Hydroelastic Behavior of a Floating Ring-Shaped Plate

Abstract

The interaction between incident surface water waves and floating elastic plate is studied. This paper considers the diffraction of plane incident waves on a floating flexible ring-shaped plate and its response to the incident waves. An analytic and numerical study of the hydroelastic behavior of the plate is presented. An integro-differential equation is derived for the problem and an algorithm of its numerical solution is proposed. The representation of the solution as a series of Hankel functions is the key ingredient of the approach. The problem is first formulated. The main integro-differential equation is derived on the basis of the Laplace equation and thinplate theory. The free-surface elevation, plate deflection and Green's function are expressed in polar coordinates as superpositions of Hankel and Bessel functions, respectively. These expressions are used in a further analysis of the integro-differential equation. The problem is solved for two cases of water depth: infinite and finite. For the coefficients in the case of infinite depth a set of algebraic equations is obtained, yielding an approximate solution. Then a solution is obtained for the general and most interesting case of finite water depth analogously in the seventh section. The exact solution might be approximated by taking into account a finite number of the roots of the plate dispersion relation. Also, the influence of the plate's motion on wave propagation in the open water field and within the gap of the ring is studied. Numerical results are presented for illustrative purposes.

Hydroelastic analysis of a floating plate of finite draft

“…However, the case of finite water depth is the general case, and the solution presented can be used for all water depths, as was previously reported [4,8,11,29,30]. This is the major advantage of the method presented.…”

“…The study presented is a practically relevant extension of those given for the case when the plate draft d is assumed to be zero [4,11,[28][29][30]. The approach presented can be extended to the case of oblique incident waves or to a strip of finite width and infinite length, shown in the previous section, and to plates of other horizontal planforms.…”

“…[14,15,21]. The authors in [10][11][12][28][29][30] derived the solutions for different horizontal planforms of the floating plate using the zero-draft (zero thickness) assumption, too.…”

“…Following [10][11][12]29,30], here, with the use of the Kirchhoff thin plate theory and Green's theorem, we obtain an integral equation for the potential and, further, an integro-differential one for the plate deflection. The key idea of our approach is adding a correction which is dependent on draft to the solution obtained for the semi-infinite plate with the zero-draft assumption, given in [11].…”

“…Then, the amplitudes a (1) n . For this we use the technique with which we also found the amplitudes in the previous section and in [11,29,30]. The equations for determining the amplitudes a (1) n have the following form…”