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Modèles réduits d’interfaces dissipatives en vibroacoustique par approche k-space

Abstract : In order to predict the sound pressure level and the vibratory level in vibroacoustic systems such are used in transportation industry, efficient numerical models are needed. In particular, the complexity of such systems is increased when dissipative interfaces composed of poroelastic materials are used to dissipate the acoustic or the vibrational energy. Classically, the finite element method is used, leading however to very large computational costs. One aim of this work consists in the development of a reduction procedure in the finite element method framework. A second problematic of this work is the physical justification of the efficiency of the proposed approach. We show that wave insights allow to provide an answer to both goals. In order to predict which waves are able to propagate in a medium, transfer approaches may be used. Among them can be found theWave Finite Element Method (WFE). In a first step, this method is applied to a poroelastic single layer. The role of numerical parameters, the convergence behaviour and the choice of the variational formulation are discussed. In the third chapter, wave propagation is analysed in multilayer packages including poroelastic materials.Waves predicted by using WFE are compared with simplified models, such as equivalent plate models. The behaviour of composite panels is mainly influenced by the mechanical parameters of the skeleton of the porous material. However, the fluid phase presence induces a wave which may create a displacement of the surrounding domains. In the fourth chapter, the waves propagating in an unidirectional wave guide are investigated. The relationships between the Stroh formalism, the Transfer Matrix Method (TMM) and the WFE are discussed. Using the basis of progressive waves makes it possible to compute the forced response of the structure, taking into account finite size effects, lateral boundary conditions and non-localized effects. Finally, the waves modes computed by WFE in an unidirectional wave guide are used to build a reduced order problem. Using the results of the fourth chapter, it is shown that the contribution of the dissipative interface can be represented by an additional acoustic dynamic stiffness matrix. As a result, the number of degrees of freedom is reduced with respect to the initial finite element problem. The approach presents interesting reduction factors, especially by using Component Mode Synthesis for the surrounding cavity. Two enhancements are proposed. The first one consists in the selection of the waves contributing to the main dynamic phenomena of the medium, the second in the interpoation as a function of the frequency of the additional matrix representing for the coupling between the cavity and the dissipative layer. The reduction of the numerical cost is observed in the case of Biot-Allard’s model and of an equivalent fluid model Conclusions and outlooks to enhance the method developed in this work are proposed in the concluding chapter.
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Submitted on : Wednesday, March 31, 2021 - 2:32:30 PM
Last modification on : Wednesday, September 28, 2022 - 6:00:18 AM
Long-term archiving on: : Thursday, July 1, 2021 - 6:42:43 PM

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Quentin Serra. Modèles réduits d’interfaces dissipatives en vibroacoustique par approche k-space. Mécanique [physics.med-ph]. Ecole Centrale de Lyon, 2014. Français. ⟨tel-03186901⟩

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