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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access published online on May 11, 2009
The Quarterly Journal of Mechanics and Applied Mathematics, doi:10.1093/qjmam/hbp008
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© The author 2009. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

Water-Wave Scattering by Submerged Elastic Plates

Mahmood-Ul-Hassan {dagger}, Michael H. Meylan{ddagger} and Malte A. Peter §

( Department of Mathematics, University of Auckland, Auckland 1142, New Zealand )

{ddagger} Corresponding author. (meylan{at}math.auckland.ac.nz)

Received 17 November 2008. Revise 13 March 2009. Accepted 23 March 2009.


  Abstract

We present a solution to the water-wave interaction with a submerged elastic plate of negligible thickness by the eigenfunction-matching method. The eigenfunction expansion depends on the solution of a special dispersion equation for a submerged elastic plate and this is discussed in detail. We show how the solution can be calculated for the case of normal incidence on a semi-infinite plate in two spatial dimensions and then extend this solution to obliquely incident waves, to a plate of finite length and to a circular finite plate in three dimensions. Numerical calculations showing various properties of the solutions are presented and a near-orthogonality relation for the eigenfunctions is used to derive an energy-balance relation.

{dagger} On leave from Department of Mathematics, COMSATS Institute of Information Technology, Islamabad, Pakistan.

§ Present address: Institute of Mathematics, University of Augsburg, 86135 Augsburg, Germany.


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