Department of Mathematical Engineering
University of Concepcion
Abstract: Transmission of vibrations from an elastic structure to an ideal acoustic fluid is considered when both media are separated by a thin layer of a noise damping viscoelastic material. Much attention is currently been paid to this kind of problems, mostly related to the goal of decreasing the noise level in aircrafts and cars. A simplified mathematical model is used for the damped transmission conditions. A finite element method, which proved to be efficient to compute undamped coupled vibrations, is applied to the damped problem. It consists of using standard finite elements for the structure combined with Raviart-Thomas elements for the fluid displacements. Convergence is proved and error estimates are provided. Numerical results are given for some 2D and 3D problems. In particular, a Reissner-Mindlin plate in contact with a fluid is considered. Response curves exhibiting the classical peaks at resonance frequencies are presented and these peaks are related with the real parts of the complex eigenvalues of this problem. Finally, the damped vibrations of a fluid contained in a rigid cavity with its walls covered by the damping material is considered. In this simpler case, a thorough mathematical and numerical analysis of the arising quadratic eigenvalue problem is performed.