**Abstract** : Noise reduction for passengers comfort in transport industry is now an important constraint to be taken into account during the design process. The optimization of internal thin wall positioning according to acoustic of the cavity can lead to the study of several configurations and thus may become prohibitive in terms of computational time. The aim of this work is to be able to efficiently optimize the position of thin walls in an acoustic cavity in order to reduced the generated noise of a given acoustic source in a frequency range.
A porous material is placed on the rigid walls of the cavity in order to reduced the noise. This material is modeled by a Biot-Allard theory involving 3D finite elements. The embedded structures, such as seats in a plane cabin, are assumed to have no thickness in the acoustic domain. The thin flexible structures, discretized using shell elements, are immersed arbitrarily within the acoustic mesh allowing to always use the same acoustic mesh. This makes the parametric study easier since it does not involve a meshing process anymore.
The first idea is to use XFEM in order to take into account the structure influences in the acoustic compressible fluid domain by enriching the pressure by a Heaviside function. The finite element discretization of the whole fluid-structure coupled problem leads to a linear system in the frequency domain. In this system, the only matrices needed to be recomputed when the structures are placed arbitrarily in the fluid, are those corresponding to the enrichment and the one corresponding to the coupling between the fluid enrichment and the structures. The second idea is to build reduced basis. The structure basis is composed of its eigenmodes whereas a component mode synthesis with a fixed interface is used to build the fluid basis, this reduced basis is similar to the Craig-Bampton approach. The interface degrees of freedom are thus the enriched nodes of the XFEM while the internal domain corresponds to the acoustic cavity with no structure inside. The method is implemented for flexible shell structures embedded in a 3D fluid. The third point of the proposed approach is to use a surrogate-based optimization in order to furthermore reduce the computational time of the whole optimization process. The approach is based on the Efficient Global Optimization composed of two phases: (1) a kriging metamodel is built using only a few sample points and associated responses and (2) an iterative scheme using the expected improvement allows us to find the global minimum by adding smartly new sample points to the initial surrogate model.