Modelling nonlinear hydroelastic waves

P I Plotnikov, John F Toland

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This paper uses the special Cosserat theory of hyperelastic shells satisfying Kirchoff's hypothesis and irrotational flow theory to model the interaction between a heavy thin elastic sheet and an infinite ocean beneath it. From a general discussion of three-dimensional motions, involving an Eulerian description of the flow and a Lagrangian description of the elastic sheet, a special case of two-dimensional travelling waves with two wave speed parameters, one for the sheet and another for the fluid, is developed only in terms of Eulerian coordinates.
Original languageEnglish
Pages (from-to)2942-2956
Number of pages15
JournalPhilosophical Transactions of the Royal Society A - Mathematical Physical and Engineering Sciences
Issue number1947
Publication statusPublished - 28 Jul 2011


  • Cosserat theory of shells
  • hydroelastic waves
  • Kirchoff's hypothesis
  • Willmore functional


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