Data-driven-AI and Layerwise-Variable-Kinematic models for the vibration analysis of sandwich panels with auxetic lattice core and functionally graded graphene nanoplatelet-reinforced coatings

This study investigates the vibration response of sandwich panels with auxetic lattice cores and functionally graded graphene platelet reinforced composite (FG-GPLRC) face sheets using Equivalent Single Layer (ESL), Layerwise (LW), and variable-kinematic models formulated within the robust unified formulation. The enhanced Tornabene homogenization model and Halpin-Tsai micromechanics model are employed to compute the effective properties of the auxetic core and FG-GPLRC face sheets, respectively. The dynamic governing equations, derived using the Principle of Virtual Displacements (PVD), are solved in strong form via the Boundary-Continuous Method (BCM). Several cases with increasing complexity are considered. A unique case, previously unexplored in the shell literature, is introduced, offering a new benchmark for future comparisons. The results reveal that the hybrid ESL/LW capabilities of the proposed variable-kinematic model provide highly accurate and efficient analytical solutions for these complex sandwich structures, offering 87% reduction in the computational cost against their LW counterpart. The effects of GPL reinforcements in the face sheets and the auxetic response are investigated through parametric studies using an efficient surrogate model based on Artificial Neural Networks (ANNs). This model was trained on a synthetic dataset, generated by the most accurate analytical model, where geometric dimensions, auxetic properties, and GPL parameters were used as input features.