广袤的海洋中有着十分丰富的波浪能。过去几十年，波浪能技术的发展十分迅速。在各种类型的波浪能转换装置（WEC）中，振荡浮子式波浪能转换装置有着能量转换效率高和适应性广的特点，是最先进和成熟的装备类型之一。对于由浮式截断圆柱组成的WEC阵列来说，阵列中通常有着数量较多的圆柱，并且阵列中各个圆柱可以以不同的振幅和相位进行振动，这增加了动力学系统的自由度和计算的收敛难度，使得阵列的水动力相互作用变得更加复杂。如何准确高效地计算由浮式截断圆柱组成的有相对运动阵列与波浪的相互作用是海洋工程中的重要课题。但是，目前关于此问题的研究还存在许多不足，尤其是阵列中各个圆柱存在多个运动模态的情况。在已有的大多数研究中，WEC阵列中的浮子仅在垂荡自由度上振动和提取能量。由在多个方向振动并提取能量的浮子组成的WEC阵列的水动力性能和布局优化仍然存在研究空白，并且具有重要应用前景。本文针对此类问题开展了以下研究：

建立了波浪作用下截断圆柱阵列的水动力分析模型。本文通过多项伽辽金方法将不同区域交界面上的流体速度展开成一组包含Gegenbauer多项式的基函数，准确高效地表征了截断圆柱体边缘附近流体速度的立方根奇异性，发展了有入射波存在的情况下，截断圆柱阵列绕射和辐射的解析解，阵列由具有五个运动模态（纵荡、横荡、垂荡、纵摇和横摇）的截断圆柱组成。通过动力学平衡方程，给出了阵列中圆柱各自由度运动振幅的求解方法，并将水动力模型扩展到了多向不规则波的工况。本文方法有着很快的收敛速度，只需要较少的截断项就可以得到高精度的水动力响应结果。对于四柱阵列，在同一精度条件下（<1%），传统方法（Zeng et al., 2022d）的计算耗时比本文方法多3.9倍。随着圆柱数量的增多，本文方法在收敛速度上的优势更加明显。基于建立的水动力模型，考察了截断圆柱阵列在规则波和不规则波中的水动力响应。

研究了由浮式截断圆柱组成的WEC阵列在规则波和不规则波中的水动力性能及布局优化问题。为了更有效地捕获波浪能，发展了一种新型的波浪能转换装置（五自由度WEC），装置可以在五个自由度（即纵荡，横荡，垂荡，横摇和纵摇）上进行振动并提取能量。建立了WEC阵列在不规则波浪中的能量计算模型，并与已发表的研究结果进行了验证。考察了近捕获波模态对线性阵列能量捕获性能的影响，在近捕获波频率附近，纵荡波浪能转换装置的能量提取性能大幅提升，而垂荡波浪能转换装置的性能则明显下降。考察了等距线性排列五自由度WEC阵列在规则波和不规则波中的能量提取性能。结果表明，将线性阵列垂直于波浪传播方向进行布置可以更有效地提高WEC阵列的能量捕获性能。同时，相比于单自由度WEC模型，五自由度WEC模型可以大幅度提高阵列的能量捕获性能，尤其是在高频区(k₀a > 1.0)。针对有着不同数量浮子（2, 3, 4和5）的四个案例，分别考察了五自由度WEC阵列和单自由度WEC阵列在规则波、不规则波和真实波浪场景中的布局优化问题。与规则波不同的是，不规则波的最优布局都是线性排列的，并且与波浪传播方向垂直。

研究了直线海岸前WEC阵列的水动力性能。基于线性水波理论，发展了直墙前截断圆柱阵列的绕射和辐射的解析解，阵列中所有浮子都建模为可以独立做五自由度运动的截断圆柱。在求解过程中，通过镜像原理将水动力问题转化成在开阔水域中的等效问题。将五自由度WEC与直墙结合，考察了直墙前五自由度WEC阵列在规则波和不规则波中的性能，阵列中各个浮子可以在五个自由度上振动并提取能量。结果表明，直墙的存在能够显著提高WEC阵列在规则波和不规则波中的能量捕获性能，并且五自由度WEC的能量捕获效率始终高于单自由度WEC。当波浪入射角较小（ ）时，波浪入射角的变化对直墙前WEC阵列在不规则波中的性能有着较小影响。然而，当 时，WEC阵列的捕获宽度出现了显著的降低。因此，应避免将直墙前线性排列的WEC阵列平行于波浪的传播方向进行布置，以减少破坏性效应对阵列性能的影响。

