自然界中的生物通常利用主动或被动驱动下的变形和运动维持自身生存，例如飞行和游动生物的高性能推进，及水生或陆生植物的叶片结构在流体载荷作用下的弯曲变形，这些策略同时也成为各类人造仿生装置设计中的重要灵感来源。此类问题通常涉及到生物扁平状的身体结构(如翅、鳍、叶片等) 和流体环境之间的相互作用，对这些流固耦合现象的深入研究，有助于我们以此为基础对相应结构的仿生设计提供一定的理论指导。本文使用基于精确投影的直接力浸入边界方法，系统研究了三个与仿生柔性薄板结构在主动和被动驱动下的变形和运动相关的典型流固耦合问题。
本文的主要创新性工作可概括如下：
(一) 主动驱动下“张合式”双翼结构的自主推进
针对主动驱动下仿生薄板结构的自主推进问题，以静止流体中一对反相扑动的薄翼作为简化模型，考察双翼结构在主动驱动下的悬停性能及稳定性特征。首先，在仅允许垂向位移的条件下，考察关键参数对系统推进性能的影响，得到实现悬停所需要的扑动振幅与频率之间的关系。分析上升、下落、悬停三种状态下系统的尾迹结构特征，发现悬停状态由涡量在物体附近的持续积累而引起的尾迹自发对称破缺现象，这一现象使悬停状态难以长期维持。随后，在三自由度自由飞行的情况下讨论系统的姿态稳定性特征，结果表明，上升及悬停状态均具有较好的姿态稳定性，但由于悬停状态的尾迹自发失稳特征，在物理或数值扰动下，悬停均无法长时间维持。
(二) 振荡流中柔性双翼结构的被动推进
针对柔性结构在间接驱动下的被动推进问题，以振荡流中具有集中柔性自由度的“Λ-形”双翼结构为例，讨论系统在平均流速为零的垂向振荡流体驱动下所实现的被动推进和运动，研究柔性对被动推进性能和稳定性的影响。首先，从推进状态、扑动模式及尾迹对称性特征等方面考察关键结构参数和驱动参数对系统被动推进的作用，结果表明，结构固有频率与振荡流驱动频率之间的共振显著改变被动扑动的振幅与相位，二者的协同作用引起结构与背景流体之间相对速度的大幅变化，使柔性对被动推进产生增强或削弱的双重作用，这一机制同样导致了系统的尾迹对称性特征在不同驱动频率区间表现出的显著差异。随后，在施加初始扰动的情况下，讨论结构的姿态稳定性特征，发现了不同驱动条件下，系统可能出现的单稳定、双稳定及不稳定等状态，并与刚性情形进行比较，结果显示，由共振引起的相对速度调制使柔性对于稳定性同样体现出双重作用。此外，当驱动频率较高时，柔性的存在削弱了结构的几何非对称性，对其被动推进不利，但可显著增强其姿态稳定性。
(三) 层流边界层中壁面固支柔性薄板的动力学特性
针对局部约束柔性结构在流固耦合作用下的流致振动问题，考察固支于壁面的单个及多个柔性薄板结构在层流边界层作用下的被动运动响应。对于单薄板系统，讨论刚度、质量比、雷诺数等参数对系统动力学状态的影响，发现系统可能出现的倒伏、静态弯曲及涡激振动等三类典型运动模态，对涡激振动模态的频率特性进行分析，得出了相应的二阶本征频率锁定机制。对于串列薄板系统，除单一薄板的三类典型状态之外，还出现由于平板之间的动力学耦合而出现的“空腔振动”模态，且这一特殊状态的出现与平板间距及刚度直接相关。进一步考察涡激振动与空腔振动模态的频率特征，发现了分别对应于两类状态的二阶和一阶本征频率锁定机制。

Creatures in nature always utilize the deformation and motion under active or passive actuations for survival, such as the high performance locomotion strategies used by flying and swimming animals, and the bending deformation of leaves among aquatic or terrestrial plants when facing the flow-induced loads. These strategies are also considered as the source of inspiration for the design of man-made biomimic devices. Motions of creature always involve the interaction of the flat structures (such as wings, fins and leaves) and the surrounding fluid medium. The in-depth study of such fluid-structure interaction (FSI) can provide some theoretical evidences to the biomimic design of corresponding devices. In this dissertation, three typical FSI problems involving the deformation and movement of bio-inspired flexible plates under active and passive actuation are studied numerically by using the direct-forcing immersed boundary method based on the exact projection formulation. The dynamic behaviours and the underlying mechanisms of the corresponding FSI systems are explored in detail.

