深海柔性结构广泛应用于深海探索、油气开采、矿产开采等领域，是工程设 备的重要组成部分。深海柔性结构通常在 10²～10³ 米的深海服役，受复杂荷载作 用产生复杂响应，这对结构安全产生巨大威胁。恶劣的服役环境使深海柔性结构 一旦破坏将无法修复，导致工程设备不能正常运行，将造成巨大的经济损失和严 重的生态环境污染。此外，深海柔性结构与流体的相互作用属于典型流固耦合问 题，其中涉及高柯西数，大几何非线性，复杂动响应等内容，一直是科研领域的 热点问题。因此，研究深海柔性结构在荷载作用下的响应具有重要的经济、社会 和科学价值。随着工程向深海进军，柔性结构尺寸迅速增加，为了减小由于自重 产生结构应力过大问题，通常会减小截面尺寸降低自重或增加分布式浮力装置以 抵消自重。但是，减小截面尺寸会降低结构刚度，使结构柔性增加，而分布式浮 力装置使深海柔性结构成为了非均匀结构，使结构的响应更加复杂。因此，本文 采用数值与实验相结合的方法，在前人成果的基础上进行拓展，对非均匀浮力分 布深海柔性结构在流体作用下的响应与控制进行了系统研究。本文将具有非均匀 浮力分布的深海柔性结构称为深海非均匀柔性结构。主要研究成果如下： 首先，基于静力学平衡方程推导了具有非均匀浮力分布柔性结构的常微分控 制方程，给出了直接积分法和有限差分法对非线性常微分方程进行数值求解的步 骤，与现有文献进行对比，验证了模型的正确性。同时，进一步研究了非均匀浮 力与浮力位置对柔性结构形状和所受荷载的影响规律。数值结果表明：在柯西数 C_Y=10⁰～10³ 时，非均匀浮力可以减小柔性结构变形，延缓了重构数 R 和 Vogel 指数的下降。重构数 R 曲线和 Vogel 指数曲线存在多个交叉点，说明了结构在不 同形状也存在阻力相同的情况。非均匀浮力梁 Vogel 指数有时升高有时降低，呈 现振荡的形式。 其次，建立了含有非均匀浮力分布柔性结构的动力学偏微分控制方程，其柔 性结构可以是任意截面，拓展了方程的适用范围。利用有限差分法对方程进行时 域计算，结果与现有文献相同验证了理论模型的正确性。在振荡流作用下，研究 了浮力与浮力位置对柔性结构变形和流体荷载的响应规律。数值结果表明：在振 荡流下柔性结构受到的荷载比刚性结构受到的荷载小；C_Y=10⁰～10¹，浮力较大 （B_b=50、100）且浮力位置值大（s^*=0.75、1.00）时，浮力可以延缓重构数 R 和Vogel指数随着柯西数CY的增加而减小。在柯西数C_Y=10³时，振荡流下Vogel 指数为-0.6～-0.9，呈现振荡。 第三，设计并搭建了实验平台，开发了实验平台的拖曳力测量系统和变形测 量系统，对柔性梁、非均匀柔性梁、柔性管、非均匀柔性管等试件进行了实验研 究。最后，通过数值与实验的对比分析了研究柔性梁和非均匀柔性梁的变形形状 和流体荷载的响应规律。进一步通过实验研究了柔性管和非均匀柔性管的变形形 状和流体荷载的响应规律。实验发现柔性管的响应比柔性梁的响应更加复杂，存在面外运动。 第四，针对深海立管振动的特点，设计了多模态主动控制的方法。通过简化 升力系数与模态能量输入区重叠消除方法，建立了深海柔性结构的多模态振动动 力学方程，然后运用 LQR 方法设计了两种控制策略，模态平均控制法和模态加 权控制法。数值结果表明：模态加权控制法优于模态平均控制法。另外，流速会 影响 LQR 控制的效果。

Deepsea flexible structures are widely used in deep-sea exploration, oil and gas mining, mineral mining and other fields, and are an important part of engineering equipment. Deep-sea flexible structures are usually in service in the deep sea of 10²~10³ m and are subject to complex loads to produce complex responses, which pose a huge threat to the safety of the structure. The harsh service environment makes it impossible to repair the deep-sea flexible structure once it is damaged, causing engineering equipment to fail to operate normally, which will cause huge economic losses and serious ecological environmental pollution. In addition, the interaction between deep-sea flexible structures and fluids is a typical fluid-solid coupling problem, which involves high Cauchy numbers, large geometric nonlinearities, and complex dynamic responses, and has always been a hot issue in the field of scientific research. Therefore, studying the response of deep-sea flexible structures under load has important economic, social and scientific value. With the advancement of engineering into the deep sea, the size of flexible structures has increased rapidly. In order to reduce the problem of excessive structural stress due to its own weight, the cross-sectional size is usually reduced to reduce its own weight, or distributed buoyancy devices are added to offset its own weight. However, reducing the cross-sectional size will reduce the rigidity of the structure and increase the flexibility of structure, and the distributed buoyancy device makes the deep-sea flexible structure a non-uniform structure, which makes the response of structure more complex. Therefore, this paper adopts the method of combining numerical value and experiment, and expands on the basis of previous results, and systematically studies the response and control of the deep-sea flexible structure with the non-uniform buoyancy distribution under flow. In this paper, the deep-sea flexible structure with non-uniform buoyancy distribution is called the deep-sea non-uniform flexible structure. The main research results