参数激励驱动微陀螺系统的非线性振动特性研究

摘要

对于一类典型的切向梳齿驱动型微陀螺，建立两自由度、具有刚度立方非线性和参数激励驱动的微陀螺系统动力学模型。考虑主参数共振和1∶1内共振的情况，利用多尺度法获得周期解的解析形式，并利用分岔理论，得到Hopf 分岔条件，结合数值模拟系统的动力学响应，揭示系统参数对驱动和检测模态振幅和分岔行为的影响机制。研究结果表明，在1∶1内共振和较大的载体角速度下，激励频率的变化容易引起微陀螺振动系统的多稳态解、振幅跳跃现象和概周期响应等复杂动力学行为。%For a typical non-interdigitated comb-finger actuated micro-gyroscope,a 2-DOF dynamic model with cubic nonlinear stiffness and parametric excitation was established.For the principal parametric resonance case and 1 :1 internal resonance,the periodic solutions were obtained with the multi-scale method.Conditions of Hopf bifurcation of the periodic solutions were derived according to the theory of bifurcation.Then the dynamic responses of the system were simulated.Finally,the effect mechanism of the system's parameters on the modal amplitudes and bifurcation behaviors was analyzed.It was shown that the variation of the excitation frequency is easy to cause various complex dynamic behaviors of the microgyroscope vibrating system,such as,multi-stable solution,amplitude jump phenomena and quasi-periodic responses under a large angular speed of the carrier and 1 :1 internal resonance.