浮式柱群结构常见于各种海洋工程中。因此对这样的结构进行完善准确的水动力建模显得十分重要。尤其是对于超大浮体和波浪能转换装置阵列这种新兴的海洋工程来说，要考虑阵列中各个圆柱之间存在相对运动的情况，这会使得结构的水动力特性更加复杂，对该问题的准确建模对结构的设计有重要意义。本文以浮式圆柱群阵列为主体研究对象开展了水动力分析和考察，通过摄动展开和泰勒展开给出了速度势的定解问题，包括满足拉普拉斯方程的速度势控制方程，自由面条件和物面条件。结合绕辐射理论，在频域内将问题分解为绕射问题和辐射问题。推导并给出了柱坐标下满足拉普拉斯方程和自由表面条件的波浪组份波的基础解系。

研究了截头圆柱阵列在入射波、辐射波和绕射波作用下的水动力学响应，该阵列的各个圆柱之间有相对运动、且每个圆柱均可以做纵荡、横荡、垂荡、横摇和纵摇五自由度运动。发展了一种基于特征函数展开法和贝塞尔函数加法定理的半解析方法来处理有相对运动的截头圆柱阵列与波浪相互作用的水动力学问题。首先通过求解漂浮截头单柱在传播模态入射波和耗散模态入射波作用下的绕射问题，得到了截头单柱的固有绕射传递矩阵，然后求解了截头单柱的辐射问题，得到了各个自由度的单柱辐射速度势。在对截头柱群阵列的水动力分析中，把阵列运动产生的辐射–绕射速度势用待求的每个圆柱各方向运动振幅的线性组合来表示，继而获得用待求运动振幅表示的辐射水动力，再考虑波浪激振力、辐射水动力、圆柱阵列惯性力、回复力和辐射阻尼力之外其他阻尼力之间的平衡，就可得到每个圆柱各自由度振幅以及阵列的辐射和绕射速度势。基于水动力理论编写了计算程序，通过与已发表的数值结果对比验证了理论分析和程序计算的准确性。开展了案例参数研究，计算分析了入射波、辐射波和绕射波作用下有相对运动截头圆柱阵列各自由度振幅，得到了不同入射角和不同圆柱间距情况下阵列中各个圆柱各自由度振幅随波数的变化，并给出了不同波数下自由表面升高幅值分布。

围绕浮式柱群的工程应用背景波浪能转换装置阵列展开了多自由度参数影响研究以及构型优化研究。完善了波浪能转换装置阵列的水动力方面建模，考察了能够进行五自由度运动的波浪能转换阵列，相比于传统的只考虑垂荡的水动力分析，该模型更加贴合实际工程情况同时也更加复杂，垂荡模态之外的其他方向的运动也参与了波浪能转换装置阵列间的水动力相互作用。首先考察了几种典型的波浪能转换装置阵列的构型布局，对不同阵列构型布局的捕获宽度和相互作用因子进行了研究。提出了适用于大数量波浪能转换装置阵列构型布局优化的一种分层的遗传算法，发展了一种矩阵编码方式，简化了交叉和变异等算子的操作。采用上述优化方法对具体案例进行了优化研究。案例研究了两层优化。第一层优化对小阵列开展，研究了具有不同数量装置的四种情况，并给出了每种情况下的最佳布局和相应的波浪场波幅等值线图，将优化后的布局作为子阵列使用。研究发现，相互作用因子q随装置数量的增加而增加，但趋势变缓。与已发表的文献相比，采用本文优化方法可以得到具有更高提取功率的阵列布局方式。此外，还研究了这些阵列在不同波浪入射角度和无量纲波数下的性能，考察了阵列对波浪条件改变的适应性。对于大阵列开展第二层优化，考察了包含十二个装置的阵列，它将第一层优化得到的最优的四柱阵列作为基本子阵列展开优化。与传统遗传算法相比，该算法在优化速度上有很大的优势。对比研究了多自由度的引入对波浪能转换装置阵列能量提取的影响，分为两种工况展开研究：只考虑垂荡方向提取波浪能和能够多自由度提取波浪能。对于前一种情况，通过将其他方向的约束模型化为等效刚度，研究了其他自由度贡献不同的多种工况。当其他自由度的等效刚度小于静水回复刚度时，其他自由度对波浪能提取功率的影响可以超过35%，此时建议考虑其他自由度的水动力响应。对于后一种情况，本文提出了一种新型的振荡浮子式波浪能转换装置的概念，其中波浪能转换装置的浮子可以在五个自由度进行振荡并同时吸收能量。我们对这种五自由度波浪能转换装置进行了案例研究和评估并与传统的垂荡波浪能转换装置阵列进行了比较。初步计算表明，五自由度波浪能转换装置有助于进一步提高波浪能提取效率。

