Theoretical analysis for sound-absorbing materials using layered narrow clearances between two planes

We investigated the sound absorption coefficient within a sound-absorbing structure made of layered clearances between two planes. We discussed the experimental results from the existing literature and conducted a theoretical analysis on several different sound-absorbing structures that take into account the viscosity of the boundary layer at the clearances. First, we examined the case of thin sheets placed in parallel. Then, we examined the case where the size of the clearance continuously changed perpendicular to the direction of incidence of the sound waves. Subsequently, we examined the case where the clearance continuously decreased in the direction of incidence of the sound waves. In latter two cases, the transfer matrix used in the calculations was divided into elements perpendicular or coincident to the direction of incidence of the sound waves and the size of the clearance for each element was changed in a stepwise fashion. We then calculated the sound absorption coefficients for various structures and dimensions and observed that the calculated and experimental data agreed well. On the basis of the calculation simulation, the differences between the calculated and experimental absorption coefficient data were attributed mainly to the changes in the flexure of the sheet materials. The proposed calculation methods will be useful in determining the absorption coefficient of such shapes, and in the design of sound-absorbing materials that use such shapes.