Perturbation analysis on non-linear behaviors of the offshore structure

本文首先从实验和理论两方面研究了海洋结构物在波浪和海流中所受的二阶水动力，包括波浪漂移阻尼，并分析了波浪漂移<nd>阻尼对海洋结构物的影响。本文测量了<nd>在慢流和规则波列中作用于平台模型上的二阶波浪力和力矩。将实验结果与基于摄动理论和本征函数展开的半解析解进行了比较。在低速运动的偏航模式的数据处理中，对每个旋转位置进行准稳态假设。为了计算波浪漂移阻尼，慢振荡近似为相应的稳定运动。对自由面积分提出了新的处理方法，提高了计算的收敛性和精度，证实了斜向波和流对横摇力矩的影响，并从理论上给出了合理的解释。其次，考虑波浪斜率，将截断圆柱绕射问题的方程推广到三阶。用特征函数展开法解决了这一问题。采用适合压力分布问题的绿色函数，给出了满足高阶问题中非均匀自由面条件的特解。特解用自由曲面上的积分表示，并讨论了被积函数中的奇异性。提出了一种新的方法来提高解的收敛性，与以前的方法相比，该方法具有简单的优点。收敛性测试也显示了令人满意的结果。计算了三阶波浪力，并与已有结果进行了比较。

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.