Dynamics Of Primary And Parametric Resonance Of Multi-segment Micro-beam And Application To Micro-gyroscope

In order to solve the contradiction between improving sensitivity and broadening bandwidth in linear micro-gyroscope,we propose to use nonlinearity to solve the problem that high sensitivity and wide bandwidth cannot be combined in the linear case.In this paper,multi-segment micro-beam which a kind of elastic support beam with nonlinear characteristics is taken as the research object,and its influence law of nonlinear dynamics and size effect are analyzed and discussed,which provides a theoretical basis for using multi-segment micro-beam to improve the performance of micro-gyroscope.Firstly,the dynamic model of the plane model of multi-segment micro-beam structure is carried out,the configuration vector of the structure is given,and the natural frequency and mode of the system are calculated,which are verified by finite element simulation.Based on the modified couple stress theory,the deformation energy of a multi-segment micro-beam including material scale parameters is calculated.After considering the size effect,the first and second natural frequencies of the micro-beam increase;The mode of the multi-segment micro-beam at different angles is basically consistent with the classical theory,which shows that the size effect has little effect on the mode of the micro-beam.Analyzing the influence of parametric vibration and size effect on the nonlinear response and stability of multi-segment micro-beam,analyze the stability of system parametric vibration through Floquet theory,and verify the accuracy of stability theory prediction with phase diagram and time history.It is shown that the nonlinear behavior of the system increases with the increase of the fold angle;The existence of parametric excitation enhances the nonlinear behavior of the system,and the peak amplitude is significantly increased,the bifurcation occurs under a smaller excitation amplitude.Therefore,parametric vibration can be used to improve the peak amplitude of the system and strengthen the nonlinear behavior of the system;With the increase of damping,the threshold value increases continuously,and higher excitation amplitude is needed to excite the parametric vibration.At the same time,damping enlarges the stability area and enhances the stability of the system,but with the increase of fold angle,the stability of the system decreases;The existence of size effect causes the peak amplitude of the system to decrease,and the nonlinear behavior to weaken,especially in the case of small excitation amplitude.Considering the size effect makes the threshold of parametric vibration increases and the instability boundary of the system expands.The multi-segment micro-beam is applied to the micro-gyroscope,and the influence of the parameters of the multi-segment micro-beam on the performance of the micro-gyroscope is analyzed.The research shows that parametric vibration is beneficial to improve the gain and bandwidth of micro-gyroscope;when the beam length is short,due to the large stiffness,the gain generated under the same excitation amplitude is small and the degree of nonlinearity decreases.With the increase of the beam length,the bandwidth gradually increases.Therefore,on the premise of meeting the anti-vibration performance of the micro-gyroscope,the bandwidth and sensitivity of the micro-gyroscope can be improved by the increase of the beam length;With the increase of the fold angle,the detection gain is gradually reduced,but the reduction amplitude is not obvious,however the bandwidth is obviously widened with the increase of the angle.Therefore,compared with the multi-degree-of-freedom microgyroscope,increasing the bandwidth is inevitably accompanied by a significant decrease in sensitivity,and at this time,the sensitivity of the system can be reduced less by adjusting the fold angle of the multi-segment micro-beam while significantly widening the bandwidth,thus achieving both high sensitivity and wide bandwidth characteristics.In addition,when the excitation amplitude is relatively large,the system appears to have a higher gain,and the angular velocity detection can be carried out in a wide range of frequencies.