Dynamic instability analysis of graphene origami-enabled auxetic metamaterial plates

This study presents the dynamic instability analysis of shear and normal deformable graphene origami (GOri)-enabled auxetic metamaterial (GOEAM) square plates under harmonic in-plane edge excitation for the first time. Some new results are provided for the bifurcation buckling behaviors and free vibration responses of GOEAM plates under the in-plane edge loads as well. By incorporating a finite element model (FEM) that accounts for normal deformation effects, the structural response of GOEAM plates is evaluated considering the influence of GOr patterns, weight fractions, hydrogen coverage (H-coverage), aspect ratios, boundary conditions (BCs), and loading conditions. GOri configurations such as U-, X-, and O-type patterns are explored in detail to understand their impact on dimensionless critical buckling loads, fundamental frequencies, and excitation frequencies accompanied with a dynamic instability analysis. Verification studies against available results in the open literature including ones from the 3D elasticity solutions confirm the accuracy of the developed FEM. Computed results reveal that increased GOri content enhances the performance of the system in terms of the buckling, free vibration and dynamic stability. The dynamic load factor and GOri weight fraction synergistically influences the dynamic stability performance of the GOEAM plate for all cases studied here. H-coverage reduces structural stiffness which leads to a deterioration in the structural performance of the GOEAM plates. Among various GOri patterns, the X-type consistently yields better structural performance due to improving the stiffness of the GOEAM plate.