Reflection and Transmission Coefficients from Rectangular Notches in Pipes

Stoyko, D.K., Popplewell, N., Shah, A.H.


The use of a single, nondispersive ultrasonic guided wave mode is one important approach to monitoring a structure’s health.  It is advantageously nondestructive with the ability of propagating over tens of metres to detect a hidden defect.  The dimensional assessment of a defect, on the other hand, requires reflection coefficients for two or more such modes.   Multiple modes may be excited simultaneously by applying a short pulse to a structure’s external surface.  This situation is examined here for a circular, hollow and homogeneous, isotropic pipe having negligible damping and an open rectangular notch.  A finite element model is employed in a region around a notch.  It is coupled to a wave function expansion in the two adjacent, effectively, semi-infinite pipes.  Representative longitudinal and flexural modes are investigated for different notch dimensions.  A nonaxisymmetric, unlike an axisymmetric, notch introduces a plethora of cross modal couplings that lead to more singularities in a reflection coefficient’s frequency dependence.  There is, however, a common pattern to these distinctive singularities. It is conjectured that singularities corresponding to propagating modes may enable a notch to be detected and its dimensions determined.


Stoyko, D.K., Popplewell, N., and Shah, A.H., "Reflection and Transmission Coefficients from Rectangular Notches in Pipes," Accepted for inclusion at the 11th International Conference on Recent Advances in Structural Dynamics (RASD 2013), July 1-3, 2013, Pisa, Italy.