深水半潜式平台Mathieu不稳定问题研究

半潜式平台的垂荡运动相对较大, 当平台的纵摇固有有周期和垂荡固有周期处于一定的倍数关系时, 平台的纵摇/横摇运动可能落入Mathieu不稳定区。该文对半潜式平台Mathieu 方程进行了推导, 获得了各参数的计算公式;根据Mathieu不稳定图谱或数值计算方法, 可判断纵摇/横摇运动的稳定性。选取了一个生存状态下的半潜式平台为算例, 分析了平台发生Mathieu 不稳定问题的条件, 并通过调整关键参数抑制不稳定问题的发生, 从而获得了避免Mathieu不稳定问题的工程措施, 为今后半潜式平台设计提供参考。

MATHIEU INSTABLITY STUDY OF A DEEPWATER SEMI-SUBMERSIBLE PLATFORM

The heave response of a semi-submersible platform is relatively significant than other floaters. While a certain ratio of heave natural period and pitch/roll natural period is reached, the pitch/roll motions of the platform will fall into a Mathieu instability zone. In the paper, a damped Mathieu equation for the semi-submersible platform was derived and the formulae of the control parameters were obtained to determine the stability of its pith/roll motion according to the parameter diagram of Mathieu instability or via numerical simulations. A semi-submersible platform was analyzed to investigate the Mathieu instability conditions. Furthermore, engineering measures on avoiding possible Mathieu instability are proposed and they may be some references for the design of semi-submersible platforms.