are as follows: Firstly, based on the statics balance equation, an ordinary differential control equation with a flexible structure with non-uniform buoyancy distribution is derived, and the steps of direct integration method and finite difference method to numerically solve nonlinear ordinary differential equations are given. Compared with the existing literature, the correctness of the model is verified. The influence of non-uniform buoyancy and buoyancy position on the shape and load of the flexible structure is further studied. The numerical results show that when Cauchy number C_Y=10⁰~10³, the non-uniform buoyancy can reduce the deformation of the flexible structure and delay the decrease of reconfiguration number R and Vogel exponent. There are multiple intersections in reconfiguration number R and the Vogel exponent curve, which indicates that different shapes of boards also have the same resistance. The Vogel exponent of non-uniform buoyancy beam sometimes increases and sometimes decreases, showing the form of oscillation. Secondly, a dynamic partial differential governing equation of a flexible structure with non-uniform buoyancy distribution under oscillatory flow is established. The flexible structure can be any cross-section, which expands the scope of application of the equation. The finite difference method is used to calculate the equation in time domain. Moreover, the correctness of the theoretical model is verified as the same as the existing literature. Under oscillatory flow, the response law of buoyancy and buoyancy position to the deformation of flexible structure and fluid load is studied. The numerical results show that the load on the flexible structure is smaller than the load on the rigid structure under oscillatory flow; CY =10⁰~10¹, the buoyancy is large (B_b = 50, 100) and the buoyancy position is large (s^*=0.75, 1.00), buoyancy can delay reconfiguration number R and Vogel exponent decrease with the increase of Cauchy number CY. When the Cauchy number C_Y=10³, Vogel exponent -0.6~-0.9 under oscillatory flow. Third, the experimental platform was designed and built, the drag force measurement system and the deformation measurement system of the experimental platform were developed, and the experimental research was carried out on flexible beams, non-uniform flexible beams, flexible pipes, non-uniform flexible pipes and other test pieces. Finally, through the comparative analysis of numerical value and experiment, the deformation shape of flexible beam and non-uniform flexible beam and the response law of fluid load are studied. The deformation shape and fluid load response law of flexible pipes and non-uniform flexible pipes are further studied through experiments. Experiments have found that the response of the flexible tube is more complex than that of the flexible board, and there is out-of-plane motion. Fourth, according to the characteristics of deep-sea riser vibration, a multi-modal master control method is designed. By simplifying the overlap elimination method of lift coefficient and modal energy input area, the multi-modal vibration dynamics equation of the deep-sea flexible structure is established, and then two control strategies are designed using the LQR method, the modal average control method and the modal weighted control method. The numerical results show that the modal weighted control method is better than the modal average control method. In addition, the flow rate will affect the effect of LQR control.