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Shock and Vibration
Volume 2016 (2016), Article ID 2890857, 17 pages
Research Article

Fractal Model for Acoustic Absorbing of Porous Fibrous Metal Materials

1School of Mechanical Engineering and State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China
2College of Mechano-Electronic Engineering, Lanzhou University of Technology, Lanzhou 730050, China

Received 1 May 2016; Accepted 10 August 2016

Academic Editor: Yuri S. Karinski

Copyright © 2016 Weihua Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


To investigate the changing rules between sound absorbing performance and geometrical parameters of porous fibrous metal materials (PFMMs), this paper presents a fractal acoustic model by incorporating the static flow resistivity based on Biot-Allard model. Static flow resistivity is essential for an accurate assessment of the acoustic performance of the PFMM. However, it is quite difficult to evaluate the static flow resistivity from the microstructure of the PFMM because of a large number of disordered pores. In order to overcome this difficulty, we firstly established a static flow resistivity formula for the PFMM based on fractal theory. Secondly, a fractal acoustic model was derived on the basis of the static flow resistivity formula. The sound absorption coefficients calculated by the presented acoustic model were validated by the values of Biot-Allard model and experimental data. Finally, the variation of the surface acoustic impedance, the complex wave number, and the sound absorption coefficient with the fractal dimensions were discussed. The research results can reveal the relationship between sound absorption and geometrical parameters and provide a basis for improving the sound absorption capability of the PFMMs.