Nonlinear vibration analysis of graphene nanoplatelet-reinforced polymer plates incorporating hyperelastic material behavior

This research presents an analytical investigation into the nonlinear vibrational behavior of graphene nanoplatelet-reinforced polymer (GPL-R) plates subjected to external excitation. The novelty of the proposed methodology lies in establishing a direct test-to-dynamics framework in which tensile-test-derived Mooney–Rivlin constants are embedded into the forced nonlinear vibration formulation of GPL-reinforced polymer plates, rather than treating the nanocomposite as an equivalent linear elastic or purely homogenized material. To develop a more realistic constitutive model for the nanocomposite plate, this study integrates experimentally derived hyperelastic parameters of GPL–epoxy nanocomposites into a nonlinear plate vibration model governed by a Mooney–Rivlin strain-energy formulation. Following the derivation of the nonlinear governing equations of motion via Hamilton’s principle, Galerkin’s method is applied to discretize the system. The effective mechanical properties of the nanocomposite are obtained through experimental tensile testing performed on specimens containing varying concentrations of graphene nanoplatelets. Subsequently, the discretized equations are solved numerically to characterize the nonlinear dynamic behavior of the system. To this end, the influence of key parameters on various nonlinear phenomena is assessed using time-history responses, phase-plane portraits, Poincaré maps, and frequency-response curves. The experimentally calibrated analytical–numerical methodology avoids arbitrary hyperelastic-parameter assumptions and enables direct transfer of the measured GPL-dependent nonlinear material behavior into the vibration model. The results demonstrate that increasing the GPL content up to 1.0 wt% increases the resonant frequency by 57.9% and reduces the maximum vibration amplitude by 50% compared with pure epoxy. Furthermore, the formulation captures a softening-to-hardening transition governed by the competition between Mooney–Rivlin material nonlinearity and von Kármán membrane stretching. Accounting for hyperelastic material behavior is shown to be crucial for accurately predicting the dynamic response, particularly at larger amplitudes, where linear elastic models overestimate deflections.