The main innovative works of this dissertation are summarized as follows:

1. Self propulsion of a bio-inspired flyer powered by one pair of pitching foils

The hovering performance and postural stability of a bio-inspired flyer composed of two thin foils which are forced to pitch in antiphase fashion is studied systematically. We first consider the constrained-flying condition where the model is only allowed to move in the vertical direction. The influences of the control parameters on the hovering performance are discussed, and the scaling laws between the driven frequency and amplitude are obtained. With the variations in parameter values, three different locomotion states, i.e., ascending, descending, and approximate hovering, are identified. The wake structures corresponding to these three locomotion states are explored. It is found that the approximate hovering state cannot persist due to the occurrence of wake symmetry breaking after long-time simulation. The occurrence of the wake symmetry breaking can be attributed to the vorticity accumulation near the flyer due to the lack of a translation velocity. Then we consider the free-flying condition where the motions in three degrees of freedom are allowed. The postural stability behaviours of the flyer are studied numerically. The results show that the orientation angle of ascending and approximate hovering state is recoverable after the physical perturbation. But the hovering state is irrecoverable after the physical or numerical perturbations due to the occurrence of the wake symmetry breaking. 

2. Passive locomotion of a flexible dual-wing flyer in a vertically oscillatory flow

In this work, we numerically investigate the passive locomotion of a flexible $\Lambda$-shaped flyer in a vertically oscillatory flow with zero mean stream. In the simplified model, the flexibility of the flyer is introduced by a torsional spring installed at the hinged joint of the two foils. First, we study the effects of structural and driven parameters on the passive locomotion, angular oscillation patterns and wake structures. The results suggest that the occurrence of resonance between the flexible flyer and the oscillating flow can result in significantly different performances in flexible and rigid flyers. It is found that flexibility can have two opposing effects, reducing or increasing the actuation efforts for hovering, depending on the range of driving frequency. This result is explained by the modulation of relative velocity between the flyer and the imposed background flow due to the drastic change on both the amplitude and phase difference of the angular oscillation. The significant difference of the wake symmetry properties in different range of driven frequency can also be interpreted by the modulation of relative motion. The responses of both the flexible and rigid flyer at different driven condition to initial perturbations are examined. The stable, bistable and unstable states are identified, and the differences on the postural stability behaviour of the flexible and rigid flyer are also analysed. The results suggest that the modulation of the relative motion can also have two opposite influences on the postural stability. Besides, the geometric asymmetry of the flexible flyer is reduced when the driven frequency is high enough. The geometric effect is unfavorable to the hovering performance, but is beneficial to the postural stability.

3. Dynamic behaviours of wall-mounted flexible plates in the laminar boundary layer

The flow-induced vibration of both a single and multiple wall-mounted flexible plates in the laminar boundary layer is investigated numerically in this work. For the single-plate system, the influences of various control parameters, including bending rigidity, density ratio and Reynolds number on the dynamic behaviours of the system were explored systematically. Three distinct modes, that is, lodging, regular vortex induced vibration (VIV), and static reconfiguration, are identified. And the second natural frequency lock-in phenomenon in the regular VIV mode is illustrated. For the multi-plate system, the cavity oscillation mode due to the coupling of the adjacent plates is also observed. The occurrence of the cavity oscillation mode is directly related to the bending rigidity and the interspace between the nerghbors. Furthermore, two different frequency lock-in phemonema correspond to the regular VIV mode and the cavity oscillation mode are elucidated.