Slender-body approximation for slowly-varying wave loads in multi-directional waves
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Second-order slowly-varying wave forces can, in principle, be obtained from the second-order diffraction potential. However, the theory is complicated and relevant computation is very costly. Instead, in this paper, a very simple second-order slender-body approximation is developed, which can be used when inertia effects are important and characteristic length scale of the structure is small compared to the wave length. In the slender-body approximation, the second-order difference-frequency inertia force is obtained from the complete description of the second-order acceleration field which includes both temporal and convective terms. Additional second-order contributions due to the axial divergence correction and fluctuation of the free surface are also included. The resulting explicit force quadratic transfer functions (QTFs) are obtained for both uni- and multi-directional waves. The slender-body analysis is applied to the computation of slowly-varying pitch moments on an articulated loading platform (ALP) and the results agree well with the second-order diffraction computation. In particular, the approximation method is found to be several orders of magnitude faster than the second-order diffraction computation. From our numerical results, it is seen that slowly-varying-force spectra are in many cases sensitive to the wave directional spreading, hence wave directionality needs to be considered for the reliable or cost-effective design of future compliant offshore platforms. 1994.
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