为了提高阵列捕获的总能量和布局优化效率，提出了一种基于遗传算法的多级优化方法。多级优化方法能够有效地提高优化结果的性能，兼顾了优化效率和优化结果的稳定性。在规则波中，采用多级优化方法考察了直墙前五自由度WEC阵列和单自由度WEC阵列的布局优化问题。结果表明，规则波中的最优布局中，浮子基本都在驻波场波幅的波峰位置附近。考察了直墙前线性排列的单自由度WEC阵列和五自由度WEC阵列在不规则波和真实波中的布局优化问题。相比于单自由度WEC模型，五自由度WEC阵列的最优布局对波浪场产生了更明显的扰动，五自由度WEC阵列吸收了更多的波浪能量，并降低了直墙附近的自由面显著扰动系数。因此，将五自由度WEC阵列与直墙进行联合开发，不仅有利于提高阵列的能量捕获性能，也可以降低作用于直墙的波浪载荷。

研究了圆柱阵列在波流共同作用下的绕射问题。根据线性叠加原理，将波流绕射速度势分解成三个部分，并分别用不同的方法求解。采用已发表的研究结果验证了水动力模型的正确性。考察了流的引入对八柱阵列的一阶力和二阶力的影响。结果表明，在特定波数条件下，流的引入对圆柱阵列的一阶力和二阶力均产生了显著的影响。

There are very abundant wave energies in the vast ocean. Wave energy technology has developed rapidly over the past few decades. Among various types of wave energy converters (WEC), oscillating body WEC has the characteristics of high energy conversion efficiency and wide adaptability, and is one of the most advanced and mature types of equipment. For wave energy converter (WEC) arrays composed of floating truncated cylinders, there are usually a large number of cylinders in the array, and each cylinder in the array can vibrate with different amplitudes and phases, which increases the degree of freedom of the dynamic system and the difficulty of computational convergence, making the hydrodynamic interactions of the array more complex. More importantly, a large number of cylinders will exhibit near-trapped phenomena, i.e., the hydrodynamic response increases several times at certain frequencies. The accurate prediction of these frequencies is of great significance to the design of ocean structures. How to accurately and efficiently calculate the interactions between waves and relative motion arrays composed of floating truncated cylinders is an essential topic in ocean engineering. However, there are still many shortcomings in the current research on this issue, especially when there are multiple motion modes for each cylinder in the array. In most existing studies, the buoys in the WEC array vibrate and extract energy only in the heave direction. There are still research gaps in the hydrodynamic performance and layout optimization of WEC arrays composed of buoys that vibrate and extract energy in multiple degrees of freedom (DOFs), which has important application prospects.This paper conducts the following research on such issues:

The hydrodynamic analysis model of arrays composed of truncated cylinders under the action of waves is established. The multi-term Galerkin method is used to expand the fluid velocity at the interface of different regions into a set of basis functions containing Gegenbauer polynomials, which accurately and efficiently characterizes the cube root singularity of the fluid velocity near the edges of the truncated cylinders. Analytical solutions have been developed to solve the diffraction and radiation of arrays composed of truncated cylinders in the presence of ambient incident waves. Each cylinder in the array can oscillate with five DOFs, i.e., surge, sway, heave, roll, and pitch. Using the dynamic equilibrium equation, the amplitudes of each DOF of the cylinders in the array are solved. The hydrodynamic model is extended to the situation of multi-directional irregular waves. The analytical solution presented in this paper converges rapidly, and high-precision hydrodynamic response results can be obtained using just a few truncated terms. For the 4-cylinder array, under the same accuracy conditions (the error less than 1%), the computation time of the traditional method (Zeng et al., 2022d) is 3.9 times longer than that of the present method. As the number of cylinders increases, the advantage of the present method in terms of convergence speed becomes more apparent. Based on the established hydrodynamic model, the hydrodynamic responses of the truncated cylinder array in regular waves and irregular waves are examined.

