A Physics-Informed Deep Neural Network Based Beam Vibration Framework for Simulation and Parameter Identification

Abstract

Physics-Informed Neural Networks (PINNs) integrate Neural Network (NN) models with physical phenomena governed by differential equations. This study proposes a PINN framework that can be used to simulate transverse vibrations in beams and determine their dynamic parameters. Previous studies have shown that it is difficult for neural networks to learn high-frequency dynamics. Therefore, a Neural Tangent Kernel (NTK) is used to manage the spectral bias phenomenon for high-frequency learning. The proposed model is used to simulate cases with different boundary conditions, and the results are validated using the finite element solutions. For the forward problem solutions, the error is found to be approximately O(10−5) at lower frequencies and O(10−1) at higher frequencies. For the inverse problem, the system parameters are identified with an error of 1.41%. Furthermore, physical experiments are used to demonstrate the validity of the proposed framework. The differences between the PINN results and the analytical and measured data were less than O(10−1). The results show that PINNs have the potential to approximate the solutions of high-order partial differential equations and identify the dynamic parameters of structures governed by them. © 2024