Recent progress in the theory of localised elastic waves in immersed wedge-like structures

Recent analytical results in the theory of antisymmetric localised elastic modes propagating along edges of immersed wedge-like structures of arbitrary shape and curvature are briefly described with the emphasis on methodological aspects of using geometrical-acoustics approach for developing the theory. The velocities of localised modes are calculated for wedges of linear geometry, wedges with a cross section described by a power law, and curved cylindrical wedges. It is shown that deviations of a wedge shape and curvature from linear geometry result in frequency dispersion of wedge modes. The comparison is given with the experimental investigations and numerical calculations of wedge waves carried out by independent researchers.