| Guided wave inspection of pipelines is an important and growing area of Non-Destructive Evaluation (NDE). This technique can be used for remote inspection or monitoring of buried pipelines, or pipelines with insulation. Guided waves are sensitive to flaws such as corrosion pits and cracks. They can be used to locate flaws existing on either the outer or the inner surface of a pipe. Guided wave energy focusing can be performed to concentrate guided wave energy at particular combinations of circumferential and axial locations in straight pipes. When it can be used, this practice enhances the circumferential resolution of defects.;Elbows in a piping system are sufficiently disruptive to guided wave energy that the focusing methods used in practical inspections of straight pipe have not been extended to the region beyond an elbow. Counter-intuitively, elbows with a 45 degree bend are more harmful to guided waves than those with a 90 degree bend. A simple and elegant explanation for this phenomenon is provided in this dissertation.;Theoretical advancements to guided wave physics propagating around an elbow have tended to be few and slow. This is at least partly due to the complexity of the mathematics involved in the conventional description of guided wave mechanics. Parametric focusing for pipes with bends has not been previously possible as it is for straight sections of pipes. While some techniques such as time-reversal mirrors and blind finite-element-method modeling have existed for focusing beyond elbows, these techniques have been limited and largely of academic value. Also, the understanding of wave behavior in a pipe elbow has in the past been generally unclear. Consequently, signal interpretation has also been very limited for guided waves initiating in, or returning from, the far side of an elbow.;A new approach to understanding guided wave propagation is developed in this work. This understanding consists of the idea that the pathway a guided wave will take across a waveguide can be predicted from the geometric features of the waveguide and a set of initial conditions pertaining to the wave. One such feature is the geometric cross-section in which the wave is propagating. This cross-section refers to a plane that contains both the propagation direction of the wave and the coinciding surface normal of one of the boundaries guiding the wave.;Thinking of guided waves from this perspective enables a clear answer to some important questions about wave propagation beyond an elbow that have not been effectively answered before. For example, before this work, it was not understood if and when full guided wave coverage exists in a pipe beyond an elbow. This new thinking also enables the calculation of the elbow transfer function--the mapping of guided wave energy impinging on an elbow to the configuration it will have on the other side of the elbow. Each of these examples separately represents significant practical advancements in the guided wave community.;The new approach also introduces a forward focusing model for controlling and focusing guided wave energy in pipe sections in and beyond an elbow. It is believed that this is the first such forward-oriented apparatus for controlling guided wave energy beyond an elbow. It is expected that this will be of great practical consequence. In addition to these specific benefits, it is anticipated that this dissertation will serve as a foundation for a good deal of future work and contributions to guided wave understanding and non-destructive testing equipment. |
