Nonlinear Vibration And Control Analyses Of A Class Of Microbeam-Based Resonators Actuated By Two Electrodes

Micro-electro-mechanical systems(MEMS)technology,as the most advanced technology in the 21 st century,is widely applied in aerospace,precision instrument,biotechnology,national defense and military,communication,etc.Meanwhile,the rapid development of MEMS technology also brings many multi-disciplinary crossed issues,especially some dynamic ones.For dynamic MEMS devices such as MEMS resonator,gyroscope and micromotor,dynamic characteristics of their moving components can directly affect the working performances of the systems.In-depth investigations of the dynamic behaviors of these components will contribute to the optimal design and extended application of MEMS devices.Doubly clamped microbeam-based resonator,as one kind of dynamic sensor with high precision,mainly works through the mechanical resonance of its internal oscillator.However,this component is highly nonlinear in geometry.Under the excitation of nonlinear electrostatic force,this system may present typically nonlinear properties.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.Here,this thesis focuses on a doubly clamped microresonator with two symmetrically located electrodes and includes some investigations on its static bifurcation,nonlinear vibration,dynamic design and vibration control.The research contents and main results of this thesis are as follows.(1)The static bifurcation property of this microresonator is investigated in detail.The unperturbed Hamilton system is used to deduce the variation of static equilibriums versus some typical parameters.Static bifurcation set and its phase properties are then obtained.Dynamic pull-in conditions are identified and then verified by numerical simulations.And the difference of phase manifold under the same equilibrium number is successfully explained from the viewpoint of potential barrier/well energy.(2)The frequency response characteristics of this microresonator under primary resonance condition are investigated in detail.With the static bifurcation results and small amplitude assumption,dynamic behaviors and natural frequencies of the system in the neighborhood of zero/non-zero equilibrium are investigated.And the secondary pull-in phenomenon is successfully explained.The criterion for the existence of hard to soft transition is then 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-type state appears are deduced,respectively.In addition,the effects of physical parameters on linear-type behavior are discussed according to these two formulas.(3)The effects of delayed velocity feedback control on the dynamic properties of this microresonator are investigated in detail.With the application of Hopf bifurcation theory,stability domains of the system in all delays region are found.Results show that stability switches do exist in this system.The differences of the stability domains via Hopf bifurcation analysis and via the method of multiple scales method are thoroughly distinguished.Effective natural angular frequency and damping coefficient are derived and frequency and damping trimming phenomena are studied.Finally,the decoupling problem for frequency and damping trimming is discussed.(4)Together with physical parameters,large amplitude design considerations of this microresonator are investigated in depth.Large amplitude design conditions of the unperturbed Hamilton system are firstly defined.The effects of natural frequency,initial gap width,thickness of the microbeam and DC voltage on this vibration state are then investigated.Moreover,numerical Melnikov simulation and local maximum method are both used to investigate the effects of disturbed parameters on chaotic dynamics of the system.These investigations can provide some theoretical references on large amplitude dynamic design.(5)Two fractional-order sliding mode controllers are designed respectively and then used to control the chaos of the microresonator.With the application of fractional calculus and sliding mode control theories,Fuzzy Fractional-order Fast Terminal Sliding Mode Controller and Fractional-order Nonsingular Fast Terminal Sliding Mode Controller are designed.The stabilities are then verified via fractional-order Lyapunov stability theory.In addition,Matlab/Simulink programs are used to verify the effectiveness of these two controllers in chaos control of the system.These investigations offer some theoretical references for the application of fractional-order controller on dynamic MEMS control.