A homogenization approach for characterization of the microscopic viscous-thermal effects in acoustic poroelastic materials

Invited paper

Kun Gao

Eindhoven University of Technology

Tuesday 2 june, 2015, 15:40 - 16:00

0.7 Lisbon (47)

Acoustic shielding is very important for high-tech systems and in human life. Porous materials like acoustic foams can be used for shielding and their absorption abilities depend on the interaction of the acoustic wave and the complex microstructure. In this paper, a homogenization approach is proposed to investigate the relation between the microstructure and the macroscopic properties. The macroscopic absorption ability is due to the microscopic viscous-thermal coupling between an elastic solid skeleton and a gaseous fluid in the associated Representative Volume Element (RVE). In the homogenization method, the boundary conditions of the microscopic RVE reply on the macroscopic solid deformation and fluid pressure gradient. By assuming that the macroscopic energy equals the volume average of the microscopic energy, the macroscopic solid stress and fluid displacement can be calculated from the corresponding microscopic quantities. With additional assumptions, this homogenization approach corresponds to Biot's poroelastic theory. A numerical experiment is performed in the form of simulations of sound absorption tests on three porous materials made from aluminum and two different polyurethanes respectively. For simplicity, an idealized partially open cubic microstructure is adopted. The homogenization results are evaluated by comparison with Direct Numerical Simulations (DNS), showing a good performance of the approach for the studied porous material. By comparing the results of difference solid materials, it is found that the solid stiffness has a very limited effect when resonance does not occur. Nevertheless, due to the ignorance of the microscopic inertial effects, Biot's equations with the parameters obtained from the homogenization approach predict a higher resonance frequency than the DNS, whereas a modification fully based on the homogenization approach improves the prediction.

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