Purpose <p>Graphene origami-enabled (GOri) auxetic metamaterials (GOEAM), due to their negative Poisson’s ratio, have attracted significant attention from researchers in recent years. This paper presents a nonlinear axisymmetric free vibration analysis of GOEAM annular plates under various boundary conditions. Four different configurations for arranging the GOEAM layers are considered.</p> Methods <p>To analyze the problem, the dynamic equations of the annular plate are first derived using the first-order shear deformation theory (FSDT) and Hamilton’s principle, while accounting for large deformations. The linear mode shapes of the annular plate are then obtained through the generalized differential quadrature method. Subsequently, the nonlinear equations of the plate are solved using the Galerkin method in combination with the second-order homotopy perturbation method. After performing convergence studies and validating the results, the effects of parameters such as the GOri weight fraction and folding degree, GOEAM layer-stacking patterns, boundary conditions, inner-to-outer radius ratio, and thickness-to-outer-radius ratio on the nonlinear frequency and the hardening/softening behavior are investigated.</p> Results and Conclusion <p>The new results presented in this paper demonstrate that increasing the weight fraction of GOri increases the nonlinear frequency and enhances hardening behavior while weakening softening behavior in the plate. However, the findings also reveal that increasing the GOri folding degree reduces both the nonlinear frequency and the hardening/softening behavior. The outcomes of this research can serve as a benchmark for the dynamic design of annular plates in various engineering applications.</p>