Computing leaky circumferential and axial guided wave dispersion curves with spectral collocation

Leaky waves propagating around the circumference or along the axis of immersed or buried cylindrical waveguides play a prominent role in the guided wave non-destructive evaluation inspection of submerged or embedded structures; a thorough understanding of the complex characteristics of leaky waves in such systems is essential for a range of applications. In this contribution, we apply a spectral collocation approach for the computation of the dispersion curves of both leaky circumferential and axial waves radiating from submerged or embedded multilayered cylinders. Therein, a complex coordinate transformation of the exterior ensures the numerical decay of the wave field of interest, while also preserving all of its physical characteristics. The proposed discretization enables the dispersion curves of leaky waves to be retrieved as eigenvalues of a simple polynomial eigenvalue problem and avoids the numerical instabilities associated with Bessel functions or the non-linear eigenvalue problems one often encounters in such calculations. Results were validated against both analytical methods and dispersion curves from commercially available root-finding software.