The higher order leaky Lamb wave sensitivity of a notch in a fluid-immersed plate

We present an ultrasonic method of detecting cracks in pipelines based on using normally incident transducers in a pitch-catch setup, which can only excite Lamb modes of higher order than the fundamental modes A0 and S0 commonly used in crack detection applications. By excitation and measurements of the Lamb modes S1, S2, and A3, in a steel plate immersed in fluid with and without a notch (to emulate a crack), the performance of the modes towards crack detection is quantified by assessing whether it returns a high leaky component and whether the notch has a large impact on the leaky component. In order to narrow the scope of measurements necessary to investigate notch sensitivity for different system parameters, and to potentially optimize the system setup, we present a computationally efficient theoretical model based on angular spectrum method (ASM) and the theoretical sensitivity kernel formulation from the field of seismology that accounts for a scatterer in the wave path between the transmitter and receiver. The model is compared against measurements, which show that the frequency components of the S2 mode has both the largest leaky frequency component in the given setup and the largest sensitivity at a frequency close to the maximum leaky frequency such that a difference caused by the notch is easily measured. By using the measurements and the validation calculation as baseline reference, we calculate the expected S2 mode sensitivity and leaky components for larger plate thicknesses and larger standoffs, which exemplifies how the model can be applied in measurement system design and optimization.