Impact of the irregular microgeometry of polyurethane foam on the macroscopic acoustic behavior predicted by a unit-cell model

Abstract

This paper deals with the prediction of the macroscopic sound absorption behavior of highly porous polyurethane foams using two unit-cell microstructure-based models recently developed by the authors [J. Appl. Phys. 110, 064901 (2011) and J. Appl. Phys. 113, 054901 (2013)]. In these models, the porous material is idealized as a packing of a tetrakaidecahedra unit-cell representative of the disordered network that constitutes the porous frame. The non-acoustic parameters involved in the classical Johnson-Champoux-Allard model (i.e., porosity, airflow resistivity, tortuosity...) are derived from characteristic properties of the unit-cell and semi-empirical relationships. A global sensitivity analysis is performed on these two models in order to investigate how the variability associated with the measured unit-cell characteristics affects the models outputs. This allows identification of the possible limitations of a unit-cell micro-macro approach due to microstructure irregularity. The sensitivity analysis mainly shows that for moderately and highly reticulated polyurethane foams, the strut length parameter is the key parameter since it greatly impacts three important non-acoustic parameters and causes large uncertainty on the sound absorption coefficient even if its measurement variability is moderate. For foams with a slight inhomogeneity and anisotropy, a micro-macro model associated to cell size measurements should be preferred.

Prediction of the acoustic behavior of a parallel assembly of hollow cylinders

“…sound absorption and sound transmission) of rigid porous materials can be predicted following, mainly, three model types: empirical model [1], phenomenological or semi-phenomenological model [2] and microstructural model [3][4][5]. Unlike the first two model types, microstructural models have the advantage of linking the microstructure to the acoustic properties.…”

“…Those models are based on the observation of the microstructure of porous materials to define an elementary unit cell. Then, finite element method [3] or semi-empirical approach [4] are used to obtain the parameters of an acoustic model to predict absorption coefficient and transmission loss. In particular, for cylindrical pores and slits, the link is well modeled [5].…”

Generation of random microstructures and prediction of sound velocity and absorption for open foams with spherical pores

“…used by the Johnson-Allard model. Thus, the influence of microstructure on some of those parameters may now be also thoroughly studied 8,34,35 (separately from the whole poro-acoustic model). The authors of microstructure-based analyses usually propose very simplified periodic cells to represent the studied porous media; in the case of materials with spherical pores the representative micro-geometries are based on some regular sphere-packings.…”

Investigation of the effects of the microstructure on the sound absorption performance of polymer foams using a computational homogenization approach

“…On the other hand, the non-acoustical parameters can also be obtained by using semi-phenomenological models. partially-open foams respectively [26] and used their models in a corresponding sensitivity study [27]. Moreover, Yang et al developed an empirical model based on a simple cubic unit cell [28].…”

“…The influences of the geometrical properties and the solid properties are investigated by focusing on the effective material parameters involving both mechanical and acoustical properties of polymer foams. For the geometrical properties, earlier investigations on these factors [22,23,24,25,26,27] were based on the JCAPL model, in which the solid deformation is not considered.…”