Rodolfo Rodriguez

Department of Mathematical Engineering

University of Concepcion

Chile

**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.