| With the increasing popularity of the Internet of things in semiconductors,the market share of MEMS devices is increasing day by day.However,there are many problems to be solved at the same time.In the machining process,due to the small size and insufficient accuracy,the machining error is inevitable.Electrostatically driven microbeam resonator is a typical MEMS sensor.Its structure has obvious nonlinearity,and even complex modal coupling vibration may exist inside.The existence of machining error will lead to stronger nonlinearity of the resonator system.Therefore,considering the influence of machining error on the modal coupling vibration of micro resonator system has significant guiding significance for expanding the application field of MEMS devices.In this paper,the effects of thickness form error and initial deformation on the vibration mode,static displacement,dynamic displacement and modal coupling vibration of the resonator system are deeply studied.The specific research contents and results are as follows:(1)The modal coupling vibration of micro resonator driven by monopole plate is studied,and the section parameters used to describe the changes of upper and lower surfaces of micro beam are introduced.Based on Euler Bernoulli beam model,the coupling vibration between modes of micro beam resonator under thickness form error is studied.The corresponding nonlinear coupling equations are obtained by using Galerkin discretization and multi-scale method,and the critical threshold of coupling vibration under different section parameter errors is obtained.The theoretical solution of frequency response curve is numerically verified,which shows that modal coupling vibration can effectively suppress the midpoint displacement of micro beam;At the same time,the reduction of section parameters will promote the modal coupling within the system,restrain the midpoint displacement of the micro beam to a greater extent,and broaden the frequency response bandwidth of the system.The modal coupling resonance of the system under different section parameters analyzed in this study has potential application value for improving the stability and rated voltage of the micro resonator system.(2)The static and dynamic characteristics of micro beam resonator driven by monopole plate are studied.The static displacement equation of the resonator system is obtained by Galerkin discretization,and the effects of section error coefficient and initial rise coefficient on the static displacement are obtained.The multi-scale method and Runge Kutta method are used to solve the dynamic equation of the system,and the effects of section error coefficient and initial rise coefficient on the soft and hard characteristics of the system are obtained.Taking the linear vibration of the resonator system as the target,the variation relations of different section coefficients,initial rise coefficients and DC voltage are obtained,which provides theoretical guidance for improving the performance of the resonator.(3)The modal coupling vibration of micro beam resonator driven by bipolar plate is studied.Based on D’Alembert principle,a resonator model considering thickness error and initial deformation is established.Through the mutual verification of frequency response curve theory and numerical method,the effects of section error coefficient,initial rise coefficient,DC voltage and AC voltage on the modal coupling vibration of the system are obtained.The results show that the increase of AC voltage and section coefficient will enhance the hardening nonlinearity of the system.When the external excitation amplitude remains unchanged,the first-order maximum amplitude will not change with the change of parameters,and the third-order maximum amplitude will reach the minimum when the section coefficient is close to zero.The modal coupling vibration of the system under different parameters analyzed in this study has potential application value to improve the efficiency and stability of the resonator. |
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