基于波浪速度势的解，进一步考察了流的引入对柱群波浪二阶力的影响，对波流共同作用下柱群的绕射的水动力问题进行了分析。通过对两个小参数的摄动展开得到波流势的定解条件。在求解波流速度势的定解问题的过程中，将波流速度势自由面的非齐次项拆分为三部分，采用了不同的方法进行求解，并依次求解了坐底柱群和截头柱群的波流速度势，通过匹配内外域的方法求解了截头单柱的叠模式。通过与已发表的文献进行对比验证了水动力分析和编程计算的准确性，并开展了浮式柱群的波漂力参数影响研究，考察了不同的波浪入射角和柱间距对柱群中各个圆柱的定常二阶波漂力和波漂阻尼的影响。

The floating cylinder array structures are commonly used in various offshore engineering. Therefore, accurate hydrodynamic modeling of such structures is very important. Especially for the emerging ocean engineering such as very large floating structures and wave energy converter arrays. The relative motions among cylinders in the array should be considered, which will make the hydrodynamic characteristics of the structure more complex. The accurate modeling of this problem is of great significance to the design of the structure. Taking the floating cylinder array as the main research object, this paper carries out hydrodynamic analysis and investigation. Through perturbation expansion and Taylor expansion, the definite solution problem of velocity potential is given, including velocity potential control equation satisfying Laplace equation, free surface condition and, object surface condition. Combined with the theory of diffraction and radiation, the problem is decomposed into diffraction problem and radiation problem in the frequency domain. The basic solution system of wave component waves satisfying Laplace equation and free surface conditions in the cylindrical coordinates is derived and given.

The hydrodynamic responses of truncated cylinder array under the action of incident waves, radiation waves, and diffraction waves are studied. There are relative motions among cylinders in the array and each cylinder can move with five degrees of freedom: surge, sway, heave, roll and pitch. A semi-analytical method based on eigenfunction expansion method and Graf’s addition theorem for Bessel function is developed to deal with the hydrodynamic interactions among truncated cylinders and waves. Firstly, by solving the diffraction problem of a single floating truncated cylinder under the action of propagating and evanescent mode incident waves, the inherent diffraction transfer matrix of a truncated single cylinder is obtained, then the radiation problem of a truncated cylinder is solved, and the radiation velocity potential of a single cylinder with five degrees of freedom is obtained. In the hydrodynamic analysis of the truncated cylinder array, the radiation-diffraction velocity potential generated by the array motion is expressed by the linear combination of the motion amplitudes in all directions of each cylinder to be calculated, and then the radiation hydrodynamic force expressed by the motion amplitude to be calculated is obtained. Then, the balance between wave excitation forces, radiation hydrodynamic forces, cylinder array inertia forces, recovery forces, and other damping forces other than radiation damping force is considered, the amplitude of each degree of freedom of each cylinder and the radiation and diffraction velocity potential of the array can be obtained. The calculation program is compiled based on the hydrodynamic theory. The accuracy of the theoretical analysis and program calculation is verified by comparing with the published numerical results. The case studies are carried out, and the amplitude of each degree of freedom of the truncated cylinder array with relative motions under the action of incident waves, radiation waves, and diffraction waves is calculated. The variations of the amplitude of each degree of freedom of each cylinder in the array with wave number under different incident angles and different cylinder spacing are obtained, and the amplitude distributions of free surface rise under different wave numbers are given.

