Vibration And Stability Analysis Of Graphene Reinforced Functionally Graded Piezoelectric Microplate Based On The Nonlocal Elastic Theory

With the trend of miniaturization and portability of modern manufacturing technology,the research on MEMS has been widely concerned by scholars.At the same time,with the continuous emergence of more micro structures,the basic mechanics research at the micro scale becomes particularly important.As an emerging material,graphene has excellent electrical,thermal,and mechanical properties,which can greatly improve the overall performance of composite materials.In this paper,graphene is distributed in a gradient form in polyvinylidene fluoride and piezoelectric ceramics to form a functionally graded material.Based on nonlocal theory,first-order shear deformation plate theory,Von Karman large deformation theory,Hamilton principle and minimum potential energy principle,the vibration and stability of graphene enhanced functionally gradient piezoelectric plate at micro scale are studied and analyzed.The research content is mainly divided into the following parts:(1)The characteristics of linear vibration and nonlinear vibration of graphene enhanced functionally graded piezoelectric plate are studied.Establishing plate model on Winkler elastic foundation,with applied voltage,the control equation is derived by Maxwell equation,nonlocal theory,one stage shear deformation plate theory,von Karman large deformation theory and Hamilton principle.The control equations are discretized and solved by differential quadrature method and direct iteration method.The linear and nonlinear vibration FG-GR piezoelectric microplate under different boundary conditions and different graphene distribution modes are discussed.(2)Considering the influence of temperature,the buckling and postbuckling behaviors of nonlocal FG-GR piezoelectric microplate are analyzed.Temperature field,electric potential,uniaxial load and biaxial load are applied to the microplate model.Combined with Maxwell equation,nonlocal theory,first-order shear deformation plate theory,von Karman large deformation theory and minimum potential energy principle,the governing equations are derived.The control equations are discretized and solved by differential quadrature method and direct iteration method.The effects of boundary conditions,graphene distribution,physical and geometric properties of graphene on the buckling and postbuckling behavior of nonlocal FG-GR piezoelectric microplate are studied.