A homogenization approach for characterization of the microscopic viscous-thermal effects in acoustic poroelastic materials
Invited paper
Eindhoven University of Technology
Tuesday 2 june, 2015, 15:40 - 16:00
0.7 Lisbon (47)
Abstract:
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.