一类静电驱动双边电容型微谐振器振动系统的复杂动力学特性研究

Complex dynamics of the vibrating system of a micro mechanical resonator with electrostatic forces on both sides

以一类静电驱动双侧平行板电容型微谐振器为研究对象,基于分岔理论研究微结构的复杂动力学行为的机制。通过分析微结构动力系统的静态分岔,发现直流偏置电压的增大会直接引起微结构的静态吸合。在此基础上获得系统的多稳态解的解析形式,解析预测与数值结果吻合,研究发现系统的振动跳跃来源于双平衡点失稳引起的多稳态现象。进而发现继续驱动交流电压幅值的增大则会引起微结构的混沌和吸合不稳定现象。该结果对静电驱动微谐振器的设计中如何避免出现复杂响应具有实际意义。

A class of micro mechanical resonator with electrostatic forces on both sides was considered whose complex dynamical behaviors were studied by the theories of bifurcations.It followed from the static bifurcation of the dynamical system that the increase of bias DC voltage would induce the static pull in of the microstructure.Basing on it,the obtained theoretical multiple periodic solutions were in agreement of the numerical results,which show that the safe jump phenomenon meant the multiple periodic solutions that caused by the losing stability of the two equilibriums.In addition,it was found that the increase of AC voltage would lead to the chaotic motion and pull-in instability.The investigation above may be helpful for preventing the complex dynamics,which can be applied to design the electrostatic micro resonators.