Machine learning-assisted investigation on nonlinear vibration analysis of bio-inspired auxetic tubes

Purpose Auxetic tubular structures with negative Poisson’s ratios have gained significant attention in biomedical applications, particularly in vascular and esophageal stents, due to their potential to reduce embolism risks. This study aims to investigate the nonlinear vibration characteristics of such structures and develop accurate predictive models using machine learning (ML) techniques. Design/methodology/approach The governing equations of auxetic tubes are derived using Hamilton’s principle and von-Kármán’s nonlinear assumptions, while Malek-Gibson relations determine their effective mechanical properties. The mechanical behavior of polylactic acid (PLA) is experimentally analyzed through tensile testing and digital image correlation (DIC) with additional insights from scanning electron microscopy. The nonlinear vibration equations are solved via the Ritz method, and vibrational behavior is assessed using the direct displacement control approach. Predictive modeling is performed using six ML algorithms – CatBoost, decision tree, random forest, gradient boosting tree, extreme gradient boosting (XGBoost) and support vector regression (SVR) – along with an artificial neural network (ANN). Response surface methodology is employed to optimize the effects of edge supports, radius ratios and auxetic cell geometry on vibrational behavior. Findings The results demonstrate a strong agreement between ML/ANN predictions and the analytical Ritz method, confirming the reliability of the developed models. The analysis reveals that variations in edge supports, radius ratios and auxetic cell geometry significantly influence the vibrational response of the structures. The optimized configurations enhance the structural performance, making these auxetic tubular metastructures highly suitable for biomedical applications. Originality/value This study uniquely integrates analytical modeling, experimental analysis and ML-based predictive modeling to comprehensively assess and optimize the vibrational behavior of auxetic tubular metastructures. The findings provide valuable insights for the design of next-generation auxetic stents, improving their mechanical performance and expanding their potential biomedical applications.