A Benchmark Study of Modeling Lamb Wave Scattering by a Through Hole Using a Time-Domain Spectral Element Method

Ultrasonic guided waves (GWs) are being extensively investigated and applied to nondestructive evaluation and structural health monitoring. Guided waves are, under most circumstances, excited in a frequency range up to several hundred kilohertz or megahertz for detecting defect/damage effectively. In this regard, numerical simulation using finite element analysis (FEA) offers a powerful tool to study the interaction between wave and defect/damage. Nevertheless, the simulation, based on linear/quadratic interpolation, may be inaccurate to depict the complex wave mode shape. Moreover, the mass lumping technique used in FEA for diagonalizing mass matrix in the explicit time integration may also undermine the calculation accuracy. In recognition of this, a time domain spectral element method (SEM)—a high-order FEA with Gauss–Lobatto–Legendre (GLL) node distribution and Lobatto quadrature algorithm—is studied to accurately model wave propagation. To start with, a simplified two-dimensional (2D) plane strain model of Lamb wave propagation is developed using SEM. The group velocity of the fundamental antisymmetric mode (⁠$A0$⁠) is extracted as indicator of accuracy, where SEM exhibits a trend of quick convergence rate and high calculation accuracy (0.03% error). A benchmark study of calculation accuracy and efficiency using SEM is accomplished. To further extend SEM-based simulation to interpret wave propagation in structures of complex geometry, a three-dimensional (3D) SEM model with arbitrary in-plane geometry is developed. Three-dimensional numerical simulation is conducted in which the scattering of $A0$ mode by a through hole is interrogated, showing a good match with experimental and analytical results.