Finite element analysis of the vibration problem of a plate coupled with afluid

We consider the approximation of the vibration modes of an elastic plate in contact with a compressible fluid. The plate is modelled by Reissner-Mindl in equations while the fluid is described in terms of displacement variable s. This formulation leads to a symmetric eigenvalue problem. Reissner-Mindl in equations are discretized by a mixed method, the equations for the fluid with Raviart-Thomas elements and a non conforming coupling is used on the interface. In order to prove that the method is locking free we consider a family of problems, one or each thickness t > 0, and introduce appropriate scalings for the physical parameters so that these problems attain a limit when t --> 0. We prove that spurious eigenvalues do not arise with this dis cretization and we obtain optimal order error estimates for the eigenvalues and eigenvectors valid uniformly on the thickness parameter t.