Buckling,Post Buckling And Vibration Of Graphene Reinforced Functionally Graded Beams

The unique two-dimensional structure of graphene gives it many excellent mechanical properties.A small amount of graphene platelets or its derivatives are added into the matrix as reinforcements to form graphene reinforced composites,which can significantly improve the strength and stiffness of the structure compared with traditional carbon fibers and carbon nanotubes.The excellent design concept of functionally graded materials is extended to graphene reinforced composites,that is to say,small pieces of graphene platelets(GPL)are used as reinforcements,which are randomly and evenly distributed in each layer of matrix.The content of graphene is gradient or even distributed layer by layer in the thickness direction of matrix,forming a new generation of advanced composites,namely functionally graded graphene reinforced composites(FG-GPLRC).In this paper,the buckling and post buckling characteristics and free vibration of FG-GPLRC beams are studied,the main contents are as follows:1.The nonlinear buckling and post buckling behaviors of functionally graded beams strengthened with graphene platelets are studied.It is considered that graphene is evenly distributed in each layer of the beam,but its weight fraction changes gradiently or uniformly along the thickness direction of the beam,which leads to the gradient change of material properties along the thickness direction.At the same time,the equivalent physical parameters of the material are obtained by Halpin-Tsai model and mixing rate rule.According to Euler-Bernoulli beam theory and Von-Kármán nonlinear strain displacement relation,the nonlinear governing equations of FG-GPLRC beam are obtained.The analytical expressions of critical load,buckling mode and post buckling deformation are obtained.Finally,the effects of weight fraction,geometry,size and distribution of GPL on the nonlinear buckling and post buckling of the composite beam are discussed.2.The free vibration of the beam is studied.Based on Hamiltonian principle and Euler-Bernoull beam theory,the free vibration differential equation of graphene platelet reinforced functionally graded beam is derived.At the same time,the equation is solved analytically,and the analytical expressions of natural frequency and vibration mode of the beam are obtained.Finally,the effects of different boundary conditions,weight fraction of GPL,geometric shape and distribution form on the natural frequency of the composite beam are analyzed and discussed.It is found that adding a small amount of GPL can significantly improve the natural frequency of the FGM beam,and when there are more GPL distributed on the upper and lower surfaces of the beam,the strengthening effect is the most obvious.