中文摘要：

本文将薄膜式微谐振压力传感器谐振子简化为对边简支对边自由机电耦合微薄膜谐振系统,给出了考虑分子力作用时微薄膜压力敏感元件机电耦合系统动力学方程,推导其振型方程及频率方程,研究了分子力对系统固有频率及自由振动的影响规律.结果表明：分子力对于机电耦合微薄膜的自由振动固有频率具有重要的影响.随着系统初始间隙的减小、工作电压的增大、微薄膜厚度的减小以及薄膜长度的增大,分子力对系统固有频率的影响更加显著.在低阶模态下,分子力对固有频率的影响变大,应该予以考虑.当初始间隙减小到0.1μm时,Casimir力对固有频率的影响比van der Waals力明显,必须考虑Casimir力的影响.论文有助于薄膜式微谐振压力传感器谐振子的动力学理论分析,研究结果对于MEMS压力传感器进一步小型化具有指导意义.

英文摘要：

The dynamical equations of electromechanieal coupling thin film are deduced by considering molecular forces.The vibra- tion and frequency equations of thin film with two opposite edges simply supported and other two free are derived.Using the equa- tions, the influences of the molecular forces on natural frequency and free vibration are investigated. Results show： the molecular forces have obvious influences on the natural frequency.As the initial clearance drops, voltage grows, the thickness decreases, and the length increases, the influences becomes larger.As the order number of the modes decreases, the effects on the natural frequency are more significant.At clearance to = 0. 1 μm, the Casimir forces have more obvious effects on the natural frequency than van der Waals forces, and the Casimir forces must be considered.The results are helpful to the study of dynamic characteristics of thin film resonant pressure sensor and can be applied to MEMS dynamic design.