The acoustic modelling of fibrous materials is fundamental for the design of a sound-absorbing acoustic treatment. Several analytical formulas have been proposed to calculate the acoustic performance of materials made of fibres with a homogeneous diameter and a mono, bi, or three-dimensional distribution, while only a few studies have been carried out on materials made up of a mixture of fibres with non–homogeneous diameter. Fibrous materials for automotive applications, developed both for acoustic and thermal applications, are commonly obtained by moulding mixtures of recycled fibres of different nature, bonded together and compacted with a wide range of variability in density and thickness. The acoustic modelling of the mixtures is thus relevant for the simulation of the performance of the final component.

The main goal of the study was to determine the physical properties of a given mixture of fibres to compute its acoustic performance, based on the knowledge of the characteristic of each kind of fibre in the blend composition. A homogenisation process is proposed to determine the effective density and radius of a given mixture according to its composition and the characteristics of each kind of fibre. The normal incidence sound absorption coefficient of the investigated mixtures was computed according to the Johnson-Champoux-Allard-Lafarge (JCAL) model, by using the physical parameters, analytically computed from the effective properties of the mixture, as input data. The reliability of the approach was validated by comparing the computed results with the experimental airflow resistivity and the normal incidence sound absorption coefficient measured for five different fibre mixtures, at different compression rates.

纤维材料的声学建模是吸音声学处理设计的基础。已经提出了几个解析公式来计算由具有均匀直径和单、双或三维分布的纤维制成的材料的声学性能，而对由混合纤维制成的材料进行的研究很少具有不均匀的直径。用于汽车应用的纤维材料，为声学和热学应用而开发，通常是通过将不同性质的回收纤维的混合物模塑而成，粘合在一起并压实，密度和厚度的变化范围很广。因此，混合物的声学建模与最终组件的性能模拟相关。

该研究的主要目标是根据对混合成分中每种纤维的特性的了解，确定给定纤维混合物的物理特性，以计算其声学性能。提出了一种均化过程，以根据给定混合物的成分和每种纤维的特性来确定给定混合物的有效密度和半径。根据 Johnson-Champoux-Allard-Lafarge (JCAL) 模型，通过使用从混合物的有效特性分析计算的物理参数作为输入数据，计算所研究混合物的法向入射吸声系数。