Analysis Of Nonlinear Statics And Dynamics Of Piezoelectric Microstructures With Damage

Piezoelectric material,a kind of intelligent material,is widely used in MEMS components.As the MEMS structures are on the order of microns or sub-microns,the mechanical and physical properties of the microstructure are very different from the macroscale which is called as size effect.On the other hand,microstructures can be damaged in the process of production and use.The damage will reduce the working performance and service life of the structures.It is significant to study on damage.In this dissertation,the nonlinear static and dynamic behaviors and damage evolution of piezoelectric microstructures are investigated with the consideration of the size effect,damage and geometric nonlinearity.The main research works are as follows:The static and dynamic collapse behavior of a cantilever microbeam with a piezoelectric layer bonded on the top surface is studied.Based on the modified couple stress theory,isotropic damage theory and von Karman nonlinear theory,the nonlinear motion equation of the piezoelectric microbeam with damage is derived by using Hamilton principle.Through applying the differential quadrature method and the Newmark method,the governing equation is solved.The influences of the piezoelectric layer voltage,material length scale parameter and damage on the static and dynamic collapse voltage of the microbeam are discussed.Considering the damage evolution and size effect,the nonlinear governing equation of a fixed-fixed microbeam with two piezoelectric layers is established with Hamilton principle.The Kachanov damage evolution law and the Chaboche high cycle fatigue damage model are employed for once time load and long time cyclic load,respectively.With the differential quadrature method,Newmark method and Newton-Raphson method,the governing equation is solved.The effects of the piezoelectric layer voltage,material length scale parameters and load parameters on the nonlinear dynamic response and fatigue damage curve of the damaged piezoelectric microbeam are discussed in detail.Based on the von Karman nonlinear plate theory and modified couple stress theory,the nonlinear motion equations of the microplate are derived by using theHamilton principle.The constitutive relation of the piezoelectric microplate is established by the isotropic damage theory and piezoelectric theory,and the damage analyses of the piezoelectric microplate are conducted with the Kachanov damage evolution model and Chaboche high cycle fatigue damage model.The numerical calculation of the motion equations is implemented by the generalized differential quadrature method,Newmark method and Newton-Raphson method.The influences of the piezoelectric layer voltage,length scale parameters and load parameters on the nonlinear dynamic response and fatigue damage evolution are analyzed.