Abstract

Ultrasonic guided waves are often used in the detection of defects in oil and gas pipelines. It is common for these pipelines to be buried underground and this may restrict the length of the pipe that can be successfully tested. This is because acoustic energy travelling along the pipe walls may radiate out into the surrounding medium. Accordingly, it is important to develop a better understanding of the way in which elastic waves propagate along the walls of buried pipes, and so in this article a numerical model is developed that is suitable for computing the eigenmodes for uncoated and coated buried pipes. This is achieved by combining a one dimensional eigensolution based on the semi-analytic finite element (SAFE) method, with a perfectly matched layer (PML) for the infinite medium surrounding the pipe. This article also explores an alternative exponential complex coordinate stretching function for the PML in order to improve solution convergence. It is shown for buried pipelines that accurate solutions may be obtained over the entire frequency range typically used in long range ultrasonic testing (LRUT) using a PML layer with a thickness equal to the pipe wall thickness. This delivers a fast and computationally efficient method and it is shown for pipes buried in sand or soil that relevant eigenmodes can be computed and sorted in less than one second using relatively modest computer hardware. The method is also used to find eigenmodes for a buried pipe coated with the viscoelastic material bitumen. It was recently observed in the literature that a viscoelastic coating may effectively isolate particular eigenmodes so that energy does not radiate from these modes into the surrounding [elastic] medium. A similar effect is also observed in this article and it is shown that this occurs even for a relatively thin layer of bitumen, and when the shear impedance of the coating material is larger than that of the surrounding medium.

Abstract

Guided waves are widely used as a non-destructive technique for the detection of defects or damage in structures due to the their excellent propagation characteristics. Developing an efficient calculation of guided waves is crucial in this context. In this work we present an approach named semi-analytical isogeometric analysis (SAIGA) for computation of dispersion properties of fluid-coupled waveguides in three-dimensional structures. The proposed approach is based on the use of Non-Uniform Rational B-splines (NURBS) as the basis functions for the geometry representation and for solution's approximation. It is shown that the using NURBS basis functions has significant advantage over using Lagrange basis functions for computing the dispersion of leaky waves in immersed waveguides due to their higher smoothness feature.