Interaction of free-surface waves with a floating dock

Abstract

A new method to describe the interaction of waves with a rigid or flexible dock, with zero draft, is derived. By means of Green's theorem an integral equation along the platform for either the velocity potential or the deflection is obtained. In the two-dimensional case this equation is solved by means of a superposition of exponential functions. With a specific choice of the Green function the integration with respect to the space coordinate can be carried out analytically. The integration left is the integration in the k-plane that occurs in the chosen Green function. Subsequently the contour of this integral is modified in the complex plane. This results at first in a dispersion relation for the phase functions in the expansion. Then the set of algebraic equations for the amplitude coefficients follows from the same singularity analysis in the complex plane. These equations are very simple and easy to solve. In contrast to the classical approach of eigen-mode expansions, there is no need to split the problem in a symmetric and antisymmetric one. An other advantage is that the transmission and reflection coefficients are determined seperately by means of Green's theorem, applied at the free surface in the far field. The method is first explained for the semi-infinite rigid dock, followed by the rigid strip, the moving strip and the flexible moving platform. In the appendix it is explained how to derive a set of algebraic equations in the case when the incident wave is not perpendicular to the strip.