Nonlinear dynamics of graphene origami enabled auxetic metamaterial third-order beams

This study investigates the nonlinear forced and free dynamic behaviour of metamaterial beam-type structures within the framework of a third-order shear deformation theory incorporating the von Kármán-type geometric nonlinearity. The effective material properties of the metamaterial beam are approximated using a modified Halpin–Tsai micromechanical model adapted from the literature. The coupled nonlinear motion equations are obtained using Hamilton’s principle. They are discretised using the Galerkin method and then this set of discretised nonlinear differential equations is solved using the finite difference technique. Reliability of the current methodology is studied through comparison with simplified cases available in the literature. After verifying the model, a detailed analysis of both the forced and free dynamics of the metamaterial beam structure is presented for different metamaterial parameters. The results reveal key nonlinear phenomena, including frequency shifts and jump discontinuities, providing new insights into the nonlinear dynamic behaviour of architected metamaterial beams under external excitations.