On the existence of flexural edgewaves on fluid‐loaded plates

Thin elastic plates in vacuo support flexural edge waves with wave speed proportional to and slightly less than the speed of flexural waves on a plate of infinite extent. This phenomenon has been known for 40 years, and has been experimentally verified. In this talk, the existence of edge‐supported flexural waves on fluid‐loaded plates is established theoretically. While the analogous in vacuo edge waves exist for all parameter values, submerged plates are shown to support such waves only under very light fluid‐loading conditions. For example, thin plates of aluminum, brass, or Plexiglas will not support edge waves in water, although edge waves are permissible for each of these materials in air. More specifically, the nondimensional fluid‐loading parameter must be less than 0.0462 for edge waves to exist on plates with Poisson’s ratio of 0.33. The analysis is based on classical thin‐plate theory and employs the Wiener–Hopf technique to derive the dispersion relation for the edge wave number as a function of frequency. In the limit of zero fluid loading, the dispersion relation predicts the well‐known result of Konenkov (1960) for edge waves on thin plates.