This research conducts a nonlinear analysis of free vibrations in a cylindrical panel comprising auxetic metal metamaterials enhanced with graphene origami (GOri), subjected to thermal loading and supported by an elastic foundation. The integration of GOri particles is observed to markedly improve the panel’s mechanical characteristics, which are quantified through a micromechanical modeling approach. The investigation incorporates five distinct through-thickness schemes for distributing GOri particles within the structure. Governing equations for the panel are formulated using first-order shear deformation theory alongside Hamilton’s principle, while von Karman’s nonlinear kinematic assumptions are implemented to capture geometric nonlinearities. Once the nonlinear partial differential equations are established and simply supported boundary conditions applied, Galerkin’s procedure is utilized to condense the system into a single nonlinear equation describing transverse displacement. Perturbation analysis and the modified Poincaré–Lindstedt technique are then adopted to determine the structure’s nonlinear natural frequencies. A notable feature of nonlinear free vibrations, as opposed to the linear case, is the dependence of natural frequencies on initial system conditions. The roles of various factors such as the dimensionless magnitude of initial disturbance, temperature variations, GOri concentration and distribution styles, fold parameters, structural geometry, and foundation stiffness are systematically explored. To ensure robustness and reliability, the analytical framework, solution process, and computed results are cross-validated through comparative analysis. Findings indicate that the initial state significantly influences vibrational characteristics, and higher temperatures lead to a pronounced reduction in nonlinear frequency.
Bidgoli et al. (2026) studied this question.