Vibration analysis of multilayer graphene origami-enabled metamaterial plates

This study investigates the free vibration behavior of auxetic metamaterial plates using a refined plate theory. The research focuses on the integration of functionally graded graphene origami (GOri) into the plate structures, examining various content levels and folding patterns to enhance dynamic performance. The GOri-reinforced plates are analyzed within the context of a Winkler–Pasternak elastic substrate. Hamilton’s principle is applied to derive the kinetic equations governing the auxetic metamaterial plates, facilitating an analytical solution for the governing equations. A comprehensive comparison of numerous parameters is conducted, including graphene content and dispersion type, GOri folding degree and distribution pattern, temperature effects, and elastic foundation coefficients, all of which influence the vibrational characteristics of the plates. The findings identify critical factors affecting natural frequency, providing a thorough understanding of the relationship between the physical configuration of auxetic metamaterial plates and their dynamic response. This study ultimately aims to leverage these insights to optimize the design of auxetic metamaterials for improved vibrational performance in engineering applications.