Evaluation of Numerical Methods for Dispersion Curve Estimation in Viscoelastic Plates

This study aims to evaluate the effectiveness of five analytical and semi-analytical methods for estimating Lamb wave dispersion in viscoelastic plates—the Rayleigh–Lamb solution, the Global Matrix Method (GMM), the Semi-Analytical Finite Element (SAFE) method, the Scaled Boundary Finite Element Method (SBFEM), and the Legendre Polynomial Method (LPM). The Rayleigh–Lamb equations are solved using an optimized Newton–Raphson algorithm, enhancing computational efficiency while maintaining comparable accuracy. The SAFE method exhibited a remarkable balance between computational efficiency and physical accuracy, outperforming SBFEM at high frequencies. For epoxy and high-performance polyethylene (HPPE) plates, the SAFE method and the LPM significantly outperform the GMM in relation to computational efficiency, with errors below 1% for fundamental symmetric and antisymmetric modes across the tested frequency range of 0 to 100 kHz. In addition, the ability of the SAFE method to accurately predict both phase velocity and attenuation in viscous media supports their use in guided-wave-based structural health monitoring applications. Among the investigated approaches, the SAFE method emerges as the most robust and accurate for viscoelastic plates, while the SBFEM and LPM show limitations at higher frequencies. This study provides a quantitative and methodological foundation for selecting and implementing numerical methods for guided wave analysis, emphasizing the dual necessity of physical fidelity and numerical stability.