The hydrodynamic performance and layout optimization of the WEC arrays composed of floating truncated cylinders in regular waves and irregular waves are studied. To extract wave energy more efficiently, a new wave energy converter (5-DOF WEC) that can oscillate and extract energy in five DOFs (i.e., surge, heave, heave, roll, and pitch) is developed. The energy calculation model of the WEC array in irregular waves is established and verified with published research results. The impacts of the near-trapped wave mode on the energy capture performance of the linear array are investigated. Near the frequency of the near-trapped mode, the energy extraction performance of the surge wave energy converters is greatly improved, while the performance of the heave wave energy converters is significantly reduced. The energy extraction performances of the equidistant linear arrays composed of 5-DOF WEC in regular and irregular waves are investigated. The results show that arranging the linear array perpendicular to the wave propagation direction can more effectively improve the energy capture performance of the WEC array. Compared with the 1-DOF WEC model which only oscillates and extracts wave energy in the heave direction, the 5-DOF WEC model can greatly improve the energy capture performance of the array, especially in the high-frequency region (k₀a > 1.0). For four cases with different numbers of buoys (2, 3, 4, and 5), the layout optimization problems of 5-DOF WEC arrays and 1-DOF WEC arrays in regular and irregular waves are investigated. Different from the situation of regular waves, the optimal layout of irregular waves is linearly arranged and perpendicular to the direction of wave propagation.

The hydrodynamic performances of WEC arrays in front of a vertical wall are studied. Based on the linear water wave theory, analytical solutions have developed to solve the diffraction and radiation of arrays composed of truncated cylinders near a vertical wall in waves. All buoys in the array are modeled as truncated cylinders that can independently oscillate in five DOFs. During the solution process, the hydrodynamic problem is transformed into an equivalent problem in an open water domain through the image principle. Combining the 5-DOF WEC with a vertical wall, the energy capture performances of the 5-DOF WEC array near a vertical wall in regular and irregular waves are investigated. Each buoy in the array can move and extract wave energy in five DOFs. The results show that the presence of the vertical wall can significantly improve the energy capture performance of the WEC array in regular and irregular waves, and the energy extract efficiency of the 5-DOF WEC is always higher than that of the 1-DOF WEC. For small incident angles ( ), the change in the incident angle has a slight impact on the performance of the WEC array in front of a vertical wall in irregular waves. However, the capture widths of the WEC array are significantly decreased for . Therefore, arranging linear WEC arrays in front of the vertical wall parallel to the propagation direction of waves should be avoided to reduce the impact of destructive impacts on energy capture performance.

In order to improve the total energy extracted by WEC arrays and layout optimization efficiency, a multi-level optimization method based on a genetic algorithm is proposed. The multi-level optimization method can effectively improve the performance of optimization results, taking into account both optimization efficiency and stability of optimization results. In regular waves, the layout optimization problems of the 5-DOF WEC array and the 1-DOF WEC array near a vertical wall are investigated using the multi-level optimization method. The results show that the buoys in the optimal layout are basically located near the peak position of the standing wave field for regular waves. The linear layout optimization problems of 1-DOF WEC arrays and 5-DOF WEC arrays near a vertical wall in irregular waves and real wave scenarios are investigated. Compared with the 1-DOF WEC model, the optimal layouts of the 5-DOF WEC array produce more obvious disturbances to the wave field. The 5-DOF WEC arrays absorb more wave energy and reduce the significant disturbance coefficient of the free surface near the vertical wall. Therefore, the combined development of the 5-DOF WEC array and the vertical wall will not only improve the energy capture performance but also reduce the wave load acting on the vertical wall.

Aiming at the working conditions where waves and currents coexist, the diffraction problem of the cylindrical array is investigated. According to the principle of linear superposition, the velocity potential of wave-current diffraction has been separated into three parts and analyzed using distinct methods. The hydrodynamic model is verified with published research results. The influences of the introduction of current on the second-order and first-order forces of the array composed of eight cylinders are studied. The results show that the introduction of current has a significant impact on both the first-order force and the second-order force of array composed of cylinders for specific wavenumber conditions.