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The low frequency reflection characteristics of the fundamental antisymmetric Lamb wave a0 from a rectangular notch in a plate.

An analysis of the reflection of the fundamental Lamb mode a0 from surface-breaking rectangular notches in isotropic plates is presented. The results are obtained from finite element time domain simulations together with experimental measurements. Good agreement is found between the simulations and the measurements. Results are shown for a range of notch widths and depths, including the special case of a crack, defined as a zero-width notch. The reflection coefficient, when plotted as a function of the notch width, exhibits a cosinusoidal periodic shape, and this is explained by interference between the separate reflections from the start and the end of the notch. The reflection coefficient, when plotted as a function of notch depth, shows that in general the reflection increases with both frequency and notch depth, but the shapes of the functions are complex and there are some surprising features. An analysis of the reflection from cracks using the S-parameter scattering approach and some simplified descriptions of the crack-opening behavior yields physical explanations of the nature of these reflection functions. It is found that opening of the crack can be described adequately by a quasistatic assumption only when the crack is small, and in other cases a ray theory approach is more representative. The reflection function is shown to be a result of contributions from both the axial stress and the shear stress in the wave, and the relative importance of these varies with the crack depth and the frequency.