Semi-analytical and machine learning approaches for investigating the torsional vibration behavior of nano-sized viscoelastic tubes

This study investigates the torsional vibration behavior of viscoelastic nanotubes under elastic boundary conditions using semi-analytical and machine learning (ML) approaches. Strain gradient theory is employed to account for size effects in the semi-analytical solution. Material’s time-dependent behavior is represented using the Kelvin-Voigt viscoelastic model. This approach uses Fourier sine series and Stokes’ transforms to establish an eigenvalue problem that allows for the calculation of vibrational frequencies under elastic conditions. In parallel, six distinct ML models including Adaptive Boosting, XGBoost, ANN, Support Vector Regression, Random Forest Regression and k-nearest Neighbors Regression, are trained on a comprehensive dataset generated using Sobol sequence sampling. A comparative analysis of all ML models is conducted by evaluating their performances using various statistical error metrics and visualization techniques. The results show that the Random Forest Regression model achieves the highest accuracy, followed by ANN and XGBoost. SHAP analysis is conducted to assess the feature importance and influence of each parameter on the predicted frequency. Its results revealed that the viscous damping parameter has the most significant impact on the predicted frequency and its lower values contribute positively to the real values of predicted frequency. SHAP results aligned closely with the analytical findings. The findings highlight the potential of ML models to accelerate the analysis of torsional vibration in nano-sized structures, offering a reliable alternative to traditional methods while maintaining high accuracy and computational efficiency.