Hello, my name is Tristan Leclercq, and I'm a PhD student in Fluid-Structure interactions at the Ecole Polytechnique. Today I would like to tell you about some of the work I've done during my PhD on the interaction between a flexible cantilever structure and an oscillatory current of fluid. Such coupled system can for instance be found when sea waves move near-shore kelp or even these flexible corals called gorgonas. To understand this type of dynamics, I put together models designed to describe the deformation of the plate and the forcing by the flow, and I performed numerical simulations. Then, I analyzed the results depending on the parameters of the forcing that are its amplitude and frequency. First, let's consider the case where the amplitude is small. Because the deflection of the plate is small, the equations governing its behaviour are linear. In this situation, the dynamics can be decomposed on independant modes. The global dynamics is then simply the superposition of these modes, as you have seen in the course. As you can see on the left of this graph, when the frequency of oscillation of the flow is small, the deflection remains small. But above some critical frequency, the deflection becomes of the order of magnitude of the forcing. This critical frequency is the first natural frequency of the plate, and you also notice a peak of amplitude there, due to the resonance of the first natural mode. The shape of the beam for this specific value of the frequency demonstrates that the motion is dominated by this mode. The following peaks also correspond to resonances with the successive beam modes: mode 2 here, mode 3 and so on... So this is what happens when everything is linear. But what happens if we increase the amplitude of oscillation of the flow? Well, the first thing is that damping by the fluid becomes important. The consequence is that the resonances are damped out, but the overall shape of the motion is not really affected. If the amplitude of flow oscillation is increased further, the motion is really modified. We do not recognize the modal shapes anymore, even though the amplitude of motion still remains quite small. When the amplitude of flow oscillation is even larger, the large deflections of the structure add geometrical non-linearities to the system that complicate the dynamics even more, as you can see on these examples. So this is what happens when the amplitude of the flow is increased. But a large amplitude is not the only situation in which complex dynamics may occur. During my PhD, I also conducted experiments in which I oscillated flexible plates in a small water tank. Here is an example of the type of videos I could obtain. When the frequency of flow oscillation is small, the motion is symmetric and is well predicted by the linear theory. But when I increase the frequency... ... The plate slowly drifts to the side, until it finally oscillates about an average position that is not in the center anymore. So here we found a case where non-linearities in the system are responsible for breaking the symmetry of the dynamics even though the amplitude remains small, just by changing the frequency! All these phenomena are very good examples of the huge diversity of dynamics we can observe when a system is non-linear, even when it looks simple at first glance! I hope you enjoyed this video about my research, and of course, I'll be happy to answer any question you may have on the course forum.