Abstract
This paper is a fundamental study that theoretically estimates the acoustic properties of a simplified structural model of a sound-absorbing foam material, which is porous. This study adopts a simplified foam-structure model consisting of continuous spherical pores arranged as a simple cubic lattice. This model is termed a negative simple cubic lattice, and fundamental research was conducted to estimate its acoustic properties theoretically. An experiment was performed by 3D-printing samples and measuring the normal-incidence sound absorption coefficient using a two-microphone impedance measurement tube. In this theoretical analysis, the void region, which consists of the negative simple cubic lattice, was elementally divided perpendicular to the direction of sound incidence and modeled as a gap enclosed by two parallel planes. The calculated characteristic impedance and propagation constant were substituted into a transfer matrix for sound pressure and volume velocity based on the 1D wave equation, and the normal-incidence sound absorption coefficient was derived using the transfer matrix method. Furthermore, the theoretical values that consider Helmholtz resonance and tortuosity closely follow the trend of the experimental values. In addition, theoretical values were derived from mathematical models whose dimensions were approximated to those of an actual sound-absorbing foam material.