Performance Analysis Of Size-dependent Piezoelectric Microbeams / Microplates

The size of internal structures of micro-electro-mechanical systems(MEMS)is usually in the order of micrometers or even nanometers.When the scale is reduced to the order of micrometers or submicrons,the structure of MEMS would exhibit size effect,which is quite different from the phenomenon observed in the macroscopic scales and has gone far beyond the concept and scope of traditional machinery.Therefore,the study of MEMS requires the establishment of theoretical model which consider the size effect to predict the various mechanical behavior of microstructures.Microstructures such as microbeams and microplates are the basic components of MEMS.In this paper,a unified functionally graded piezoelectric microbeams model is established by using modified couple stress theory and a model of composite laminates structures induced by piezoelectric actuators is developed with the new modified couple stress theory which could be used for orthotropic materials.The modified couple stress theory and the new modified couple stress theory only introduce one material scale parameter related to microstructures to describe the size effect.By studying the static bending and free vibration of microbeams and the static behavior of microplates,the influence of size effect is discussed.The main research works are as follows:1.The size-dependent functionally graded piezoelectric Reddy beam model is established based on the modified couple stress theory.The analytical solution for static bending and free vibration under simple supported condition is given by using Naiver method.The numerical results show that the introduction of material scale parameters will increase the stiffness of the microstructure.2.Based on the modified couple stress theory,a unified high-order shear model for functionally graded piezoelectric mirobeams is established and its analytical solution for static bending and free vibration under simple supported condition is given.It is found that the uniform beam theory can degenerate to existing beam theory through proper selection of shape function.For any existing high-order shear deformation theory,the establishment of unified beam theory can easily establish the size-dependent higher order shear deformation beam theory.3.Based on the new modified couple stress theory which could be used for orthotropic materials and Kirchhoff plate theory,a model of composite laminates induced by piezoelectric actuators is developed.The effects of material parameters and the size of piezoelectric actuators on the deflection of composite structure were analyzed.Research shows that the effect of size effect on the composite laminates structures and piezoelectric actuators is not negligible.The research in this paper can be used to evaluate the mechanical behavior of microstructures in MEMS quantitatively.In the same time,theoretical basis can be provided for the design of microstructures.