Instabilities and optimization of elastic structures interacting with laminar flows ; Instabilités et optimisation de structures élastiques en interaction avec des écoulements laminaires

The interaction between elastic solids and viscous flows can lead to large deformations. In addition to unsteady non-linear simulations, linearised modal approaches are useful to identify the hydro-elastic instabilities at the origin of these vibrations, and can also be used to design control strategies. The objectives of this thesis are to develop and apply methods, first to describe fluid-solid linear dynamics, then to control it by optimizing the shape or elastic properties of the solid.The first part presents the methods developed to study the linear dynamics of strongly coupled fluid-solid disturbances. Fluid dynamics is governed by incompressible Navier-Stokes equations, while the solid is described by hyperelastic models. An Arbitrary Lagrangian-Eulerian coupling is chosen. An exact linearization of this formulation is derived, and the resulting modal analysis is validated.The second part is devoted to the analysis and control of the vibrations of elastic plates fixed downstream of a rigid circular cylinder, and immersed in a uniform incoming flow. Fluid-solid eigenmodes are identified by means of an eigenvalue analysis of the linearised operator, and time-marching simulations are performed to clarify non-linear interactions. Secondly, an adjoint-based shape optimization is proposed to control unstable modes. A stabilization of the modes is achieved, as well as a modification of unstable frequencies.The last part is devoted to the delay of the laminar/turbulent transition of a boundary-layer flow thanks to viscoelastic coatings. A resolvent analysis of the linearised fluid-solid operator is used to quantify the attenuation of unstable Tollmien-Schlichting waves when the stiffness of the coating is reduced. On the other hand, the eigenvalue analysis shows that high-frequency modes, linked to the dynamics of the solid, are destabilised when the solid viscous damping is too low. A strategy to optimize the distribution of the coating's rigidity with respect to the energetic amplification of both instabilities ...