Dynamic flow resistivity based model for sound absorption of multi-layer sintered fibrous metals

The sound absorbing performance of the sintered fibrous metallic materials is investigated by employing a dynamic flow resistivity based model, in which the porous material is modeled as randomly distributed parallel fibers specified by two basic physical parameters: fiber diameter and porosity. A self-consistent Brinkman approach is applied to the calculation of the dynamic resistivity of flow perpendicular to the cylindrical fibers. Based on the solved flow resistivity, the sound absorption of single layer fibrous material can be obtained by adopting the available empirical equations. Moreover, the recursion formulas of surface impedance are applied to the calculation of the sound absorption coefficient of multi-layer fibrous materials. Experimental measurements are conducted to validate the proposed model, with good agreement achieved between model predictions and tested data. Numerical calculations with the proposed model are subsequently performed to quantify the influences of fiber diameter, porosity and backed air gap on sound absorption of uniform (single-layer) fibrous materials. Results show that the sound absorption increases with porosity at higher frequencies but decreases with porosity at lower frequencies. The sound absorption also decreases with fiber diameter at higher frequencies but increases at lower frequencies. The sound absorption resonance is shifted to lower frequencies with air gap. For multi-layer fibrous materials, gradient distributions of both fiber diameter and porosity are introduced and their effects on sound absorption are assessed. It is found that increasing the porosity and fiber diameter variation improves sound absorption in the low frequency range. The model provides the possibility to tailor the sound absorption capability of the sintered fibrous materials by optimizing the gradient distributions of key physical parameters.