Finite element computation of the vibrations of a plate-fluid system with interface damping

This paper deals with a finite element method to compute the vibrations of a coupled fluid-solid system subject to an external harmonic excitation. Th e system consists of an acoustic fluid and a plate, with a thin layer of a noise damping viscoelastic material separating both media. The fluid is des cribed by displacement variables whereas the plate is modeled by Reissner-M indlin equations. Face elements are used for the fluid and MITC3 elements f or the bending of the plate. The effect of the damping material is taken in to account by adequately relaxing the kinematic constraint on the fluid-sol id interface. The nonlinear eigenvalue problem arising from the Ree vibrati ons of the damped coupled system is also considered. The dispersion equatio n is deduced for the simpler case of a fluid in a hexahedral rigid cavity w ith an absorbing wall. This allows computing analytically its eigenvalues a nd eigenmodes and comparing them with the finite element solution. The nume rical results show that the coupled finite element method neither produces spurious modes nor locks when the thickness of the plate becomes small. Fin ally the computed resonance frequencies are compared with those of the unda mped problem and with the complex eigenvalues of the above nonlinear spectr al problem, (C) 2001 Elsevier Science B.V. All rights reserved.