Analytical-machine learning framework for free vibration of functionally graded porous sandwich microplates with auxetic graphene origami cores in a thermo-fluidic environment

This investigation presents a pioneering computational framework that synergistically combines analytical modeling with advanced machine learning (ML) techniques to examine the free vibration characteristics of functionally graded graphene origami (GOri)-enabled auxetic metamaterial (FG-GOEAM) core sandwich microplates with functionally graded porous (FGP) face sheets operating under coupled thermal-fluid loading conditions. The advanced core architecture has strategically positioned GOri components throughout the thickness, providing remarkable negative Poisson’s ratio characteristics and improved thermal transfer characteristics. The structural mechanics are represented using first-order shear deformation theory (FSDT) combined with modified strain gradient theory (MSGT) to precisely depict size-dependent mechanical responses at the microscale. Thermal loading scenarios include uniform, linear, and nonlinear temperature distributions, while fluid-structure interaction effects are meticulously examined using hydrodynamic pressure distributions based on Navier-Stokes fluid mechanics concepts. The governing size-dependent dynamic equations arise from Hamilton’s variational principle and are then analytically solved using Galerkin’s weighted residual approach, providing a full parametric solution database. The ANN architecture features four dense layers (256-128-64-11 neurons) with batch normalization, trained on 31,796 samples spanning the complete design space. This optimized model achieves 99.99% accuracy on both datasets while reducing computational cost by several orders of magnitude relative to analytical solutions. Thorough parametric studies demonstrate the significant impacts of GOri distribution patterns, porosity structures, material length scale characteristics, thermal gradient intensities, temperature profile arrangements, and fluid coupling effects on the natural frequency spectrum.