Physics-Informed Neural Networks (PINNs)-Based Solution of the Lamb Wave Dispersion Equation for Isotropic Plates

Abstract Dispersion characterization is crucial for nondestructive testing (NDT) and structural health monitoring (SHM). To understand the propagation of dispersive Lamb waves in isotropic plates, this paper presents physics-informed neural networks (PINNs) to calculate the frequency-wave number domain dispersion curves of Lamb waves propagating in aluminum plates. Considering the physical properties, boundary conditions, and wave equations of isotropic metal plates, the dispersion equation for the propagation of Lamb waves in an aluminum plate is derived. Then a deep neural network is constructed using PINNs to obtain the solution of the wave equation, which enables the network to satisfy both data fitting and physical constraints by fusing the priori information of the dispersion equation. To verify the accuracy of the PINNs algorithm, the solutions are compared with those of the Legendre orthogonal polynomial expansion method. The results of this study reveal that the PINNs-based approach has the ability to solve the dispersion relations of Lamb waves in isotropic plates. In our future research, we will extend the PINNs-based algorithm to the solving of wave equations of guided waves in complex structures such as anisotropic composites and arbitrary cross-sectioned waveguides.