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Composites périodiques fonctionnels pour l'absorption vibroacoustique large bande

Abstract : The understanding of wave propagation in periodic structures is proposed in this work. Periodic structures exhibit very specific properties in terms of wave propagation. First, some numerical tools for dispersion analysis of periodic structures are presented. The classical Floquet-Bloch approach is first presented, as a reference. This technique uses proper boundary conditions on the unit cell, but dealing with damping is not easy for 2D or 3D cases. Secondly, a metamaterial with hierarchical, auxetic (negative Poisson ratio) rectangular perforations is presented using the Floquet-Bloch method as a reference. Some numerical eigenvalue tools are used for the dispersion analysis of this structure. A geometric parametric investigation of these rectangular perforations using a numerical asymptotic homogenisation finite element approach is done. The experimental validation is performed with a network based on polymethyl methacrylate (PMMA) using a 3D scanning vibrometer. Third, the Shift cell operator technique is described. It consists in a reformulation of the PDE problem by shifting in terms of wave number the space derivatives appearing in the mechanical behavior operator inside the cell, while imposing continuity boundary conditions on the borders of the domain. Damping effects can be introduced in the system. This strategy make it possible to solve the problem with an arbitrary frequency dependency of the physical properties of the cell. A focus is proposed on tools for the post-processing of dispersion diagrams in damped configurations like group velocity. Finally, an adaptive metamaterial based on the combination of metallic parts with highly dissipative polymeric interface is designed. In order to validate the design and the adaptive character of the metamaterial, results issued from a full 3D model of a finite structure embedding an interface composed by a distributed set of the unit cells are presented. After this step, a comparison between the results obtained using the tunable structure simulation and the experimental results is presented.
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Kevin Billon. Composites périodiques fonctionnels pour l'absorption vibroacoustique large bande. Mécanique des solides [physics.class-ph]. Université de Franche-Comté, 2016. Français. ⟨NNT : 2016BESA2018⟩. ⟨tel-01458153⟩

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