Nonlinear vibration and buckling analyses of sandwich arch with titanium alloy face sheets and a porosity-dependent GPLRC core

This work presents the vibration and buckling analyses for a sandwich arch with Titanium alloy face sheets and a metal foam core via a new porosity-dependent model. Porous aluminum core consists of six layers so that each of them reinforce by graphene platelets (GPLs) with different values of porosity to achieve a piece-wise functionally graded media. The mathematical modelling is formulated to reveal nonlinear responses of the porous sandwich arch embedded in an elastic nonlinear medium. The higher-order equations of motion are achieved by taking Hamilton’s principle within the framework of the von Kármán nonlinear hypothesis. Afterwards, the established nonlinear problems are solved analytically with the aid of a perturbation-based technique implementing the Galerkin procedure. The investigation results show effects of the weight fraction of GPLs, porosity distribution, geometrical characters and foundation stiffness on nonlinear vibration and buckling of the porous sandwich arch.