The Research On Mechanical Properties Of Functional Graded Material Microplate Under Size-effect

The size-dependent phenomenon is that the particle properties inside the microstructure can affect the mechanical properties of the microstructure when the microstructure is extremely small and reaches the micron or nanometer scale.At the same time,the traditional theory of continuum classical mechanics shows some limitations on explaining the size effect of microstructure,so the proposing and application of Modified couple stress theory play an important role on studying the size effect of microstructure.Casimir forces is an interaction force between molecules,which was proposed by Dutch physicist in 1948,and the influence of Casimir force on the mechanical properties of objects is obvious at the microscopic scale.Functionally gradient Material(FGM)is a new type of heterogeneous Material which is composed of two different materials.The material component is graded and effectively overcome the deficiency of traditional composite materials.FGM usually be used as coating and interface layer and reduce residual stress and thermal stress,increase the connection strength and reduce the crack driving force compared with the traditional composite materials.The microplate is widely used in chip,microelectronics and micro device,however,the microplate can be easily damaged under thermal stress and mechanical stress.Therefore,the application of FGM material in microplate is very important.In this paper,we study a square microplate based on the Kirchhoff classical plate theory and the von-Karman geometric nonlinear theory,the nonlinear dynamic equation of the microplate is derived by using the modified coupling theory and Hamilton principle and we take functionally graded materials,size effect and Casimir force into consideration.The main research contents of this paper are as follows:(1)The governing equations and boundary conditions of FGM microplate is drived based on Hamilton principle and displacement field of FGM plates is determined by Kirchhoff classical plate theory and stress and strain constitutive relation is derived by modified coupling stress theory.(2)According to the consitutive relation of microplate model,we create the three-dimensional model of the homogeneous material microplate in COMSOL and we use gemetrical structure size of microplate in existing literature as references.The simulation results of static pull-in instability and dynamic nonlinear free vibration of microplate are compared with the conclusion in the existing literature to prove the correctness of the model.(3)The characteristics of static pull-in instability and dynamic nonlinear free vibration of the microplate are studied by using Multiphysics simulation software COMSOL and the three-dimensional static and dynamic mechanics model of microplate,which is drived based on the theoretical model of microplate.(4)The effects of paramters like size effect,functional gradient material and geometry of microplate on the static pull-in instability and dynamic nonlinear free vibration of microplate are analyzed.