We analyze an isoparametric finite element method to compute the
vibration modes of a plate, modeled by Reissner-Mindlin equations,
in contact with a compressible fluid, described in terms of
displacement variables. To avoid locking in the plate, we consider
a low-order method of the so called MITC (Mixed Interpolation of
Tensorial Component) family on quadrilateral meshes. To avoid
spurious modes in the fluid, we use a low-order hexahedral
Raviart-Thomas elements and a non conforming coupling is used on
the fluid-structure interface.
Applying a general approximation theory for spectral problems,
under mild assumptions, we obtain optimal order error estimates
for the computed eigenfunctions, as well as a double order for the
eigenvalues. These estimates are valid with constants independent
of the plate thickness. Finally, we report several numerical
experiments showing the behavior of the methods.