Nonlinear Vibration And Control Analyses Of A Micro-Resonator Considering Multi-physics Coupling

Micro-electro-mechanical systems(MEMS)technology,as the most advanced technology in the 21st century,is an important development direction pointed out clearly by the national plan for medium and long term scientific and Technological Development.MEMS technology is widely applied in aerospace,precision instrument,biotechnology and artificial intellegence,etc.With the decrease of the size of MEMS devices,the improvement of accuracy and performance,all kinds of mechanical problems need to be solved.In-depth investigations of the dynamic behaviors and coupling mechanisms of these components will contribute to the optimal design and extended application of MEMS devices.Micro beam/comb structure,as the core component of MEMS resonator,mainly works through the mechanical resonance of its internal oscillator.However,under the excitation of nonlinear electrostatic force,this system present complex energy transformation relations and complex modal coupling within the structure.Meanwhile,the scale effect and creep characteristics of the materials under micro scale have important effects on the system.Complex environment coupling conditions and the unavoidable nonlinear factors inhibit the development of MEMS technology.Considering the scale effect,nonlinear dynamic behavior and optimization problems are studied.Energy transfer and dissipation mechanism under complex motion have significant theoretical and engineering meanings for improving the level of research and broadening the application area of MEMS.Here,this thesis focuses on micro-beam and micro-comb structure and includes some investigations on its static bifurcation,nonlinear vibration,energy transfer and dissipation mechanism,random vibration and vibration control.The research contents and main results of this thesis are as follows.(1)Considering the scale effect,an improved single degree of freedom model to describe electrically actuated microbeam-based resonators is obtained by using Nonlinear Galerkin method.Compared with the spring oscillator model,it can accurately predict the pull in voltage and resonance frequency of the system.An efficient unfolding analysis method is proposed.Then,theoretical expressions about system parameter space and maximum amplitude of monostable vibration are then deduced.Results show that reasonable decrease of this ratio can be more beneficial to monostable vibration.(2)Considering nonlinear coupling between vibrational modes of advanced micromechanical devices,this article investigates coupled dynamic behavior of microbeam-based resonators.Under higher order modes excitation,the influence of antisymmetry mode on nonlinear dynamic characteristics of electrically actuated microbeam is systematically studied.Through Hopf bifurcation analysis,the bifurcation sets for antisymmetry mode vibration are theoretically derived,and the mechanism of energy transfer between antisymmetry mode and symmetry mode is detailed studied.The pseudo-trajectory processing method is introduced to investigate the influence of external drive on amplitude and bifurcation behavior.An effective way is proposed to suppress midpoint displacement of the microbeam and to reduce the possibility of large deflection.The quantitative relationship between vibrational modes is also obtained.The displacement of one mode can be predicted by detecting another mode,which shows great potential of developing parameter design in MEMS.(3)Considering creep property and scale effect of materials,Maxwell model and Fractional Kelvin model are used to study the static bifurcation and global dynamics behavior of MEMS resonators.For a MEMS resonator actuated by one electrode,the concept of equivalent geometric nonlinearity is proposed to explain the influence of the scale effect on static pull-in.Meanwhile,two kinds of pull-in are proposed.In this paper,a perturbation method for dealing with time memory is presented and the parameters of the resonator under different materials are optimized.For a MEMS resonator actuated by two symmetrical electrodes,the bistable physical parameters of continuum model are obtained,and this paper puts forward a simple numerical method to deal with fractional order system and obtains the global dynamics behavior of fractional viscoelastic system.The influence of creep properties on nonlinear vibration and pull-in is obtained.(4)Considering environment perturbation,the coupling model of temperature field,electric field,structure field is built.An efficient approximation method is proposed to qualitatively study nonlinear stochastic dynamical behavior under small perturbation of stochastic parameter.It is found that the randomness of temperature field suppresses nonlinear behavior and reduces the possibility of large amplitude vibration.Monte Carlo simulation is put forward to verify the validity of the theoretical method,and to quantitatively give the effects of noise strength and correlation rate on the nonlinear dynamic behavior.The present work provides theoretical framework for analyzing the effects of the perturbation of temperature field on nonlinear system response.(5)A conceptual model of parametrically excited micro-comb structures is proposed.This article theoretically investigates global dynamical behavior of the system with time-delay feedback controller.Considering the comb structure consisting of flexible beam and shuttle mass,a perturbation method for handling rigid-flexible coupling systems is proposed.Through a detailed mathematical analysis,the critical point and type of Hopf bifurcation,saddle-node bifurcation and global bifurcation are theoretically derived.Theoretical expressions about system parameter space and maximum amplitude of monostable vibration are deduced.It is found that the time-delay feedback force can effectively control the global dynamic behavior.