单晶硅微机械谐振子的非线性决定了谐振结构的振动能量存储能力，直接影响到由微机械谐振子构成的振荡器的性能，因此需要对微机械谐振结构中的非线性效应进行研究。文献和我们的研究工作表明，体声波模态谐振结构中不但存在类似于杜芬谐振子的非线性幅频特性，而且还会存在类似于振动碰撞系统中的幅值饱和特性。本课题拟基于非线性振动碰撞模型和体声波模态的非线性耦合振动模型两种假设，通过对体声波模态谐振子的结构设计和振动特性表征，探索在高阶椭圆体声波模态振动下幅值饱和特性的产生机理。同时，我们提出利用幅值饱和效应简化微机械谐振子振荡器中放大器增益的自动控制电路设计，并研究该非线性效应对频率稳定性等振荡器性能的影响。该课题的研究不但可以加深对微机械谐振子中非线性效应的理解，而且为研究新型微机械振荡器奠定理论和实践基础。

Nonlinearities in single-crystal silicon micromechanical resonators set the limit for vibration energy storage capacity, which directly affects the performance of micromechanical oscillators. Therefore, it is necessary to investigate the nonlinear effects in micromechanical resonators. As demonstrated in the literature and our work, for bulk acoustic wave mode micromechanical resonators, there exists not only a Duffing resonator like characteristic of nonlinear frequency-amplitude behavior, but also a Vibro - Impact system like characteristic of amplitude saturation behavior. This project is going to explore the mechanism of amplitude saturation behavior in the high order elliptical bulk acoustic mode resonators, through structural design and vibration characterization, based on the assumption of Vibro-Impact Model and Nonlinear Coupled Bulk Acoustic Modes Model. In addition, we propose to simplify the electronic design of automatic gain control for the amplifier in micromechanical oscillators by making use of the amplitude saturation effect, whose effects on the oscillator performance like frequency stability are also studied. We believe that this project will not only increase our knowledge of nonlinear effects in micromechanical resonators, but also lay a good foundation for developing novel micromechanical oscillators.