Perturbation analysis on non-linear behaviors of the offshore structure

首先，从实验和理论两方面研究了平台慢漂移运动的含漂移阻尼的水动力。众所周知，在海流和波浪中作用在海洋结构上的2^<和>阶水动力随波浪数的变化而变化。我们测量了在不同入射角的慢流和规则波列下作用在平台模型上的2^<和>阶波浪力和力矩。实验结果与基于微扰理论和本征函数展开的半解析解结果进行了比较。该模型仅限于对波激励的线性响应。在慢动作偏航模式的数据处理中，假定每个旋转位置都具有准稳态。为了计算波漂阻尼，将慢振荡近似为相应的稳态运动。为了提高计算的收敛性和精度，提出了一些新的处理自由曲面积分的方法。结果表明，斜波和斜流对偏航力矩有明显的影响，并能很好地解释这一现象。其次，根据波的斜率给出了三阶截断圆柱的衍射问题。用特征函数展开的方法解决了这一问题。利用适用于压力分布问题的格林函数，给出了高阶问题中满足非齐次自由曲面条件的特殊解。用自由曲面上的积分来表示其特解，并讨论了被积函数所包含的奇异性。提出了一种改进解的收敛性的新方法，该方法与以前的方法相比具有简单的优点。收敛性检验也得到了满意的结果。计算了三阶波浪力，并与前人的结果进行了比较。

Firstly hydrodynamic forces including a wave drift damping for a slow drift motion of a platform are investigated both experimentally and theoretically.It is well known that the 2^<nd> order hydrodynamic forces acting on the marine structures in both current and waves vary with the wave number. We measured the 2^<nd> order wave forces and moment acting on a platform model in both slow current and regular wave trains of various incident angles. The experimental results were compared with the results of semi-analytical solutions based a perturbation theory and eigenfunction expansion.The model is restricted to the linear responses to wave excitations. An assumption of a quasi-steady state for each position of rotation is made in data processing for the yaw mode of slow motion. To calculate wave drift damping, the slow oscillations are approximated by the corresponding steady motions. Some new treatments to deal with the integral over the free surface are presented to improve the convergence and accuracy.It was confirmed that the yaw moment is significantly induced by oblique waves and current, and that those phenomena are well explained by the theory.Secondly the diffraction problem for a truncated circular cylinder is formulated up to the third order referring to the wave slope. The problem is solved by means of eignfunction expansion. The Green function suitable for the pressure distribution problem is used to give a special solution which satisfies the inhomogeneous free-surface condition in higher-order problems. The special solution is expressed by an integral over the free surface and the singularity contained in the integrand is discussed. A new method to improve the convergence of the solution is proposed, which has the advantage of simplicity compared with the previous approach. A convergence test also shows satisfactory results. The third-order wave forces are evaluated and compared with the previous results.