On the existence of flexural edge waves on submerged elastic plates

The existence of flexural waves confined to the free edge of a fluid-loaded plate is established theoretically. Whereas analogous in vacuo edge waves exist for all parameter values, submerged plates are shown herein to support such waves only under very light fluid–loading conditions. For example, thin plates of aluminium, brass or Plexiglas will not support edge waves in water, although edge waves are permissible for each of these materials in air. The analysis is based on classical thinplate theory and employs the Wiener–Hopf technique to derive the dispersion relation for the edge–wave wavenumber as a function of frequency. In the limit of zero fluid loading the dispersion relation predicts the well–known result of Konenkov for edge waves on thin plates in vacuo.