Abstract

This paper deals with a finite element method to compute the vibrations of a coupled fluid-solid system subject to an external harmonic excitation. The system consits of an acoustic fluid and a plate, with a thin layer of a noise damping viscoelastic material separating both media. The fluid is described by displacement variables whereas the plate is modeled by Reissner-Mindlin equations. Face elements are used for the fluid and MITC3 elements for the bending of the plate. The effect of the damping material is taken into account by adequately relaxing the kinematic constraint on the fluid-solid interface. The nonlinear eigenvalue problem arising from the free vibrations of the damped coupled system is also considered. The dispersion equation is deduced for the simpler case of a fluid in a hexahedral rigid cavity with an absorbing wall. This allows computing analytically its eigenvalues and eigenmodes and comparing them with the finite element solution. The numerical results show that the coupled finite element method neither produces spurious modes nor locks when the thickness of the plate becomes small. Finally the computed resonance frequencies are compared with those of the undamped problem and with the complex eigenvalues of the above nonlinear spectral problem. © 2001 Elsevier Science B.V. All rights reserved.