Coupling of Bloch waves and Finite-Element models: case of metaporous sandwich structures, by Mathieu Gaborit (KTH Royal Institute of Technology)

DENORMS Action’s Workshop “Modelling of high performance acoustic structures Porous media, metamaterials and sonic crystals”, Rome, 24-25th January 2017

Website of DENORMS Action

Programme of the Workshop

Session on New trends in traditional noise treatments – porous materials and microperforated plates

Speaker: Mathieu Gaborit (KTH Royal Institute of Technology)

Abstract:

Numerical simulation of sandwich panels with periodic inclusion of arbitrary shape and size is a challenging task. A classical approach for this task makes use of the Finite-Element Method (FEM) which can handle complex geometries, general deformation states for various physical constituents (poroelastic media, elastic structures, air cavities, etc.). In a FEM model the structure is meshed, leading to a linear system with the value of the physical fields at the nodes of the mesh as unknowns. In order to study the response due to a plane wave excitation, the amplitudes of the reflected specular and Bloch waves are added to the unknowns of the problem and specific coupling matrices are introduced in the linear system. In the case of radiation in a semi-infinite medium, similar techniques could be applied for the transmitted Bloch waves. In the case of sandwich panels, elastic plates are generally added to the core as face sheets increasing the bending stiffness and the air/skeleton coupling. As these are thin with respect to the overall dimensions of the structure; they tend to drive the mesh refinement in order to correctly simulate their behaviour. In the general case, the coatings need to be modelled as solid layers with finite thickness, special care needs to be taken in order to avoid distortion effects, increasing the complexity of the model. In the current work, a method is proposed which adds the face plates to the structure without adding degrees of freedom. An approach based on the Transfer Matrix Method is set up for each individual Bloch wave in order to propagate the fields through the plates surrounding the porous core. It will be shown how the linear equation system is modified to include the coupling matrices between the degrees of freedom of the FE scheme and the Bloch waves' amplitudes. The method will first be applied to homogeneous multilayered systems for which analytical solutions can be obtained. In a second step, the case of metaporous materials with inclusions will be considered and a comparison to multiple scattering techniques[1] and pure FEM models will be made.

[1] T. Weisser et al. J Acoust Soc Am, 139(2): 617-630, 2016