Study Of Feedback Control For Nanobeam Nonlinear Vibration

As a fundamental part in MEMS/NEMS devices,nanobeam which has advantages of small size,light weight and high sensitivity is successfully applied in automotive industry,medical,military and other fields,and has become one of the hot issues in the research field.But with the structure size reducing to nano scale,the behavior of nanobeam vibration is easy to enter the nonlinear region from linear region and presents nonlinearity of multi-value phenomena and bifurcation,which affect the stability of electronic devices and hinder the development of MEMS/NEMS technology.Therefore,it is significance to investigate influence factors and control methods of nanobeam nonlinear vibration for further understanding of MEMS/NEMS,and perfecting and creating micro and nano electromechanical systems with new features.The control effect of capacitance controller and piezoelectric controller for the nonlinear vibration of the electrostatically actuated nanobeam is investigated,using the methods of theoretical analysis and numerical simulation with model of a clamped-clamped Euler-Bernoulli beam.Firstly,capacitance control model is established for the clamped-clamped electrostatically actuated nanobeam.The capacitance of parallel-plate capacitor changes with nanobeam vibration.The capacitive sensor is applied to extract vibration signals according to the change of capacitance,and transform the enlarged vibration signals into the controller to control the nonlinear vibration of nanobeam.The control equation of nanobeam nonlinear vibration is obtained by Hamilton's principle,the equation of amplitude-frequency response and phase-frequency response is obtained by multi-scale method,and the stability of nanobeam vibration is analyzed.The influence of control parameters and system parameters on the stability and m maximum amplitude of nanobeam vibration is obtained through analysis of amplitude-frequency response.The capacitive controller successively makes nanobeam vibration be in stable state.Secondly,the control of nonlinear behavior of nanobeam with the piezoelectric controller subjected to axial force is analyzed.The relationship between the initial axial force and natural frequency is studied using Rayleigh method.The control equation of nanobeam nonlinear vibration with axial force and piezoelectric control force is established.Through multi-scale method,the first-order approximate solution of nonlinear equation is analyzed,the equations of amplitude-frequency response and phase-frequency response for primary resonance and super harmonic resonance for nonlinear vibration system are obtained.The influence of excitation voltage,damping,feedback gains and axial force on the stability and maxi amplitude of nanobeam vibration is obtained by analyzing amplitude-frequency curves.And the nonlinear vibration of nanobeam can be successively eliminated through capacitive controller.Finally,considering,respectively,the Casimir force and van der Waals force,the piezoelectric control of nanobeam nonlinear vibration is studied.The influence of system parameters and control parameters on the stability and maximum amplitude of nanobeam nonlinear vibration subjected to nano-scale force is investigated using the multi-scale method.The investigation in this paper shows that the nonlinear vibration of nanobeam can be effectively controlled by piezoelectric controller and capacitor controller.The nonlinear vibration of nanobeam can be weakened or eliminated through selecting reasonable control parameters and system parameters.The study provides a new theoretical method for the nonlinear vibration control of MEMS/NEMS,and has certain theoretical significance and engineering application value.