Toward mechanistic understanding of the relationship between the sound absorption and the natural and resonant frequencies of porous media.

In this paper, the natural and resonant frequencies of porous media are studied based on Biot's equations. The governing equations of porous media are analytically solved by using the recent developed potential function method. Based on the obtained results, the natural and resonant frequencies of the porous medium can be investigated. In this research, several foams with different acoustical and non-acoustical properties are considered and the natural and resonant frequencies are studied. In addition, for a better understanding of the natural and variation of resonant frequencies of the considered foams, various damping gains are defined and by changing them gradually, the variations of absorption coefficient and field variables are studied. The results show that the trends of absorption coefficient versus frequency for porous media can be predicted by considering the arrangement of structural and fluid natural frequencies. Also, around the structural natural frequencies two types of variations in absorption coefficient occur (i.e., maximum-minimum or maximum variations). Additionally, after computing the corresponding results of rigid frame and Biot's models it can be seen that the rigid frame theory cannot correctly predict the sound absorption coefficient in the vicinity of structural natural frequencies.