Approximation of the vibration modes of a plate coupled with a fluid by low-order isoparametric finite elements

Departamento de Matemática, Universidad Técnica Federico Santa María, Casilla 110-V, Valparaiso, Chile. erwin.hernandez@usm.cl.

Received: 24 July 2004
Revised: 22 September 2004

Abstract

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.