Nonlinear Dynamics Analysis Of Cracked Functionally Graded Graphene Nanoplatelet-Reinforced Composite Beams

In recent years,graphene and its derivatives have been attracting tremendous attention as reinforcing nanofillers in nanocomposites due to their outstanding properties.In recent years,researchers have combined FG multilayer materials with graphene-reinforced nanocomposites in which GPL volume fraction varies layer-wisely,and found that the enhancement effect of graphene is obvious.Beam structures are widely applied in a variety of engineering areas and often service in complex environment by suffering various dynamic loads,such as cyclic and impact loads.During manufacturing and in service,initial defects within the materials or damage in structures resulted by fatigue or impact can never be entirely avoided.The presence of cracks in an engineering structure may dramatically reduce the local stiffness and strength,and significantly affects the structural behaviors.Besides,the change in vibration characteristics caused by cracks in structural elements has always been a matter of concern as a viable tool for non-destructive damage detection.Understanding the structural behaviors of the cracked beam structures is important for avoiding structural destruction and unexpected performance as well as carrying out damage detection.However,all the previous works for FG multilayer GPLRC structures are limited to intact structures.To the authors' best knowledge,effects of crack defects on the structural behaviors of FG multilayer GPLRC beams have not been investigated.The present study deals with the nonlinear dynamic behavior of FG multilayer GPLRC beams containing a single open edge crack.The bending stiffness of the cracked section is regarded as being equivalent to that of a massless elastic rotational spring.Each individual layer is a homogeneous mixture in which GPLs are randomly oriented and uniformly dispersed in the polymer matrix.The GPL volume fraction shows a layer-wise change along the thickness direction.Utilizing the micromechanics models,the effective material properties of GPLRC were estimated.The equations of motion of the beams were derived from the first-order shear deformation beam theory and von Kármán nonlinear strain-displacement relationship.The governing equations of the beams are discretized to ordinary differential equations by the Galerkin method and then solved by the multiply scale method.Finally,a parametric study was executed to highlight the effects of GPL distribution pattern,GPL weight fraction,GPL geometry and size,boundary condition,crack location and crack length on the free vibration and primary resonant response of functionally graded GPLRC beams.The main conclusions include:(1)A larger crack length results in larger SIFs for all GPL distribution patterns.The geometry and size of GPLs have apparent influence on the SIFs of edge-cracked GPLRC beams.(2)In UD pattern,GPL weight fraction does not affect the SIF since the UD beam is isotropic.In FG-O pattern,as GPL weight fraction increases,the SIF decreases when the crack length ratio is smaller than or equal to 0.2 and increases when the crack length ratio is larger than 0.2.As for FG-X pattern,the scenario is reversed,i.e.,the SIF increases when the crack length ratio is small and decreases when the crack length ratio is relatively large with increase in GPL weight fraction.(3)The elastic rotational spring is reliable to model the cracked section of FG multilayer GPLRC beams.The natural frequencies decrease with increasing of the crack length.Natural frequencies of the cracked GPLRC beams are significantly influenced by the concentration of GPL nanofillers.(4)The crack has no influence on the fundamental frequency of the C-C beam when it is located at the two sections with a distance of almostly 0.22 L from the left or the right ends.(5)A small amount of GPLs can significantly enhance the mechanical properties of pure epoxy resin.The bending stiffness of the FG-X distributed functionally gradient beam was the largest,while that of the FG-O distributed functionally gradient beam was the worst.The longer the crack length,the greater the reduction in the mechanical properties of GPLRC beams.