Static And Dynamic Analyses Considering Scale Effect And Fringe Effect Of The MEMS Comb Resonator

Micro-electro-mechanical systems(MEMS)is a micro mechanical electronic components with high precision and widely applied in aerospace,precision measurement,security and military,communications and other fields.The dynamic characteristics of MEMS comb resonator have attracted more and more attentions.Comb resonator is one of the most common electronic components in MEMS,made of silicone material,and easy to obtain high sensitivity.Compared with the beam structure,comb structure is more stable and has high efficiency,high precision,advantages of different forms.MEMS comb resonator is widely applied to the filter,the acceleration sensor,the optical frequency comb and energy collector,and many other products.Nonlinear dynamic analyses of the resonator have significant theoretical and engineering meanings for grasping its complex vibration mechanism,guiding its dynamic optimization and realizing its optimized control.This paper focuses on a comb microresonator,analyses the stability,resonance frequency,hard and soft behavior.The main research contents and results are as follows:(1)The MEMS comb resonator for the necessity of research on the scale effect is introduced.Due to the resonance frequencies of the micro comb fold beam theory result is less than the experimental results,at the same time,and the comb fold beam width is not far outweigh the scale parameters of the material.So it is necessary to build scale effect model and the analysis of the effect of scale effect on structure.According to the coupling stress theory we deduce the train energy expression,and then import it into the cantilever beam model.Through the comb fold beam model perturbation analysis we can get the linear stiffness and nonlinear stiffness of the system.(2)The static and dynamic characteristics of the micro comb resonator considering scale effect is been discussed in this paper.This paper focuses on a comb microresonator,improves the model for vibration considering scale effect,and analyses the influence of scale effect on the dynamic characteristics for MEMS comb resonator.Firstly,the unperturbed Hamilton system is introduced to analysis the stability of the system.Afterward,the model for vibration is solved by multi-scale method.Combined with analytical results,the criterion for the existence of spring hard to soft transition is defined and the frequency response properties are summarized.Moreover,two explicit formulas to describe the optimum DC voltage and equivalent natural frequency when a linear-like state appears are deduced,respectively.(3)Because of the particularity of comb structure,the fringe effect of the electrostatic force is very obvious.This paper improves the electrostatic force,and analyses the influence of fringe effect on the electrostatic force for MEMS comb resonator.The electrostatic force is fitted with least-squares method and solved by multi-scale method,simplifies the comb resonators complex dynamic problems.This thesis analyses the stability,resonance frequency,hard and soft behavior by theoretical analysis and numerical simulation,which have significant theoretical and engineering meanings for grasping its complex vibration mechanism,guiding its dynamic optimization and realizing its optimized control.