Effects of Folding Degree and Mass Fraction on the Static and Natural Frequency Characteristics of Functionally Graded Graphene Origami-Enabled Auxetic Metamaterials Annular Plates

This study addresses a critical gap in the literature by investigating the static and natural frequency characteristics of functionally graded (FG) auxetic metamaterial annular plates reinforced with graphene origami (GOri), a novel area previously unexplored in the context of composite constructions, particularly for circular plates. The governing equations are derived utilizing higher-order shear deformation theory along with Hamilton’s principle, and solved using the finite element approach. For the first time, a comprehensive parametric study including the folding degree and mass fraction, and distribution pattern of GOri, is investigated on the static and natural frequency properties of annular plates. It is found that the natural frequency generally increased with higher mass fractions and decreased with greater folding degrees, though the X and V patterns at a 3% mass fraction showed an atypical increase in frequency with higher folding degrees. The impact of distribution patterns varied with weight fraction: the X-pattern caused the highest deflection at 1% weight fraction but the lowest at 3%, while the O-pattern caused the least deflection overall.