Curvature effects on open-waveguide guided waves via circumferential SAFE-PML approach

Curvature coupling with irregular cross-sections fundamentally alters guided wave propagation in ways that analytical methods cannot capture. To systematically investigate these effects, we employ an established circumferential Semi-Analytical Finite Element and Perfectly Matched Layer (SAFE-PML) framework, formulated in cylindrical coordinates and implemented in a commercial finite element (FE) package. Applied to open girth-welded joints, the framework classifies four circumferential feature-guided wave (CFGW) families and quantifies curvature-induced changes in dispersion, mode shapes, modal existence, and energy confinement through normalised phase-velocity differences, similarity factors, and specific-power-flow ratios. Analysis reveals that curvature progressively elevates phase velocities, modifies modal structures, and weakens global energy confinement as radius decreases. A sub-waveguide interpretation further explains CFGW modal disappearance and energy redistribution as consequences of curvature-induced modifications in wave structure compatibility and leakage into the adjacent plate. The commercial FE implementation provides a robust, extensible tool applicable to complex geometries, advanced material constitutions, and operational loading conditions, offering a practical basis for guided wave mode selection in ultrasonic NDE and SHM of curved engineering structures.