Vibration analysis of cylindrical microshells with auxetic cores and triply periodic minimal surface layers using a hybrid analytical-machine learning framework

The article presents a novel analytical machine learning (ML)-based hybrid framework for studying vibration behavior of advanced composite cylindrical microshells based on butterfly-shaped auxetic cores and functionally graded triply periodic minimal surface (FG-TPMS) face layers reinforced using graphene platelet reinforcements (GPLRCs). The analytical framework combines first-order shear deformation theory (FSDT) with modified strain gradient theory (MSGT) to account for the effects of size that are present in microstructures. Hamilton’s concept is used to find dynamic governing equations, and Fourier series expansions are used to solve them analytically. The butterfly-shaped auxetic core signifies a notable improvement over traditional re-entrant auxetic designs, providing increased stiffness and greater structural stability while preserving negative Poisson’s ratio properties. The FG-TPMS face layers deliver optimal strength-to-weight ratios through mathematically engineered periodic structures, further enhanced by strategically positioned GPL reinforcements. An extreme gradient boosting (XGBoost) technique is designed and trained on a comprehensive dataset of 48,600 simulation points to enhance the analytical approach and facilitate swift design optimization. The collection includes essential design characteristics such as MSGT length scale parameters, TPMS pattern variations, butterfly-auxetic geometric ratios, GPL distribution patterns, porosity distributions, weight fractions, and porosity factors.