Auxetic metamaterials with negative Poisson's ratio (NPR) are attracting tremendous attention due to their unusual and intriguing mechanical properties. This paper proposes a novel functionally graded (FG) beam made of graphene origami (GOri)-enabled auxetic metamaterials (GOEAMs) and investigates its nonlinear free vibration characteristics tuned by GOri. The beam consists of multilayer GOEAMs with GOri content changed across the beam thickness in a layer-wise mode such that the auxetic property and other material properties are varied in a graded form and can be effectively estimated by genetic programming (GP)-assisted micromechanical models. The Timoshenko beam theory and von Karman type nonlinearity are adopted herein to derive the nonlinear kinematic equations that are numerically solved by the differential quadrature (DQ) approach. Detailed parametric studies are performed to discuss the influences of GOri content, distribution pattern, GOri folding degree, and temperature on the nonlinear frequencies of FG-GOEAM beams. Numerical results indicate that the nonlinear free vibration behaviors of the beam can be effectively tuned via GOri parameter and distribution.
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