Resonances of an elastic plate in a confined flow

We present a theoretical study of the resonances of an elastic plate placed in a duct in presence of a flow. We show that finding resonances amounts to solving a family of 2-D eigenvalue problems. It is well known that resonances exist for a rigid plate and without flow, corresponding to fluid vibrations trapped around the plate. Using the min-max principle for non-compact self-adjoint operators, we extend the study to the cases of an elastic plate and/or a uniform flow, and we prove the existence of resonances versus the characteristics of the plate and of the fluid.