Physics-Informed Neural Networks Techniques for Analyzing Forced Vibrations of Simply Supported Beams Featuring Variable Cross-Sections

This research explores the forced vibrations of isotropic beams with variable cross-sections, modeled by the Euler-Bernoulli beam theory. Using Hamilton's principle, the governing partial differential equations are derived, and the complex vibrational behaviors were analyzed. By introducing physics-informed neural networks (PINNs) as an innovative, mesh-free solution technique, the study highlights their ability to provide rapid and precise results by integrating physical laws directly into the machine learning framework. Compared to traditional methods like finite element (FEM) or finite difference schemes, PINNs significantly streamline the computational process by eliminating the need for mesh generation, which simplifies implementation and reduces computational effort, validation with the 6th-order Galerkin method and FEM confirms the high accuracy and efficiency of the proposed approach for analyzing vibrations in beams with varying cross-sections. Overall, this work enhances the application of PINNs in vibration assessment and offers valuable insights for optimizing design and performance across diverse engineering domains, including structural and mechanical systems.