Analysis Of Nonlinear Statics And Dynamics Of Damaged Micro-plate For MEMS

As core components of MEMS(Microelectromechanical System),micro-beam and micro-plate are extensively applied in MEMS devices such as sensors,actuators and accelerometers.Comprehensive investigation of statics and dynamics characteristics of micro-structures have been carried out by numerous researchers.However,considerable experiments have proved that mechanical performance of micro-scale structures subject to size effect.Thus,statics and dynamics behaviors of micro-scale structures cannot be explained and predicted accurately by classic mechanics.What's more,owing to the influence of material fatigue or processing and manufacturing,defects such as damage and cracks will take place in MEMS micro-structures which are under complex operating environment.As a consequence,it is significant and essential to establish and develop micro-scale model and theory considering size effect and damage.Using micro-plate with defect for the research and considering geometric nonlinearity of the size-dependent micro-plate,this dissertation aims to derive the nonlinear static and dynamic governing equation of the novel model,explore solution for the complex nonlinear system,and discuss the influence of damage,geometric nonlinearity and size effect on the static and dynamic properties of the nonlinear system.Based on Kirchhoff plate theory,modified couple stress theory and strain equivalent assumption,the governing equation of the size-dependent micro-plate with damage was derived by Hamilton principle and solved by Galerkin method and the forth order Runge-Kutta method.Relationship between length scale parameter and static/dynamic pull-in voltage of the novel model are achieved as well as relationship curves of damage variable and static/dynamic pull-in voltage.The numerical results show that size effect is conductive to structure stability while it is not the case for the damage effect.Based on Von Karman plate theory,modified couple stress theory and Talreja's damage model with tensor valued internal state variables,nonlinear equilibrium equations of the size-dependent micro-plate with damage was derived by principle of minimum potential energy and solved by finite difference method and iteration method.The Kachanov damage evolution law was employed to predict damage development of the micr0-plate.In the numerical example,influence of length scale parameter,external loads and initial geometric deflection on post-buckling behavior of the perfect micro-plate and the damaged micro-plate was discussed in detail.Results show that middle point deflection of the micro-plate increases with the increase of time due to damage,and initial geometric deflection has no discernible effect on damage development while external loads and length scale parameter has remarkable influence on it.Finally,on the basis of Von Karman plate theory,modified couple stress theory and Talreja's damage model with tensor valued internal state variables,the nonlinear governing equation of the micro-plate was derived by using Hamilton principle and solved via Galerkin method and the forth order Runge-Kutta method.The effects of the damage value and length scale parameter on the bifurcation and chaos of the plates are discussed numerically.