This study investigates the nonlinear dynamic behavior and natural frequencies of skew plates integrated with FG (Functionally Graded) origami-enabled metamaterials and supported by auxetic concrete foundations. The analysis is performed using the Carrera unified formulation (CUF), which provides a robust and accurate method for assessing the flexural response of complex plate systems. The formulation accounts for geometric nonlinearity, material gradation, and skew angles, capturing both the nonlinear natural frequencies and dynamic deflections. The inclusion of auxetic concrete foundations enhances the structural performance due to their negative Poisson’s ratio, which offers improved energy absorption and deformation characteristics. To further validate the accuracy and reliability of the proposed method, the results are verified through comparison with existing literature and are supplemented by a novel fuzzy decision tree algorithm as a machine learning tool. The fuzzy algorithm aids in automating the verification process and identifying patterns in the dynamic response, ensuring computational efficiency and robustness. Results demonstrate the significant influence of skew angles, and metamaterial properties on the dynamic behavior of skew plates. The study highlights the advantages of FG origami-enabled metamaterials in enhancing structural stiffness and reducing dynamic deflections, making them suitable for advanced engineering applications. This research bridges the gap between computational mechanics and machine learning, providing a comprehensive approach to analyzing and verifying the nonlinear dynamic performance of skew plates with auxetic foundation support.
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