Abstract:
In ultrasonic guided wave testing of pipelines, efficiently obtaining guided wave dispersion curves is critical for optimizing inspection performance and selecting appropriate modes, as these curves directly characterize modal behavior and influence wave propagation and detection outcomes. This study presents a high-precision, low-complexity method to address the computational inefficiency of traditional 3D finite element analysis in complex pipeline structures. A coupled technique combining weak-form partial differential equations (PDEs) and the semi-analytical finite element method (SAFE)—termed PDE-SAFE—is developed. By introducing harmonic solutions in cylindrical coordinates, the 3D wave governing equations are reduced to 1D semi-analytical models. Using weak-form theory, the strong-form equations are transformed into integral formulations, and a 1D finite element model of pipelines is constructed in COMSOL to systematically derive propagation equations and phase velocity formulas for longitudinal, torsional, flexural, and circumferential guided wave modes. Test functions are employed to enhance numerical stability, enabling comprehensive computation of guided wave modes in both isotropic and anisotropic pipelines. Numerical results show that PDE-SAFE successfully generates dispersion curves and wave structure diagrams for various modes in pipelines, achieving significantly improved computational efficiency compared to traditional 3D models. Validation against the global matrix method confirms good agreement in dispersion characteristics—particularly superior completeness and accuracy in multi-mode identification. By combining dimensionality reduction with weak-form formulation, the PDE-SAFE technique balances computational complexity and solution accuracy, providing a reliable framework for modal optimization and precise defect detection in pipeline ultrasonic guided wave testing. This method holds substantial practical value for structural health monitoring of industrial pipelines.