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Journal of Engineering Mathematics

, Volume 75, Issue 1, pp 81–106 | Cite as

The Wiener–Hopf and residue calculus solutions for a submerged semi-infinite elastic plate

  • T. D. Williams
  • Michael H. Meylan
Article

Abstract

We present a solution for the interaction of normally incident linear waves with a submerged elastic plate of semi-infinite extent, where the water has finite depth. While the problem has been solved previously by the eigenfunction-matching method, the present study shows that this problem is also amenable to the more analytical, and extremely efficient, Wiener–Hopf (WH) and residue calculus (RC) methods. We also show that the WH and RC solutions are actually equivalent for problems of this type, a result which applies to many other problems in linear wave theory. (e.g., the much-studied floating elastic plate scattering problem, or acoustic wave propagation in a duct where one wall has an abrupt change in properties.) We present numerical results and a detailed convergence study, and discuss as well the scattering by a submerged rigid dock, particularly the radiation condition beneath the dock.

Keywords

Elastic plates Hydroelasticity Linear water waves Residue calculus Wiener–Hopf 

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Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Nansen Environmental and Remote Sensing CentreBergenNorway
  2. 2.Department of MathematicsUniversity of AucklandAucklandNew Zealand

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