Nonlinear Dynamics Of Functionally Graded Graphene-reinforced Nanocomposite Beams

Graphene,a kind of two-dimensional materials with excellent thermoelectric properties and largest specific surface area,is successfully manufactured recently.As reinforcements,graphene and graphene platelets(GPLs)have much more excellent performance than carbon nanotubes in improving the mechanical properties of the matrix materials.Functionally graded materials are characterized by continuous variations in both material composition and mechanical properties in space,which can reduce the thermal stress concentration of engineering structures in complex environments and improve the ability of the structures to resist deformation and damage.Several researches showed that by introducing the concept of functionally gradient materials into graphene based nanocomposites,the enhancement effect of graphene can be further exerted.At the same time,graphene has a low manufacturing cost,and it can be expected that the graphene-reinforced functionally graded materials will be widely used in the fields of aerospace,automotive,biotechnology,and civil engineering.When a structure is subjected to dynamic loads,primary resonance or secondary resonance is likely to occur,resulting in larger amplitude vibrations,exhibiting complex nonlinear dynamic behavior such as dynamic instability,and causing structural damage.Till now,studies on the primary resonance and secondary resonances of graphene-reinforced functionally graded sturctures have not been reported.In this paper,micromechanical model is used to estimate the mechanical properties of graphene-reinforced functionally graded materials.A simplified first-order shear deformation beam model is established by taking into account the von Karman nonlinear strain-displacement relationship,and is used to model the graphene-reinforced functionally graded beams.According to the Galerkin method,the governing equations of the beams are discretized to ordinary differential equations,which are solved by the multiply scale method.Numerical studies are conducted to investigate the effects of parameters such as graphene distribution pattern,weight fraction,size and shape on the primary resonance,superharmonic resonance and subharmonic resonance of the beams.Finally,the influence of temperature,damping,and graphene-related parameters on the primary resonance and secondary resonances of the beam,in which the graphene nanofillers are taken oriented distributions,are studied.The main conclusions include:(1)Dispersing a small amount of graphene can significantly increase the stiffness of the pure epoxy resin beam,reduce the amplitudes of the primary and secondary resonances,and reduce the resonant regions of the secondary resonances.At the same time,the shape and geometric size of the graphene nanosheets have a great influence on the enhancement effect.The square monolayer graphene sheet has the most excellent enhancement effect.(2)The graphene distribution pattern has a great influence on the stiffness of the structure.The stiffness of the FG-X beam is highest,while that of the FG-O beam is lowest.Dispersing more graphene far away from the middle layer will result much smaller amplitude of the primary and secondary resonances,and a smaller resonant region of the secondary resonance.(3)Increasing temperature will reduce the stiffness and geometric nonlinearity of the beams at the same time.When the amplitude of the vibration is small,increasing temperature will greatly increase the amplitude of the beam.However,when the amplitude of the vibration is large,increasing temperature will reduce the amplitude of the beam due to much larger geometric nonlinearities.At the same time,it is found that the temperature has the greatest influence on the nonlinear dynamic behaviors of the FG-O beam.(4)Damping can significantly reduce the amplitudes of the primary and secondary resonances of the beams.The higher the frequency of the external excitation,the greater the influence of damping on the dynamic response of the beams.However,the effect of damping on the vibration behavior is limited.When the damping coefficient reaches a certain value,increasing its value has no obvious effect on further reducing the vibration amplitudes of the beams.