对海洋资源的有效开发与利用，在很大程度上推动了社会的发展与进步。如今，陆地石油与天然气资源日益稀少，油气资源的开发逐渐由陆地转向至海洋领域，为了寻求资源独立，资源开发由浅海领域走向深海领域是必然的趋势。时至今日，海洋资源的开发技术发展迅速，各式各样的大型海洋浮式结构物应运而生。常见的海洋浮式结构物主要包括：开采海洋油气资源的钻井储油深海平台；为了有效利用海上空间的人工岛以及海上机场等超大型浮体（VLFS）；利用波能、潮汐能等进行发电的波能发电装置。

以上这些海洋浮式结构物的水下浮体部分大多可以简化为浮式圆柱群结构，研究圆柱群与波浪的水动力相互作用问题为海洋浮式结构物的结构设计、强度校核、疲劳分析等奠定了理论基础，具有重要的指导意义。对于浮式柱群水动力性能的准确预报，其关键问题在于准确分析柱间的相互影响作用，柱间影响主要包括两方面：柱间传播模态与柱间非传播模态影响。一般情况下，柱间非传播模态影响不予考虑，但是当浮式柱群数量较大、柱间距较小时，柱间非传播模态的影响越发明显。对于不同的海洋浮式结构，由于结构之间连接形式的差异，浮式圆柱群又可分为“柱间存在相对运动”、“柱间无相对运动”两种情况。对于钻井储油深海平台此类结构物，其水下浮体部分与平台是刚性连接，所以简化后的浮式圆柱群计算模型可视一个整体，进行水动力分析时不考虑柱间的相对运动。而对于波能发电装置、超大型浮体等无连接以及弱连接的浮式结构物，水动力分析模型大多简化为柱间存在相对运动的圆柱群模型。

本文针对柱间存在相对运动情况，深入分析了柱间非传播模态对水动力系数的影响规律，探究了某一工况下是否应该考虑柱间非传播波的影响。首先，采用势流理论模拟波浪场，应用泰勒展开和摄动方法将非线性边界条件与拉普拉斯控制方程进行展开，进而得到各阶定解问题。针对一阶线性水波问题，利用特征函数法对“柱间存在相对运动浮式柱群水动力相互作用问题”进行了理论推导。其次，根据理论推导编制相应Fortran程序，通过与相关文献中的算例进行计算结果比对，验证理论推导与自编程序的正确性。之后，通过自编程序遍历不同工况，深入分析柱间非传播模态的影响程度以及影响规律，并针对截头两柱垂荡运动模态，在理论基础上分析了非传播模态对水动力系数的影响机理，探讨了水动力系数随柱间距增加而衰减的规律。根据分析结果，给出了由绕射柱间非传播模态引起的水动力特性随柱间距增加而衰减的拟合公式，且该拟合公式适用于多种工况。最后，在水深为十倍柱径条件下，对拟合公式进行了优化，并拓展至矩形排布的浮式圆柱群中。

通过上述研究，我们发现：附加质量对柱间非传播模态是否存在比较敏感，而阻尼系数基本不受柱间非传播模态的影响；附加质量系数对两种柱间非传播模态（辐射速度势和绕射速度势中的非传播模态组份）都很敏感，且考虑与忽略柱间非传播模态时附加质量的差值主要是由柱间非传播模态自身引起的；相比于绕射速度势，辐射速度势中的非传播模态对相邻圆柱的水动力特性影响更大，且当波数较大时，柱间非传播模态引起的附加质量为常量，不再随波数发生变化；当柱间距减小或者柱群中圆柱数量增加时，柱间非传播模态对附加质量产生的影响会逐渐增加，但是变化速率会越来越慢，所以在小间距以及大柱群数量时必须要考虑柱间非传播模态影响；随着柱间距的增加，柱间非传播模态迅速衰减，且由柱间非传播模态引起的附加质量呈指数形式快速衰减。

The effective exploitation and utilization of marine resources has greatly promoted the development and progress of society. Nowadays, due to the oil and gas resources are decreasing day by day, the development of oil and gas resources are  gradually turning from the land to to ocean areas. In order to seek resources independence, resources development from the shallow sea area to the deep-sea area is the inevitable trend. Up to now, the exploitation technology of marine resources is developing rapidly and various large marine floating structures have emerged. The common marine floating structures include the following types: deep-sea platforms for exploring marine oil and gas resources, artificial islands, offshore airports and very large floating structures (VLFS) that utilize sea space effectively, the wave energy generator that uses wave energy and tidal energy to generate electricity.

