Nonlinear Vibration Of Micro Structure Actuated By Fringing Electrostatic Force

Micro electro mechanical system(MEMS)is a micro-device or system that integrates micro-sensor,micro-actuator,micro-mechanical structure,micro-energy,signal processing and control circuit,interface and communication.It is widely used in high-tech industries.As the main driving force of MEMS,electrostatic force plays an irreplaceable role in the research of MEMS.The dynamic characteristics of the electrostatic actuated movable structures directly affect the overall performance of the MEMS using this driving mode.It is of great significance to study the dynamic behavior of electrostatic actuated micro-structures for optimizing MEMS.The vibration amplitude of the movable plate is limited,since the problem of pullin in the parallel plate electrostatic actuation mode.Fringing electrostatic actuation mode is an electrostatic driving method based on fringing effect.It has the advantages of simple processing,large amplitude vibration without electrode restriction and wide resonance frequency range.Under the actuation of the fringing electrostatic field,the vibration of the movable plate is nonlinear.A thorough study and mastery of the dynamic behavior of this kind of structure will help to optimize the design and broaden the application of MEMS devices.The parallel plate electrostatic actuation mode is studied.Based on the nonlinear vibration characteristics of cantilever beam actuated by parallel plate electrostatic actuation,we propose innovatively an improved resonant method for measuring the Young's modulus.We show a kind of fringing electrostatic actuation mode for the first time.Through the combination of theoretical modeling,analytical calculation,numerical verification and experimental research,the mechanism of fringing electrostatic force and the complex response law of fringing electrostatic actuation vibration system are revealed,the relationship between system parameters and vibration response is analyzed,the application scheme of this actuation mode is put forward.The research contents and achievements of this paper include the following aspects:(1)The working principle of electrostatic actuation mode is revealed.The quality factor of nonlinearity is used to characterize the nonlinearity of vibration response.The influence of nonlinear electrostatic force on vibration response is studied.The relationship between resonance frequency of resonant beam and DC voltage in actuation voltage is found out.Based on the functional relationship between resonant frequency and DC voltage,we propose an improved resonant method for measuring the Young's modulus.Furthermore,the Young's modulus of brass is got in an experiment by using this method.(2)In order to overcome the pull-in phenomenon in parallel plate electrostatic actuation mode,fringing electrostatic actuation mode is proposed.Firstly,we use the finite element method to get the numerical values of fringing electrostatic force under different parameters.Then,we use the polynomial fitting method to obtain the expression between the fringing electrostatic force and the relative position between the plates.Finally,we analyze the influence of structural parameters in fringing electrostatic actuation mode on electrostatic force fitting parameters.Results show that smaller gap and larger fixed plate thickness make the fringing electrostatic force more nonlinear.The polynomial expression of the fringing electrostatic force is put into the MEMS based on this actuation mode,which is helpful to analyze the vibration characteristics of the moving elements actuated by the fringing electrostatic force.(3)The cantilever beam actuated by fringing electrostatic force is modeled by using the elastic beam theory.The static and dynamic analysis of the structure is carried out by Galerkin Method and Method of Multiple Scales.Combining theoretical calculation and numerical verification,the bifurcation behavior of fringing electrostatic actuation beam is deeply studied.The results show that: with the increase of excitation voltage,when the static deformation of the cantilever beam reaches the neutral plane of the electrode plate,the cantilever beam will continue to deform until it reaches a limit position;the resonance frequency and vibration amplitude increase with the increase of initial displacement;the jump frequency increases with the increase of initial displacement;with the increase of beam length and excitation voltage,the nonlinearity of vibration increases;with the increase of voltage and initial displacement,the smaller excitation frequency appears bifurcation first.We propose that tactile sensors can apply this structure.The measuring principle of the sensor is to describe the external tactile pressure by measuring the relative displacement between two plates.The prototype structure of the sensor is tested,and the relative displacement between plates is detected by frequency measurement or amplitude measurement.(4)The flexible supported beam actuated by fringing electrostatic force is modeled.The parametric vibration of flexible supported beams is studied.The excitation frequency range of the stable vibration of the structure is obtained.Hopf bifurcation is found in the system.Based on the research results,we propose that sensors,filters and actuators can apple this structure.The theoretical analysis results provide useful exploration for optimizing the structure of fringing actuation mode and expanding its application.The above work expands the application of electrostatic excitation mode,develops the structure of electrostatic excitation mode,and finds abundant non-linear phenomena in edge electrostatic excitation mode.The influence of system parameters on the nonlinear vibration behavior of the system is studied,which provides a theoretical basis for the optimization and application of fringing electrostatic actuation.