Free vibration of rotating origami-inspired folded graphene-reinforced copper twisted cylindrical curved plate

Rotating flexible structures are widely encountered not only in aerospace systems but also in civil and mechanical engineering applications, such as wind turbine blades, rotating machinery, and large-scale deployable structures operating under dynamic environments. In this study, the free-vibration characteristics of a copper-based pre-twisted rotating cylindrical cantilever shell reinforced with folded graphene auxetic metamaterials are investigated. Based on the first-order shear deformation theory and the energy method, an efficient numerical framework that combines the Rayleigh–Ritz method with Gaussian–Legendre quadrature is developed to evaluate the structural vibration behavior. The proposed approach avoids cumbersome analytical derivations and can be readily extended to various graphene distribution patterns. The accuracy and reliability of the developed model are verified by comparing it with published results and finite element simulations. The results indicate that, among all graphene distribution patterns considered, the XO-type distribution exhibits the highest structural stiffness and natural frequencies. Increasing the graphene mass fraction significantly enhances vibration performance, whereas a higher folding ratio weakens the reinforcing effect, leading to a reduction in natural frequencies. Geometric parameters exhibit pronounced mode-dependent influences on the vibration characteristics. Furthermore, the centrifugal stiffening effect triggers frequency-veering phenomena accompanied by modal exchange. The findings provide valuable theoretical guidance and technical support for the vibration design and optimization of advanced rotating flexible structures across a broad range of engineering applications.