On bending and vibration analysis of graphene origami-enabled auxetic metamaterial plates via higher order finite element models

This study presents a comprehensive numerical investigation on the free vibration and bending characteristics of graphene origami-enabled auxetic metamaterial (GOEAM) plates using higher-order finite element models incorporating both shear and normal deformations. Various Gori patterns, including U, X, O, and A types, along with different hydrogen coverage (H-coverage) profiles, are examined to elucidate their influence on vibrational and flexural behaviors. Detailed convergence and verification studies are carried out to exhibit the accuracy of the developed finite element models. The computed numerical results demonstrate that increasing the GOri weight fraction significantly enhances structural stiffness, resulting in higher dimensionless fundamental frequencies and lower central deflections. Conversely, increasing H-coverage tends to reduce the dimensionless fundamental frequencies due to increased local foldability and associated softening effects. The findings reveal that certain GOri-H combinations can outperform others, even at higher hydrogenation levels, offering design tunability for specific applications.