Free and Forced Vibrations of FG Graphene Origami-Enabled Auxetic Metamaterial Annular Sector Plates Employing Variational Differential Quadrature Approach

Abstract

Auxetic metamaterials, identified by their negative Poisson's ratio, have attracted the scientific community's attention because of their superior mechanical behavior. In this investigation, the free and forced vibrations of annular plates fabricated from functionally graded (FG) graphene origami-enabled auxetic metamaterials are analyzed using a numerical approach. The micromechanical model is developed using a genetic algorithm to approximate the material properties for two distinct patterns of graphene content distribution and variations in the degree to which graphene origami is folded. The governing equations are attained utilizing Hamilton's principle, incorporating the first-order shear deformation theory of plates. Vibrational responses of annular sector plates are studied for the first time, employing the variational differential quadrature approach directly applied to the variational equations to obtain their discrete form. The proposed model demonstrates excellent agreement with reference solutions, showing a maximum deviation of less than 0.17% in dimensionless frequency values, thereby validating its accuracy and effectiveness. Numerical studies are presented to explore the influence of factors such as graphene content, the degree of graphene origami folding, distribution patterns, and boundary conditions on the free and forced vibration responses of annular sector plates. An inverse relationship between the folding degree and material strength is detected. This discrepancy is attributed to the interaction between graphene content and graphene folding degree. At low graphene content, higher degrees of folding reduce the material's strength. However, when graphene content exceeds 3%, an increase in the degree of folding enhances the material's strength, resulting in decreased lateral deflection. © 2026 World Scientific Publishing Company.