜阻尼作用下微机械谐振器动力学分析

张琪昌，周凡森，王炜

(天津大学机械工程学院天津市非线性动力学与混沌控制重点实验室，天津300072)

摘要：静电驱动微机械谐振器由于其高频率、低功耗和小型化被广泛应用于工作在空气中和液体中的化学传感器和生物物种传感器中。对于微机械谐振器，作为表面效应的空气阻尼以及三次非线性静电刚度会显著影响器件的动态响应特性。通过压膜阻尼理论，探究了双端固支梁在自由振动过程中由于环境压力引起的空气阻尼和三次非线性静电刚度对微梁的运动形态、谐振响应等性能参数的影响，发现了双极板微谐振器振动特性与环境压力以及立方非线性静电刚度的关系。结果表明：环境压力的增加会使微机械谐振器的共振频率增加，振动的幅值以及共振漂移的幅度减小。微机械谐振器在小位移振动时，通过对幅频曲线的分析发现，三次非线性静电刚度会使微机械谐振器表现出或软或硬的非线性特性且不可忽略。

关键词：微机械谐振器；压膜阻尼；环境压力

基金项目：国家自然科学基金(11372210)；国家青年科学基金(11102127)；高等学校博士点基金(20120032110010)；天津市应用基础与前沿技术研究计划(12jCYBjC12500,12jCZDjC28000)

收稿日期：2014-05-23修改稿收到日期：2014-08-14

中图分类号:O322

文献标志码：A

DOI:10.13465/j.cnki.jvs.2015.17.021

Abstract:Electrostatically actuated micromechanical resonators with advantages of high frequency, low-power consumption and small size are widely used in chemical sensors and sensors of biological species, these sensors work in air or liquid. The air damping as surface effects and the cubic nonlinear static electrical stiffness can significantly affect the dynamic response characteristics of a micromechanical resonator. Here, via the squeeze-film damping theory, the effects of air damping caused by ambient pressure during free vibration and cubic nonlinear static electrical stiffness on the patterns of movement and response performance of a mirco beam fixed at both ends were investigated in detail. The relationships between the dynamic characteristics of the resonator and ambient pressure as well as nonlinear static electrical stiffness were found. The results indicated that the resonance frequencies of the micromechanical resonator increase with increase in ambient pressure, while the vibration amplitudes and the resonance drift decline with increase in ambient pressure; the cubic nonlinear static electrical stiffness makes the resonators exhibit softening or hardening nonlinear characteristics, they can not be ignored in amplitude-frequency curves of the resonaters' small amplitude vibration.

Dynamic characteristics of a micro-mechanical-resonator with squeeze film damping

ZHANGQi-chang,ZHOUFan-sen,WANGWei(Tianjin Municipal Key Laboratory of Nonlinear Dynamics and Chaos Control, School of Mechanical Engineering, Tianjin University, Tianjin 300072, China)

Key words:micro-mechanical-resonator; squeeze film damping; ambient pressure

硅微机械谐振器因其体积小、能耗低、易集成等优点被广泛应用于微机电系统中。……