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10.1098/rspa.2000.0576 On the existence of exural edge waves

Summary: 10.1098/rspa.2000.0576
On the existence of ° exural edge waves
on submerged elastic plates
By I. David Abrahams1
a nd Andrew N. Norris2
Department of Mathematics, University of Manchester,
Oxford Road, Manchester M13 9PL, UK
2Department of Mechanical and Aerospace Engineering, Rutgers University,
98 Brett Road, Piscataway, NJ 08854-8058, USA
Received 1 July 1999; accepted 21 December 1999
The existence of Žexural waves con ned to the free edge of a Žuid-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 Žuid-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 thin-
plate 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 Žuid
loading the dispersion relation predicts the well-known result of Konenkov for edge


Source: Abrahams, I. David - Department of Mathematics, University of Manchester


Collections: Mathematics