Nonlinear forced vibration and dynamic buckling of FG graphene-reinforced porous arches under impulsive loading

Abstract

Nonlinear forced vibration and dynamic buckling of fixed functionally graded graphene platelet-reinforced (FG-GPLRC) porous arches under impulsive loading are investigated. The porosity coefficient varies along the thickness of arch based on a power law distribution with uniform dispersion of graphene platelets (GPLs) in the whole arch. The FG-GPLRC porous arch is made of closed-cell metal foams whose effective materials properties are determined by the volume fraction distribution of materials together with Halpin–Tsai model. The nonlinear motion equations of the FG-GPLRC porous under impulsive loading are derived by employed Hamilton’s principle, and numerically solved by Runge–Kutta (RK) method combined with the differential quadrature method (DQM). Based on the Budiansky–Roth (B-R) criterion of dynamic buckling, the critical dynamic buckling load of the arch is also determined. Two case studies are conducted to show the determination of the dynamic buckling load of the arch, and good accuracy of the developed method in predicting the critical dynamic buckling load of both shallow and deep arches is also verified. Numerical results show that the nonlinear forced vibration and dynamic buckling of arches are quite sensitive to impulsive load duration. In addition, FG-GPLRC porous arches have significantly higher critical dynamic buckling load when undergoing instantaneous impact loading.