A Floquet-PML framework for modelling circumferential guided waves in tubular open waveguides

Circumferential Guided Waves (CGWs) hold significant potential for detecting defects in Tubular Open Waveguides (TOWs), such as buried pipelines. However, computing their dispersion curves remains challenging, as the commonly used Semi-Analytical Finite Element method with Perfectly Matched Layers (SAFE-PML) requires customising complex stretching functions and deriving coupled equations. To provide a simpler alternative, this study established a complete and reproducible numerical framework that combined the existing Floquet Boundary Conditions and PML within COMSOL Multiphysics. Two benchmark cases — circumferential shear horizontal waves in a steel pipe embedded in infinite concrete and circumferential Lamb-type waves in a steel pipe immersed in infinite water — were studied to demonstrate the framework. Convergence studies were also conducted on PML thickness, mesh size, and coupling layer thickness. The dispersion curves of phase velocity and attenuation obtained using the framework agree closely with those derived from the SAFE-PML method, and that all three PML parameters selected converge. These findings confirm the framework’s effectiveness and, to the best of our knowledge, provide the first validation that Sorokin’s Im (ω)/cg conversion is applicable for evaluating the leakage attenuation of CGWs. The established framework is expected to be particularly beneficial for users without extensive background in finite element theory.