Spectral method for modeling the Dispersion of complex guided wave modes in anisotropic pipeline

Ultrasonic guided waves play a crucial role in the non-destructive testing of pipelines. Their dispersive nature and the diversity of modes present make them often difficult to interpret, especially in areas close to defects or when transducers are located close to the edges. In these situations, in addition to propagative modes, complex modes also appear. The aim of this study is to use the spectral method to plot the dispersion curves of ultrasonic guided waves in anisotropic pipelines. We begin by describing the mathematical formulation of the problem, then explain and apply the spectral method algorithm to plot these curves, covering different levels of anisotropy in order to test the robustness of the method to various mechanical behaviors. Particular attention is paid to complex modes, which are poorly studied in the pipeline literature. We treated longitudinal and torsional modes. This study enables us to understand the frequency ranges that favor the appearance of these modes. The results obtained are compared with analytical solutions based on classical algorithms. We also compare the computation time and coding effort required with those of previous analytical methods. These studies demonstrate the significant advantage of the spectral method in terms of accuracy, efficiency and computation time savings for plotting the dispersion curves of complex modes in anisotropic pipelines.