Excitation and scattering of guided waves: relationships between solutions for plates and pipes

The detection of localized defects such as cracks and corrosion in pipes using guided elastic waves is now an established non-destructive testing procedure. However, the prediction of guided wave excitation and scattering in pipes is a complex three-dimensional (3D) problem with many parameters that can generally only be solved using numerical methods. In many important industrial applications, the diameter of a pipe is much larger than wall thickness. In this case an approximate theory is applicable, when a pipe is considered as an unwrapped isotropic plate. In this paper, a technique for obtaining pipe mode amplitudes in terms of the solution to the forced 3D problem on a plate is presented. The same principle is extended to relate guided wave scattering from defects in plates to scattered circumferential modal amplitudes from defects in pipe. This is of practical benefit as the scattering of guided waves by defects in a plate is a much simpler problem than that in a pipe, and one that, in some cases, can be solved using analytical methods. Results are shown that illustrate the application of the method to reflection from through-thickness circumferential cracks in pipes.