Tunable Buckling and Free Vibration of Axially Functionally Graded Graphene Origami-Enabled Auxetic Metamaterial Beams

Abstract

Auxetic metamaterials have emerged as a class of advanced materials with exceptional physical and mechanical properties that are not typically found in conventional materials. This work mainly focuses on the buckling and free vibration of axially functionally graded (AFG) graphene origami (GOri)-enabled auxetic metallic metamaterial (GOEAM) beams. The beam is comprised of GOEAMs with GOri content varying through the beam length within different patterns to realize axially gradient-changing Young’s modulus, Poisson’s ratio and mass density. The material properties of AFG-GOEAMs are evaluated by using the micromechanical model including volume fraction and folding degree of GOri, geometric characteristics of graphene, material properties of matrix, and local temperature. The first-order shear deformation theory is employed to derive the governing equations via the state-space procedure, and then analytically solved with the discrete equilong segment model along beam length direction. The effects of GOri content, axial distribution pattern, folding degree and temperature on the buckling and free vibration of AFG-GOEAM beams are mainly focused on. The numerical results indicate that the development of auxetic metal metamaterials can be achieved by incorporating GOri into the metal matrix, leading to the tunable bucking and natural frequencies of AFG beams, which provide significant insights into the design of high-performance structures.