Comparison of Fig。 8 with Fig。 5(a) clearly demon- strates the importance of accounting for dynamic effects in a jack-up analysis, both because of the dynamic amplifications, and because the assumption of pinned footing behaviour is no longer the most conservative over  the  entire  period  range。  In  the  range  6–7 s (i。e。

around the fundamental period of the rig with Model B footings) the Model B analysis gives rise to the largest hull displacements。 This is evident for both the 13 m and the 6 m wave analyses。 Although this observation applies only for a narrow frequency range, it is highly significant since it is almost universally accepted that the assumption of pinned footings is always conservative; this is now seen not to be the case。 Similarly, around the resonant period of the fixed footing model (below 5 s) the Model B analyses yield the least conservative hull displacements。

In contrast to the quasi-static results, the trends of the LGMs (Fig。 9) follow closely the trends of the hull dis- placements over the entire period range。 The relationship between the windward and leeward LGMs is very close to linear, with the windward moments having slightly higher magnitude。 The relative magnitudes of the moments for the three footing assumptions are, however, slightly different from those for the displacements, with the result that the fixed footing analysis gives more con- servative results than Model B over a narrow period range around 9 s (twice the fixed footing fundamental period)。

The double amplitudes of hull displacement and wind- ward LGM for the 13 m wave are plotted in Fig。 10。 These show similar trends to the maximum values in Fig。 8 and Fig。 9: the LGMs follow the displacements quite closely, and there are period ranges where the Model B analysis gives more conservative results than the pinned analysis, and other ranges where Model B gives less conservative results than the fixed footing analysis。

4。2。2。Dynamic amplification factors for hull displacement

A clearer indication of the dynamic amplification effects can be obtained by plotting the analysis results

Fig。 9。 Dynamic maximum LGMs (windward leg) for a wave  height of 13 m。

where f and T are the frequency and period of the wave loading and fn and Tn are the natural frequency and per- iod of the rig。 These non-dimensionalised plots serve to emphasise the similarities in the dynamic responses of rigs with differing footing conditions。 In each case there is a large resonant peak at approximately K = 1 and a slightly smaller peak at approximately K = 0。5 (the exact position of the peaks is influenced by the added mass)。 The curves for the 6 and 13 m wave heights fol- low similar trends but with some discrepancies, as would be expected given the non-linearity of the structural response。 In particular, the Model B analyses give sig- nificantly different amplification factors for the two dif- ferent wave heights。 For the  6 m wave the peak  DAF for Model B is close to that achieved with fixed footings, while for the 13 m wave the Model B behaviour more closely resembles that of the model with pinned footings。 This implies that the increase in wave height has induced a substantial shift in the Model B footing    response。

Some further insight can be obtained by approximat- ing the results in Fig。 11 by dynamic amplification curves for a linear single degree of freedom (SDOF) sys- tem。 The SDOF response to a single frequency excitation is given by the well-known  formula:摘要离岸自升式单元的环境负荷的动态响应已使用二维非线性调查有限元模型。该模型包括波浪载荷的现实表现，对几何非线性钻机的腿和在定位桩罐底脚结合负荷的复杂的非线性的效果。结果是从一个参数给出研究，其中一个典型的自升式单元进行变化的高度和周期的波。它表明，在准确的非线性腿和定位桩罐底脚两者的建模对钻机动力学显著效果。普遍做法建模基脚一样简单固定支撑件可以是非保守的一些的海况。论文网