The linear-wave response of a periodic array of floating elastic plates

The problem of an infinite periodic array of identical floating elastic plates subject to forcing from plane incident waves is considered. This study is motivated by the problem of trying to model wave propagation in the marginal ice zone, a region of ocean consisting of an arbitrary packing of floating ice sheets. It is shown that the problem considered can be formulated exactly in terms of the solution to an integral equation in a manner similar to that used for the problem of wave scattering by a single elastic floating plate, the key difference here being the use of a modified periodic Green function. The convergence of this Green function in its original form is poor, but can be accelerated by a transformation. It is shown that the results from the method satisfy energy conservation and that in the particular case of a fixed rigid rectangular plate which spans the periodicity uniformly the solution reduces to that for a two-dimensional rigid dock. Solutions for a range of elastic-plate geometries are also presented.