Interaction of Lamb modes with an inclusion

The interaction of Lamb modes propagating in a steel plate containing a thin inclusion is analyzed for cases where the inclusion material has elastic parameters similar to the ones of the plate, and where the inclusion is in perfect mechanical contact with the surrounding plate material. A modal decomposition method is used to calculate the conversion of an incident Lamb mode to other modes. Hence, the influence of the type of incident mode, of the location and geometry of the inclusion, and of the elastic parameters of the inclusion and plate material on the mode conversion coefficients is analyzed. Besides the expected increase of the conversion efficiency with increasing cross section of the inclusion, it is found that due to reasons of symmetry, the presence of an inclusion leads to an efficient conversion of an incident S0 mode into reflected and transmitted A0 modes, unless the inclusion is located very close to the plate center. On the other hand, the conversion efficiency of an incident A0 mode into a reflected A0 mode is found to be strongly dependent on the depth of the inclusion, this conversion even disappearing for some location depths. For the cases studied, the inclusion location dependence of the mode conversion seems to be correlated with the normal profile of the longitudinal normal stress component σ(yy)(y). As intuitively expected, the mode conversion efficiency increases with the mismatch of an acoustic impedance like factor between the uniform plate and the inclusion region.