A closed form solution method for rapid calculation of guided wave dispersion curves for pipes

• A new method for rapidly calculating dispersion curves for pipes is presented.
• Successful verification against well-established dispersion curve solutions.
• The method can be applied without the need for purchase of commercial software.
• The method allows automatic and robust dispersion curve tracing to be achieved.

Guided wave inspection is a fast growing technology for screening pipelines for corrosion. The technique is capable of inspecting tens of metres from a single test location and examining otherwise inaccessible regions of pipeline such as cased road crossings. However, enhancements to the technique are needed if inspections are to be transformed from a screening procedure to a more quantitative assessment of the condition of the pipeline. A rapid calculation procedure to determine the dispersion curves for guided wave modes is important if enhancements are to be automatically incorporated into the technique. Commercial code for dispersion curve calculation is available but it is proprietary and typically uses an iterative procedure to calculate curves which can be unreliable and slow. Other methods for calculating dispersion curves have been published including semi-analytical finite element solutions but these require extensive programming. In this paper, a closed form solution based on known trigonometric behaviour in the circumferential and axial directions and a standard polynomial solution through the thickness is presented. The method allows rapid computation of dispersion curves for typical guided wave inspection scenarios with minimal programming required. In addition, a tracing algorithm is also presented which allows the computed points to be joined to form curves and therefore fully identify the dispersive behaviour of each wave mode. The new method has been successfully verified against the well-established software, Disperse®, for a range of pipe sizes, materials and frequencies typical to guided wave inspection.