Machine learning-enhanced CUF-based finite element models using Lagrange polynomials for the vibration analysis of sandwich plates with metamaterial cores and graphene nanoplatelet-reinforced polymer faces

Sandwich plates with auxetic metamaterial cores and functionally graded graphene nanoplatelet-reinforced composite (FG-GPLRC) skins are highly attractive for lightweight vibration-resistant structures because they combine geometry-induced stiffness tailoring in the auxetic core and material gradation in the FG skins. However, their free vibration analysis remains challenging due to the strong through-the-thickness heterogeneity generated by the auxetic core and graded nanocomposite skins. This work presents a hybrid physics-based/data-driven framework to efficiently predict their natural frequencies. First, a finite element model based on CUF is formulated under a variable-kinematic description. This hybrid scheme significantly reduces computational cost compared to full layerwise models while preserving their accuracy. Lagrange polynomials are used as expansion functions, and MITC9 elements are applied to avoid membrane and shear locking phenomena. The proposed model is validated against available 3D–2D reference solutions. Then, a multilayer perceptron surrogate model is trained using CUF-generated data to rapidly predict the first five natural frequencies within the sampled design space. Hyperparameter optimization, early stopping, and cross-validation ensure robustness, while performance metrics show excellent accuracy with mean absolute percentage error around 4%. Parametric studies indicate that maximum stiffness occurs for auxetic wall angles between −70° and −60° and for FG-X/FG-X and UD/UD skin sets.