Reflection from elastic wedges of different thickness profiles

An elastic wedge whose thickness varies with axial position according to a power law can act as an absorber of incident flexural waves and thus as an anechoic termination. Ideally, if the wedge is tapered down to zero thickness, the incident wave slows down to zero propagation velocity at the edge, thus never reaching the boundary, and, so, not undergoing reflection. In practice, however, a small truncation of the wedge always occurs, due to manufacturing restrictions, leading to non-zero thickness at the edge, so that some reflection does occur. In this paper, alternative thickness profiles are examined, such as the power-cosine, the exponential and the Gaussian profile, the latter two inevitably having a truncation within a finite length. A method based on the WKB approximation is used in order to calculate the reflection coefficient of a structure comprising a wedge connected to a uniform plate. Higher-order WKB approximations are also applied. Results are compared with those from a Finite Element analysis