Most of these marine floating structures can be simplified as floating column structures. The study of the hydrodynamic interaction between the column structures and the wave laid a theoretical foundation for the structural design, strength checking and fatigue analysis for marine floating structures. The key point for forecasting the performance of the floating column structures lies in studying the interaction between columns structures. The interaction mainly includes two aspects, propagating modes and evanescent modes. In general, the influence of the evanescent modes is not considered, but when the number of floating columns is larger and the column space is smaller, the influence of the evanescent modes on the hydrodynamic characteristics is more and more obvious. Besides, for different marine floating structures, the floating columns can be divided into "relative motion between columns" and "no relative motion between columns" due to the differences in the form of connection between structures. For theses structures like oil drilling deep-sea platforms, the floating body and the platform are rigid connections, so the floating column group calculation model can be seen as a whole. And the relative motion between columns is not considered when conducting hydrodynamic analysis. However, for the floating structures with no connection or weak connection, such as wave energy generating device and very large floating body, the hydrodynamic analysis model is mostly simplified as a cylindrical group model with relative motion between columns.

This thesis focuses on the relative motion between the columns, analyzing deeply  the influence of evanescent modes on hydrodynamic characteristics and probing into  whether taking the existence of evanescent mode under a certain condition into consideration or not. Firstly, the potential flow theory is used to simulate the wave field, and the nonlinear boundary condition and the Laplace control equation are expanded by Taylor expansion and perturbation expansion, and then we could get different order equations. In order to solve the problem of first-order linear water wave, the eigenfunction expansion method is applied to deduce the existence of  hydrodynamic interaction between columns with relative motions. Secondly, the corresponding Fortran program was developed according to the theory, and comparing with the examples in the relevant literature to verify the correctness of the theoretical derivation and self-programming. Thirdly, according to the calculation results of the Fortran program under different working conditions, the influence degree and rule of evanescent modes are analyzed in detail. Based on the floating column group containing two columns of heaving motion, the influence mechanism of local mode on hydrodynamic characteristics is analyzed, and the attenuation law of hydrodynamic characteristics with increasing column spacing is discussed. According to the analysis results, the fitting formula of hydrodynamic characteristics which caused by evanescent modes in diffraction is given, which decreases with spacing increasing and is suitable for different working conditions. Finally, in the condition of the water depth is ten times radius of cylinder, the fitting formula is optimized and then extended it to the floating columns of rectangular arrangement.

Through the above research, we found that: The additional mass is sensitive to the presence of evanescent modes between the columns, however, the damping coefficient is not affected by the evanescent modes; The additional mass coefficient is particularly sensitive to the two kind of evanescent modes (the evanescent modes in radiation velocity potential and diffraction velocity potential), and the difference of additional mass which caused by the presence of evanescent modes is mainly caused by the local mode itself; Compared with the diffraction velocity potential, the evanescent modes in the radiation velocity potential have greater influence on the hydrodynamic characteristics of adjacent columns. Moreover, when the wave number is larger, the additional mass caused by the evanescent modes of the column is constant and no longer change with the wave number; As the column spacing decreases or the number of columns increases, the influence of evanescent modes on the additional mass will gradually increase, but the rate of change will be slower and slower, so the influence of evanescent modes between columns must be considered in small spacing or large number of column groups; With the increase of column spacing, the evanescent modes rapidly attenuates, and the additional mass caused by evanescent modes between columns attenuates rapidly in exponential form.