Nonlinear Fluttering Response of Graphene Origami Composite Metamaterial Plate Unsing Bernstein Polynomials

This article introduces a novel analytical model to investigate the nonlinear supersonic flutter characteristics of auxetic metamaterial plates exhibiting a negative Poisson’s ratio (NPR). The plate consists of multiple layers through its thickness, each made from a copper (Cu) matrix reinforced with a specific weight fraction of Graphene Origami Auxetic metamaterial (GOAM). Three patterns of graphene origami (GO) distribution are considered. Utilizing classical plate theory with von-Karman nonlinear strains and linear supersonic piston theory, the nonlinear governing equations of motion are presented. Bernstein polynomials are employed to formulate mode shapes that satisfy the boundary conditions within the spatial domain. Then, Galerkin approximation is used to transform the nonlinear partial differential equations of motion to nonlinear time dependent ordinary differential equations. The Runge-Kutta method is employed to attain the nonlinear dynamic post flutter behaviors of GOAM plate. Furthermore, linear flutter characteristics are obtained through eigenvalue analysis. To validate the accuracy of the proposed approach, comparisons are conducted with results available in published literature, demonstrating excellent agreement. The impacts of material parameters, GO distribution patterns and boundary conditions on flutter behaviors of plate are examined. This model offers applicability in analyzing solid–fluid interaction studies relevant to aerospace, ocean engineering, and mechanical systems.