A hybrid Semi-Analytical Finite Element (SAFE) and standard finite element procedure is adopted to ultrasonically but locally detect and characterize an axisymmetric open notch in an infinitely long steel pipe. Interactions between incident, dispersive guided waves and the notch are shown numerically to change a radial displacement’s temporal history and introduce additional singularities in the previously unblemished pipe’s Frequency Response Function (FRF). Differences between the frequencies of the singularities of the unblemished and notched pipes appear to reflect the notch’s dimensions. They also indicate the location of a nearby notch.
Stoyko, Darryl K., Popplewell, Neil and Shah, Arvind H., “Describing an Axisymmetric Notch in a Pipe Using Singularities,” Journal of Applied Nonlinear Dynamics, Volume 1, Issue 4, pages 321-339, December 2012.