Peter, Meylan, and Chung 2004
Solution for a Circular Floating Elastic Plate.
We present a solution for a circular thin plate of shallow draft on water of finite depth subject to linear wave forcing of a single frequency. The solution, which is given in a closed form, is based on decomposing the solution into angular eigenfunctions. The coefficients in the expansion are then found by matching the potential and its derivative at the plate edge and imposing the free edge conditions for the plate. The matching is accomplished by taking the inner product with respect to the vertical eigenfunctions for the free surface. The equations that are derived are transformed so that the final system of equations involves only the unknowns under the plate. Solutions are presented and compared to the results of Meylan 2002, who presented a solution for a plate of arbitrary geometry.
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