The Research On Mechanical Behaviors And Optimization Design Of MEMS Resonator Under The Influence Of Thickness Shape Error

With the rapid development of society and continuous improvement of living standards,the demand for micro-electro-mechanical system(MEMS)devices is increasing.Compared with traditional electromechanical systems,MEMS devices have a series of advantages such as small size,light weight,low power consumption,fast response and intelligence.Nevertheless,there are some inevitable problems in the MEMS devices.The size reduction makes the fabrication of MEMS devices very difficult.In the process of fabrication,the section shape of MEMS devices usually changes due to excessive etching or inadequate etching.Causes a change in the mechanical properties.In addition,with the rapid development of MEMS devices,there will be many dynamic problems to be solved.Therefore,a comprehensive consideration of real situation influence on MEMS device mathematical model and a thorough study of its nonlinear dynamic behavior will help to optimize design and expand application of MEMS device.Electrostatically actuation microbeam resonator is a typical dynamic structure sensor in MEMS devices.It mainly works by using the mechanical resonance characteristics of structure inside the resonator.However,such structures have obvious stiffness nonlinearity and electrostatic force nonlinearity.At the same time,the shape change caused by fabrication errors will also have an important impact on system nonlinearity.Considering the mechanical properties of microresonators under error and nonlinear conditions,it has guiding significance for the design and optimization of MEMS devices.In this paper,the electrostatically actuation microbeam resonators with fixed ends are studied.The theoretical,numerical and finite element methods are used to study the Thickness shape error of unipolar plate actuation and bipolar plate actuation for static pull-in,nonlinear vibration and optimization design.(1)Considering the influence of neutral surface tension and thickness shape error,a continuum model of unipolar plate electrostatically actuation micro-resonator is established.The Galerkin method and Newton-Cotes method are used to simplify the system into a singledegree-of-freedom model.The influence of section parameter and plate gap on pull-in effect is obtained by static equation.The small amplitude vibration of micro-resonators with different section parameters and plate gap is obtained.Finally,the influence of section parameters on large amplitude vibration is discussed for the first time.(2)The static and dynamic characteristics of micro-resonator actuation by bipolar plates is studied.Firstly,the bifurcation of system without considering error is deduced.The influence of thickness shape error on bifurcation is discussed by the change of static equilibrium point,equivalent natural frequency and phase space manifold with excitation parameters.The method of multiple scales(MMS)is applied to study the influence of thickness shape error on the soft and hard characteristics under small amplitude vibration.The relationship between section parameters,DC voltage and plate gap is optimized under the condition of linear vibration.(3)The micro-resonator controlled by two-parameter equation with thickness shape error is studied.At this time,the microbeam will appear asymmetrical situation about neutral plane.Considering the influence of neutral surface tension,neutral surface bending and thickness shape error,a continuum model of bipolar plate electrostatically actuation micro-resonator is established.Perform finite element analysis on electrostatic force to verify the correctness of theoretical results.The influence of two equation parameters change on micro-resonator electrostatic force,pull-in voltage,pull-in position and safety zone are discussed.The relationship between two equation parameters satisfying the linear vibration of system is obtained by dynamic analysis.The variation of vibration amplitude and resonance frequency of micro-resonator under linear vibration conditions is also studied.The large amplitude vibration of system is obtained by Simulink dynamic simulation.It is found that the frequency response will shift from hardening to softening behavior when the amplitude increases to a certain value.The influence of the change of equation parameters on the transition point is studied.Finally,the relationship equation of DC voltage,equation parameters and soft-hard transition point is given.