Denis Bonheure - Flow-Induced Oscillations of a Spring-Mounted Body in a Navier-Stokes Liquid

We study the motion of a rigid body $\mathscr B$ subject to an undamped elastic restoring force, in the stream of a viscous liquid $\mathscr L$. The motion of the coupled system $\mathscr B$+$\mathscr L\equiv\mathscr S$ is driven by a either a periodic or an uniform flow of $\mathscr L$ at spatial infinity. In the case of a periodic excitation of the fluid, we show the occurrence of periodic oscillations of the rigid body $\mathscr B$ whatever the period and the amplitude of the periodic flow at spatial infinity. In the case of an uniform flow at spatial infinity, we discuss a scenario for the appearance of self-induced oscillations through Hopf bifurcation. These results show that, within this model, a dramatic structural failure cannot take place due to resonance effects.