The solution to the problem of a floating elastic disk subjected to a train of plane ocean waves is presented, invoking the standard formulation for a floating body of shallow draft and the eigenfunction expansion for a circular thin plate with free edge conditions. Two methods of solution are reported, the first involving solving for the coefficients in the eigenfunction expansion and the second an integral equation formulation. It is found that the body motion undergoes a complex transition as the stiffness is changed from negligible magnitude to an effectively infinite value. The wave field in the water surrounding the disk is also investigated and the resulting wave heights are shown to be of considerable amplitude.
The motion of floating bodies under the action of ocean waves is a problem of considerable practical importance and has attracted a great deal of research interest. While there are many models for the floating body motion the standard marine engineering approach, when the body size is the same order of magnitude as the open water wavelength, is to solve the linear diffraction problem (see e.g. Sarpkaya and Isaccson, 1981). Unfortunately the validity of this linear approximation cannot be verified except by a comparison with a higher order solution or by the appropriate experimental work. Nevertheless the linear theory provides an easily tractable solution which is generally regarded as a good first estimation. In this paper we will present an extension of the linear diffraction problem to the motion of a flexible floating body. The standard method of solution to the linear diffraction problem involves the use of the Green's function for linearized waves (John, 1950: Sarpkaya and Isaacson, 1981). The equations of motion for the body coupled with Bernoulli's equation then provide a further linear relationship.
