Interaction of shear and Rayleigh–Lamb waves with notches and voids in plate waveguides

This paper investigates the interaction of different shear and Rayleigh–Lamb-guided waves in plates with a discontinuity such as a notch or an internal void. The problem was solved numerically using a finite element model and by exploiting an analytical solution obtainable for the double sharp changes of the cross-section that served as a reference. We aimed to elucidate the relation between the size and shape of the discontinuity and the reflection and transmission coefficients of the scattered field. Different sizes and profiles of the discontinuity were considered, with the shapes ranging from step changes of the height to ellipses, both symmetric and nonsymmetric. Regimes related to low and high values of the product frequency multiplied by the height of the plate were investigated. These showed how the mode conversion was related to the symmetry between the incident mode and the discontinuity, and to the actual existence of multiple propagating modes. The analysis presented was motivated by the need to set up procedures that exploit propagating waves not only to detect the presence of a notch, but also to characterize its size and shape.