The fundamental periods for fully linear behaviour were found by eigenvalue analysis, using stiffness matr- ices for the legs in their undeformed positions and with no axial loads。 For non-linear behaviour, estimates of the fundamental periods were obtained by studying the responses to lateral impulse loads; the results are, of course, only indicative figures, since the period of oscil- lations will vary with the degree of non-linearity induced。 The periods in Table 1 show that:
1。the inclusion of axial loads in the legs results in a significant reduction in the sway stiffness of the rig, and
2。in the absence of yielding of the foundations, the rig with Model B footings is significantly stiffer than that with pinned feet。
The soil properties used are typical of a North Sea
deep water environment。 The initial plastic penetration of the footings was found by performing a quasi-static analysis of the preloading phase for the Model B foot- ings。 Although only the Model B analyses require esti- mates of penetration depth, the same depth was used for the pinned and fixed footing analyses in order to give the same total leg length。
The loading direction (single leg to windward) has been chosen for convenience, and does not necessarily represent a worst case。 The mean water depth is towards the upper end of the depth range for existing rigs。 Most of the analyses presented here were performed using a fixed wave height H, to study the effect of variations in wave period T。 In addition, a series of analyses was performed with fixed period and the varying wave height。
4。Analyses at a fixed wave height
The periods of most ocean waves are in the range 2– 20 s [11]。 However at the lower end of this range only very small wave heights are stable, and so these are of comparatively little interest to the rig designer。 In order to provide a wave height that can be applied across a wide period range, a value of 13。0 m was chosen for the fixed height computer simulations。 The corresponding period range was 5。8–20 s, the lower limit being the per- iod below which convergence difficulties are encoun- tered in the Stokes’ fifth order wave formulation。
To give results at the lower periods associated with the fixed-footing model (see Table 1), a second series of fixed height analyses was performed, using a wave height of 6 m, the associated period range being 4。6–9 s。 Fig。 3 shows the variation of wavelength with period for these waves。 It can be seen that, for each wave height, there is a period at which the waves arrive at the windward and leeward legs in antiphase。 This results in a reduced response, but is not strictly a cancellation per- iod, due to the presence of several harmonics in the wave loading function, and to the fact that there is a single leg to the windward side but two to leeward。 For the 6 m wave there is a reinforcement period, at which the waves arrive at the windward and leeward legs in phase。 There are many structural response parameters that could be examined, but two of the most important are the lateral hull displacement and the moment at the leg/hull connection (the lower guide moment, or LGM)。 For the sake of brevity, most of the results presented here are in terms of hull displacement, since the LGMs generally follow a very similar trend; any slight discrepancies are
highlighted below。
As can be seen in Fig。 4, the presence of steady wind and current loads causes rig oscillations to occur about a non-zero mean value。 The salient features of rig response are therefore presented in terms of both the
Fig。 3。 Variation of wavelength with period for waves of fixed height。
Fig。 4。 Dynamic response of rig with pinned feet to a wave of height 13 m, period 17 s。 离岸自升式单元非线性动力学行为英文文献和中文翻译(4):http://www.youerw.com/fanyi/lunwen_96549.html