Vibrations And Active Controls Of Graphene-reinforced Nanocomposite Beams

Graphene is a sheet-like honeycomb lattice structure formed of carbon atoms and is a basic unit constituting other graphite materials.Due to its excellent mechanical,optical,magnetic,electrical and thermal properties,the research on graphene structural and functional polymer nanocomposites has been greatly developed in recent years.the research on structural analysis of graphene reinforced polymer nanocomposite is mainly focused on the case when graphene nanosheets are randomly distributed in the matrix materials.However,with the advancement of technology and the development of manufacturing processes,researchers have been able to orient graphene platelets(GPLs)in matrix materials.The comparative analysis of the mechanical properties of graphene nanosheets in different arrangement modes important for engineering guiding.In this thesis,Halpin-Tsai micromechanical model is used to estimate the modulus parameters of graphene reinforced nanocomposites.Based on the nonlinear strain-displacement relationship of Von Kármán,the dynamic equations of graphene-reinforced nanocomposite beams are established according to Hamilton's principle.The differential quadrature(DQ)method discretizes the governing equation into a semi-analytical DQ format,and uses the weight coefficient matrix correction method to process the boundary conditions.Then through the numerical calculation,the effects of the distribution pattern,geometric size and concentration of graphene nanosheets on the static/dynamic properties of the beams are discussed under three classical constraint modes.The main conclusions are as follows:(1)Adding a small amount of graphene nanosheets to the matrix material or increasing the aspect ratio of graphene nanosheets can significantly increase the natural frequency of the composite beam and enhance its bending resistance.At the same time,the numerical calculation shows that the axial displacement of graphene reinforced composite beams under transverse loading can be neglected.(2)When the graphene platelets are arranged in the matrix material in the orientation mode,the critical buckling load of the composite beam is greatly improved;Before the buckling of the graphene-reinforced nanocomposite beam,increasing the axial pressure can reduce the natural frequency of the beam.After buckling,increasing the axial pressure can increase the natural frequency of the beam.When the buckling occurs,the natural frequency of the beam is zero.(3)Under the action of damping time-delay feedback,the linear stability region of the beam system is affected by the damping time delay ? and the gain parameter (?).When the system parameters are in this region,the vibrated beam structure can quickly return to the equilibrium state through self-adjustment.When the system parameters are outside the region,the vibrated beam structure cannot be quickly restored to the equilibrium state,exhibiting periodic,double-cycle,chaotic and other motion states.