Graphene origami-enabled auxetic metamaterial tapered beams in fluid: Nonlinear vibration and postbuckling analyses via physics-embedded machine learning model

•Effect of negative poisson's ratio on nonlinear free vibration and postbuckling behaviour of FG-GOEAM beam is investigated in detail.•Metamaterial properties of GOEAM are determined by physics-embedded machine learning assisted micromechanics model.•FG-GOEAM beam greatly outperforms its pristine metallic counterpart due to GOri reinforcement.•Added mass model is used to include the effect of fluid surrounding the FG-GOEAM beam.