Modelling guided waves in acoustoelastic and complex waveguides: From SAFE theory to an open-source tool

Guided wave (GW)-based techniques have been extensively investigated and applied in material characterization, damage detection, and structural health monitoring. A comprehensive understanding of GW is the cornerstone for the development of such techniques. Based on the semi-analytical finite element (SAFE) method, an open-source dispersion calculator of GW propagating in acoustoelastic and complex waveguides with both isotropic and anisotropic material properties is developed. First, by assuming the simple harmonic motion along the propagation direction and discretizing along the thickness direction, 1D-GLL-SAFE (one-dimensional Gauss-Lobatto-Legendre SAFE) is adopted for the solution of GW in plate waveguide, which is attributed to its superior performance in terms of computational accuracy and efficiency. Different theories on acoustoelasticity are adopted to calculate GWs under loading. Then 2D-Gauss-SAFE (two-dimensional Gauss SAFE) with triangular meshes filling the cross section is adopted for GW in general waveguides considering the ease of convenience in meshing. Finally, based on the 1D-GLL-SAFE and 2D-Gauss-SAFE algorithms, an open-source tool SAFEDC (SAFE-based dispersion calculator) is developed, which not only provides the solution of GW in pre-stressed isotropic waveguide and general cross section, but also extends to GW in laminates with arbitrary layer stacking configurations and hybrid stacking including multiple materials. Most of the GW features, including phase velocity, group velocity, wave number, wave structure in terms of displacement, stress, and strain, and animation of wave propagation are all offered in SAFEDC, which helps the researchers and engineers to understand and utilize GW.