Propagation of localized vibration modes along edges of immersed wedge-like structures: geometrical-acoustics approach

The theory of antisymmetric localized elastic modes propagating along edges of immersed wedgelike structures is developed using the geometrical-acoustics approach to the description of flexural waves in elastic plates of variable thickness. The velocities of these modes, often called wedge acoustic waves, are calculated using solutions of the dispersion equation of Bohr - Sommerfeld type following from the geometrical-acoustics description of localized wedge modes. In a subsonic regime of wave propagation, i.e., for wedge modes being slower than sound in liquid, the influence of liquid loading results in significant decrease of wedge wave velocities in comparison with their values in vacuum. This decrease is a nonlinear function of a wedge apex angle θ and is more pronounced for small values of θ. In a supersonic regime of wedge wave propagation, a smaller decrease in velocities takes place and the waves travel with the attenuation due to radiation of sound into surrounding liquid. The comparison is given with the recent experimental investigations of wedge waves carried out by independent researchers