Modeling of sound absorption based on the fractal microstructures of porous fibrous metals

Abstract

A fractal micro-structural acoustic model for sound absorption of sintered fibrous metals was established by adopting the fractal geometric theory. Based on the pore area fractal dimension and the tortuosity fractal dimension, the dynamic airflow resistivity and the sound absorption coefficient were calculated. The pore area fractal dimension is related to the number of the micro-pores of sintered fibrous metals, and the tortuosity fractal dimension describes the sinuosity of sound propagation pathway. The two fractal dimensions were determined by the theoretical calculations as well as the box-counting method. The fractal acoustic model was verified by comparing the specific surface acoustic impedance and the sound absorption coefficient with experimental measurements, with good agreements achieved. The results were also compared with those of Biot-Allard model, which demonstrates that the calculated values of the fractal acoustic model fit the tested data better than Biot-Allard model in high frequency range. In addition, the influences of the fractal dimensions on the specific surface acoustic impedance and the effect of thickness and fractal dimension on the sound absorption coefficient were presented and discussed. Results indicate that the acoustic performance of sintered fibrous metals are significantly affected by the fractal dimensions.