ABSTRACT:

An efficient and accurate numerical procedure is described for computing the second-order diffraction forces on arbitrary floating bodies in regular waves. Green" s second identity is exploited to express the second-order forces due to the second-order potential in terms of the first-order quantities alone. The resulting expressions for the second-order forces are evaluated from numerical first-order solutions based on the hybrid integral-equation method. The validity of the numerical procedure is confirmed by comparison of the computed results with the analytical solution for the second-order force on an articulated vertical cylinder. Results from the model tests on a circular dock are also presented to validate the theoretical predictions.

INTRODUCTION

The wave loads acting on floating structures in irregular seas include the second-order, high- and low-frequency force components at sum- and difference frequencies of the wave group, which arise from nonlinearities due to effects of finite wave elevation and finite body motions. These second-order forces may not be large in magnitude compared with first-order excitation at wave frequencies, but can never be ignored due to the possibilities of exciting resonance frequencies of lightly damped systems. Difference-frequency forces can excite large horizontal excursions of moored structures and large vertical-plane motions of floating structures of small water plane area. Sum-frequency forces can excite resonance oscillations in vertical modes of tension-leg plat-" forms. The prediction of the second-order forces on floating bodies is usually made on the basis of potential flow assumption. The forces can be obtained by integrating the hydrodynamic pressure over the submerged body surface and by retaining terms to second order in wave slope in a consistent perturbation expansion (Ogilvie, 1983). The resulting expressions for the second-order forces involve the contribution from the second-order velocity potential. To obtain this contribution, one may use two alternative approaches.

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