Detecting and describing a notch in a pipe using singularities

A hybrid Semi-Analytical Finite Element (SAFE) and standard finite element procedure is adopted to simulate ultrasonically generated waves traveling in an infinitely long steel pipe having an open, rectangular notch. Numerical illustrations indicate that dispersive guided waves can be used to locally detect and characterize such a notch. A frequency oriented approach is preferred because a problematic separation in time is circumvented when incident waves overlap their reflections from the nearby notch. The notch is discerned straightforwardly because distinctive singularities are introduced that differ from those observed at the modal cutoff frequencies in a Frequency Response Function (FRF) of a comparable but undamaged pipe. Its characterization is (suggested) demonstrated for a (non)axisymmetric notch by using several of the smallest differences in the frequencies at which the two set of singularities occur. Consequently an external stimulus that simultaneously excites more than one mode is beneficial.