ABSTRACT

The problem of a vertical elastic sheet subjected to a train of ocean waves in infinitely deep water is solved. The sheet is assumed to be thin and governed by the Bernoulli-Euler equations, and to extend from the water surface to a finite depth. The solution utilizes the Green's function for water waves and the transformation of the Bernoulli-Euler equation to an integral equation. The model predicts that there will be substantial reflection when the sheet is held rigidly at the top end and penetrates the water to a significant fraction of the wavelength. Resonances at which the reflection is reduced, or is zero, also exist for certain values of the stiffness, mass and frequency. A sheet which is free at both ends does not reflect significantly for any values of mass, stiffness or depth of the sheet.

INTRODUCTION

Problems involving the interaction of waves with floating or fixed bodies have obvious implications to the design of offshore structures, ships, etc, and because of this they have received considerable attention. A number of different forcing regimes have been identified depending on the ratio of the wavelength to body dimension. If the body size is considered as being of the same order of magnitude as the wavelength, then the diffraction problem for the interaction of a linearized wave with the body may be solved by the use of a Green's function. Such methods have found wide applicability and have been used extensively-the basic method is outlined in Sarpkaya and Isaacson (1981)-but only in consideration of rigid bodies, the flexural response of the body is not included. In many cases it is clear that the floating or submerged body will be capable of considerable flexure. The problem of a floating elastic or viscoelastic body acted upon by a wave tram has been considered m the context of floating breakwaters by Stoker (1957) and Tayler (1986), neither of whom solved the complete problem.

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