Hydroelasticity of an infinitely long plate in oblique waves: Linear Green-Naghdi theory

The Level I Green-Naghdi (GN) theory is developed, within the assumptions of linearity, to analyse the hydroelastic response of an infinitely long elastic plate of finite width. The plate is freely floating on the free surface of finite depth and in regular oblique waves. An equation of motion is obtained that is similar to the shallow-water wave equation of Stoker, but which possesses an improved dispersion relation and includes the added-mass force due to the vertical motion of the fluid column. Comparisons with the available experimental data for the special case of beam seas show good agreement with the present theory. An explicit solution is also obtained when the plate is very wide. A local analysis near the critical wave number is made for the solution, and it is shown that the deflection of the plate, not necessarily at its edges, can be made arbitrarily large by increasing the width of the plate.

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