A novel quasi-3D hyperbolic shear deformation theory for flutter analysis of a Dual-FG graphene origami-enabled auxetic metamaterial circular and annular plate resting on an elastic foundation

Abstract

In this study, the aeroelastic instability of circular and annular functionally graded graphene origami (GOri)-enabled auxetic metamaterials (FG-GOEAMs) plates subjected to supersonic airflow is investigated. A dual-functional grading (Dual-FG) approach is adopted, where both the distribution and folding degree of GOri vary through the plate’s thickness following two distinct patterns. The effective mechanical properties are determined through a hybrid methodology that combines genetic programming with micromechanical modeling. A novel hyperbolic shear deformation theory, developed within a three-dimensional quasi-theoretical framework, is employed to capture both shear deformation and thickness stretching effects. Aerodynamic loading is modeled using piston theory, and the structure is assumed to rest on an elastic foundation to assess its stabilizing effects on the dynamic response. The coupled axial-shear-flexural-stretching system equations are established using finite element formulation and Hamilton’s principle. The results reveal that the combination of Dual-FG patterns significantly influences the flutter boundary, offering new design insights for tuning aeroelastic performance. The effects of different influencing factors on the aeroelastic behavior of the Dual-FG-GOEAM circular and annular plate are comprehensively analyzed. The results show that increasing the GOri weight fraction expands the structure’s stability region, whereas increasing the GOri folding degree reduces it. Moreover, the elastic parameters of the foundation have a great impact on the aeroelastic instability of the structure.