Slowly-varying wave loads on slender structures in multi-directional irregular seas
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The second-order slowly-varying wave forces can in principle be obtained from the second-order diffraction method. However, the theory is very 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 the inertia force is dominant and characteristic length scale of the structure is small (say less than 20%) compared to the wave length. 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. An additional second-order contribution due to the fluctuation of the free surface is also included. The resulting explicit force quadratic transfer functions (QTFs) are obtained both for 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 addition, the new approximation method is found 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 very sensitive to the wave directional spreading, hence wave directionality needs to be considered for a reliable or cost effective design of future compliant offshore platforms.
