Mathematical Model for Estimating the Sound Absorption Coefficient in Grid Network Structures

Abstract

Although grid network structures are often not necessarily intended to absorb sound, the gaps between the rods that make up the grid network are expected to have a sound absorption effect. In this study, the one-dimensional transfer matrix method was used to develop a simple mathematical model for accurately estimating the sound absorption coefficient of a grid network structure. The gaps in the grid network structure were approximated as the clearance between two parallel planes, and analysis units were derived to consider the exact geometry of the layers. The characteristic impedance and propagation constant were determined for the approximated gaps and treated as a one-dimensional transfer matrix. The transfer matrix obtained for each layer was used to calculate the sound absorption coefficient. The samples were fabricated from light-curing resin by using a Form2 3D printer from Formlabs. The measurement results showed that a sound absorption coefficient of 0.81 was obtained at the peak when seven layers were stacked. A sensitivity analysis was carried out to investigate the influence of the rod diameter and pitch. The simulated values tended to be close to the experimental values. The above results indicate that the mathematical model used to calculate the sound absorption coefficient is sufficiently accurate to predict the sound absorption coefficient for practical application.