Physics-Informed Neural Networks for Solving Free Vibration Response of Cables Considering Bending Stiffness

Abstract Purpose Physics-informed neural networks (PINNs), leveraging their exceptional capacity for nonlinear feature learning, offer a novel approach to solving partial differential equations (PDEs) in structure dynamics. While PINNs have demonstrated feasibility in analyzing the dynamic response of idealized one-dimensional structures, such as tensioned strings and beams, their applicability is limited when addressing the vibration PDEs of real-world cables, particularly those with significant bending stiffness. To overcome this challenge, this paper presents an enhanced PINN methodology designed for the accurate and robust solution of free vibration responses in cables incorporating bending stiffness. Methods Firstly, a preferred hard-soft boundary constraints strategy is introduced to enhance the prediction accuracy of boundary values. Secondly, a sine activation function is adopted to accelerate network training, replacing conventional alternatives. Thirdly, a hierarchical gradient loss function, coupled with adaptive weights, is introduced to eliminate manual parameter tuning. Finally, a coordinate transformation technique is employed to balance the order-of-magnitude of parameters in the vibration PDEs of the actual suspension cable. Results This paper systematically explores training strategies for improved PINNs and verifies their effectiveness in solving vibration PDEs for cables considering bending stiffness. The proposed approach delivers accurate solutions for the free vibration of arbitrary cables, providing valuable insights for future research on PINN-based cable vibration analysis. Conclusion Furthermore, a sensitivity analysis of PDE parameters and network hyperparameters is conducted to examine the time-accumulative effect of PINN solution errors. Some research should focus on solving cable vibration at any time.