Investigation of the torsional dynamics of viscoelastic nanorod through Gaussian process-based surrogate modeling and semi-analytical approaches

In this study, the torsional vibration behavior of viscoelastic nanorods under elastic boundary conditions is analyzed using nonlocal strain gradient theory. The governing equations are derived and solved using Fourier series and Stokes transforms to obtain a semi-analytical solution. The influence of damping on size-dependent torsional response is examined, with significant effects observed in highly damped systems. Moreover, to overcome the computational cost of the analytical method, a Gaussian Process Regression (GPR) model is proposed as a surrogate for predicting torsional frequencies. The GPR model demonstrates strong predictive capability across varying material and geometric parameters, offering a practical and efficient alternative. To assess the model's robustness, white noise was introduced at 5%, 10%, and 15% levels; the GPR maintained R2 values above 0.96, indicating high accuracy under uncertainty. A Shapley Additive Explanations (SHAP) analysis was also conducted to interpret the model, revealing that viscous damping is the most influential parameter affecting frequency. Overall, the GPR model offers an accurate, noise-resilient, and interpretable approach for analyzing the dynamic behavior of viscoelastic nanorods.