On the sensitivity analysis of porous material models

Abstract

a b s t r a c tPorous materials are used in many vibroacoustic applications. Different available models describe their behaviors according to materials' intrinsic characteristics. For instance, in the case of porous material with rigid frame, and according to the Champoux-Allard model, five parameters are employed. In this paper, an investigation about this model sensitivity to parameters according to frequency is conducted. Sobol and FAST algorithms are used for sensitivity analysis. A strong parametric frequency dependent hierarchy is shown. Sensitivity investigations confirm that resistivity is the most influent parameter when acoustic absorption and surface impedance of porous materials with rigid frame are considered. The analysis is first performed on a wide category of porous materials, and then restricted to a polyurethane foam analysis in order to illustrate the impact of the reduction of the design space. In a second part, a sensitivity analysis is performed using the Biot-Allard model with nine parameters including mechanical effects of the frame and conclusions are drawn through numerical simulations.

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

“…l also dominates at very low frequencies (f < 100 Hz) but it is not relevant since the variability of the sound absorption is null in this frequency range. This is coherent with the known effect of Λ on α curves documented in the literature 27,28 .…”

“…Detailed calculations related to the method have been omitted for conciseness and clarity. For more information, the reader is referred to the following references [15][16][17][18][25][26][27] . A global sensitivity analysis method is able to estimate the sensitivity of a model to large variations of input parameters using a variance decomposition and identify input parameters cross coupling effects.…”

“…2 to determine for each material the frequency bands where specific non-acoustic parameters are predominant because : (i) almost all non-acoustic properties are sensitive to R w and l and (ii) the two transition frequencies f v and f t are located in the frequency range of interest meaning that the viscous, thermal and inertial interactions contribute to the foam acoustical behavior. The reader who wants to better assess the frequency bands where the macroscopic non-acoustic parameters contribute the most to the sound absorption behavior could refer to the previous work of Ouisse et al 27 .…”

“…The sensitivity analysis is applied for the 4 foams and to the 2 micromacro based models. Strut dimensions and cell size are described by Gamma probability density functions identified from maximum-likelihood estimation using the large set of local measurements available on the various foam samples 27 . Concerning the reticulation rate, the low coupling effects associated to small amount of measurements and unclear physical limits of R w on the samples of interest led us to use uniform probability density functions for this variable.…”

“…II A). A deeper analysis of the impact of the choice of probability density functions, can be found in reference 27 .…”