Nonlinear vibration analysis of sandwich plates with honeycomb core and graphene nanoplatelet-reinforced face-sheets

This paper studies nonlinear vibration analysis of a graphene nanoplatelets' composite sandwich. The core and two face-sheets of composite sandwich plate are fabricated from a honeycomb material and graphene nanoplatelet (GNP) reinforcements, respectively. Displacement field of sandwich plate is developed based on first-order shear deformation theory. Geometric nonlinearity is accounted in the constitutive relations based on von-Kar man assumptions. After derivation of the governing partial differential motion equations through Hamilton's principle, Galerkin's approach is used to reduce them into a non-linear equation of motion in terms of transverse deflection. The nonlinear frequency is found based on linear frequency and initial conditions, analytically. The nonlinear-to-linear frequency ratio is computed based on significant input parameters of honeycomb structure and graphene nanoplatelets such as thickness-to-length and thickness-to-height ratios, angle of honey-comb, various distribution, weigh fraction and geometric characteristics of graphene nanoplatelets. Before presentation of full numerical results, the comprehensive comparative study is presented for verification of the derivation and solution method.