Focusing on the important engineering application background of floating cylinder array, the influence of multi degrees of freedom and configuration optimization of wave energy converter array are studied. The hydrodynamic modeling of the wave energy converter array is improved, and the wave energy converter array capable of five degrees of freedom motion is investigated. Compared with the traditional hydrodynamic analysis considering only heave, the model is more suitable for the actual engineering situation and more complex. The motion in other directions other than the heave mode also participates in the hydrodynamic interactions among the wave energy converter array. Firstly, several typical array configurations of wave energy converter array are investigated, and the capture width and interaction factor of arrays with different configurations are studied. A hierarchical genetic algorithm is proposed for the configuration layout optimization of a large number of wave energy conversion devices, and a matrix coding method is developed to simplify the operation of crossover and mutation operators. A specific case study is conducted through the above method. The case study includes two levels of optimization. The first level optimizes the small array and the optimized structure can be used as a subarray. Four cases with different number of devices are studied, and the optimal layout and corresponding contour map of the wave field in each case are given. It is found that the interaction q factor increases with the increase of the number of devices, but the trend slows down. Compared with the published literature, the array layout with higher energy extraction power can be obtained by using the optimization method in this paper. In addition, the performance of these arrays under different wave incidence angles and dimensionless wave numbers is also studied, and the adaptability of the arrays to the change of wave conditions is investigated. For large arrays, the second layer optimization is introduced, and the array containing 12 devices is investigated. It takes the optimal four-cylinder-array obtained by the first layer optimization as the basic subarray. Compared with the traditional genetic algorithm, this algorithm has great advantages in optimization speed. The influence of the introduction of multi degrees of freedom on the energy extraction of wave energy converter array is compared and studied, which is divided into two working conditions: only considering the energy extraction in the heave direction and being able to extract energy with multi degrees of freedom. For the former case, by modeling the constraints in other directions as equivalent stiffness, various working conditions with different contributions of other degrees of freedom are studied. When the equivalent stiffness of other degrees of freedom is less than the hydrostatic recovery stiffness, the influence of other degrees of freedom on the energy extraction power can exceed 35%. At this time, it is suggested to consider the hydrodynamic response of other degrees of freedom. For the latter case, this paper proposes a new concept of oscillating buoy type wave energy converter, in which the buoy of the wave energy converter can oscillate in five degrees of freedom and absorb energy at the same time. Case studies and evaluation are conducted of this five degrees of freedom wave energy converter, and compared with the traditional heave wave energy converter array. The preliminary calculation shows that the 5-DOF wave energy converter array is helpful in further improving the power absorption efficiency.

Based on the solution of the wave velocity potential, the influence of the introduction of current on the wave second-order force of the cylinder array is further investigated, and the hydrodynamic problem of the diffraction of the cylinder array under the combined action of wave and current is analyzed. Through the perturbation expansion of two small parameters, the definite solution problem of wave-current potential is obtained. In the process of solving the definite solution of the wave-current velocity potential, the non-homogeneous term of the free surface of the wave current velocity potential is divided into three parts, which are solved by different methods. The wave-current velocity potential of the bottom-mounted cylinder array and the truncated cylinder array are solved in turn, and the current potential of the truncated single cylinder is solved by the method of matching the internal and external domain. By comparing with the published literatures, the accuracy of hydrodynamic analysis and programming calculation is verified, and the case studies of floating cylinder array are conducted. The effects of different wave incidence angles and cylinder spacing on the steady second-order wave drift force and wave drift damping of each cylinder in the cylinder array are investigated.