Hydroelastic analysis of the floating plate optimized for maximum radiation damping

In previous work, the problem of optimizing the shape of a thin floating plate to maximize radiation damping was investigated. The plate was modelled with zero draft and floated on the surface of an irrotational, incompressible ocean of infinite extent. For simplicity, only rigid heave motions were considered and the damping coefficient at one wave number was maximized. In the present work, the hydroelastic properties of the optimized plate are determined and compared with those of circular and square plates. The added mass, damping, and diffraction force coefficients in each mode are determined as a function of wave number. The amplitude responses of the plate deflection and bending moments are also presented. The finite element method is used to determine the vibration mode shapes and the flow problem is analysed using the Chen and Mei variational principle wherein the potential field inside a hemisphere surrounding the plate is represented using a spherical harmonic expansion and matched on the hemisphere to an outer field described by distributing sources on the hemisphere.