Dispersion of Guided Waves in Complex Waveguides: A Hybrid Modeling Technique Combining Gauss-Lobatto-Legendre Node Collation and Semi-Analytical Finite Element Method

Guided waves (GW) are massively used for structural health monitoring and defect evaluation in plate, pipe, and rail structures. To accurately and efficiently calculate the dispersive natures of GW in complex waveguides, this study proposes a novel Gauss-Lobatto-Legendre-based high-order semi-analytical finite element method (GLL-SAFE). Combining the GLL node collation and Lobatto quadrature into SAFE, the mass matrix in the developed GLL-SAFE is diagonal, which enables a faster solution speed and a reduced error of matrix inversion. Firstly, the GWs in the single-layer isotropic material, composite lamina, and composite laminates are calculated with both GLL-SAFE and the conventional Gauss-SAFE featuring an equidistant node collation and Gaussian quadrature. Before reaching the convergence limit, the calculated average relative errors for GLL-SAFE are smaller than those for Gauss-SAFE, and can reach an order of 10-6 and 10-4 for the phase and group velocity, respectively. Then a novel mesh automatic reconstruction with arbitrary element polynomial order is developed to calculate GW propagation in waveguides of complex cross section. As a hollow cylinder for validation, the calculated average relative errors reach below 9 × 10-5 and 9 × 10-4 for the phase and group velocity, respectively. Finally, with a complex rail track as the waveguide, the calculated dispersion characteristics with GLL-SAFE show an excellent match with those from the time-domain finite element analysis, and GLL-SAFE shows its higher calculation efficiency over Gauss-SAFE.