A Meshless Method for Free and Forced Vibration Analysis of Functionally Graded Graphene Origami Auxetic Metamaterials Curved Beams with Variable Curvature and Thickness

In this paper, a moving-least square (MLS) approximation meshless method combined with Timoshenko beam theory is proposed to first investigate the free vibration and forced vibration of functionally graded graphene origami-enabled auxetic metamaterials (FG-GOEAMs) curved beams with variable curvature and thickness. The FG-GOEAMs curved beams are composed of multiple GOMAM layers with uniform or nonuniform functional gradient layers in the thickness direction, and the determination of material characteristics is accomplished through a synergistic approach combining micromechanical modeling enhanced by genetic programming (GP) with the rule of mixture. The meshless model of FG-GOEAMs curved beams is established by a series of discrete points, and then the meshless governing equations of free and forced vibration for the FG-GOEAMs curved beams are derived by Hamilton’s principle and the principle of minimum potential energy, respectively. The enforcement of essential boundary conditions is systematically achieved by the complete transformation method. The eigenvalue method and Newmark-[Formula: see text] time integration scheme are employed to resolve the governing equations, deriving the system’s natural frequency and time–history curve, respectively. The convergence behavior and numerical precision of the present method are rigorously validated through comparative analysis against both benchmark simulations and established theoretical data documented in the prior studies. At the end of the paper, the influence of GOri’s distribution patterns, content, folding degree, damping ratios, boundary conditions and other key parameters on the natural frequency and dynamic transient response of FG-GOEAMs curved beams with variable curvature and thickness are discussed.