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

Abstract

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.

Water-wave scattering by a periodic array of arbitrary bodies

“…We have shown how to efficiently calculate the slowly convergent series which arise in this formulation and how to determine the scattered field far from the array in terms of the amplitudes in the cylindrical eigenfunction expansion. Our numerical results agree with those presented in Linton & Evans (1993) and Wang et al (2005). We have also presented results for the case of fixed, rigid and flexible arrays of bodies of negligible draft.…”

“…Due to the axisymmetry, they are particularly simple. In fact, they are diagonal with diagonal elements Next, we compare our results to those of Wang et al (2005) who considered the waterwave scattering by an infinite array of floating elastic plates in water of infinite depth. The plates were modelled in exactly the same way as our elastic plates in §8.…”

“…Recently, motivated by modelling of wave scattering in the marginal ice zone (MIZ), Wang, Meylan & Porter (2005) considered the scattering of a periodic array of elastic plates in water of infinite depth. Their method was based on an integral-equation formulation using a periodic Green's function.…”

Hydroelectromechanical modelling of a piezoelectric wave energy converter

“…Note that, in the short-circuit limit ξ → 0, the second term inside the brackets at the left-hand side of (3.23) vanishes. Within this limit, the fifth derivative of the velocity potential in (3.23) is multiplied only by the non-dimensional stiffness β and the resulting boundary-value problem is equivalent to that of a submerged elastic plate without power extraction [22][23][24][25], as expected. Indeed, the complex coefficient α 2 ωξ/(i + ωξ) in (3.23) is a dissipative term which models the extraction of energy from the system by means of the resistive circuits of figure 2.…”

Interaction between obliquely incident waves and an infinite array of multi-chamber perforated caissons

“…They considered the effect of the partition walls on the wave motion and found that the partition walls might lead to several reflected waves traveling in different directions. This interesting phenomenon also exists in wave scattering by other periodic coastal structures [25][26][27][28][29]. A review on water wave interaction with periodic structures can be found in McIver [30].…”