Mathematical modeling and experiments on the acoustic properties of a frame structure with a membrane

This study is a fundamental work conducted to theoretically estimate the acoustic properties of a simplified frame structure, that is, a simplified foam sound absorbing material, which is a porous material. The changes in the sound absorption characteristics caused by the presence of a membrane are also considered as part of the fundamental study of foam materials. In the mathematical model, the clearance composed by the frame structure with the membrane is divided into elements perpendicular to the direction of the soundwave incidence and approximated as a clearance bounded by two parallel planes. The characteristic impedance and the propagation constant are obtained for the approximated clearance and introduced into a one-dimensional transfer matrix. The transfer matrix method is used to calculate the sound absorption coefficient. The calculated theoretical values are compared with the experimental values. Sensitivity analysis is also performed for the changes in the parameters used in the theoretical analysis, such as the cylinder diameter and the pitch between the cylinders. The samples are fabricated using a three-dimensional printer. The sound absorption coefficient is measured using a two-microphone impedance measurement tube. The theoretical values based on the analysis tended to be close to the experimental ones. They showed a high prediction accuracy with respect to the peak frequency of the sound absorption curve. These values for the presence and increase of the membrane closely followed the experimental values when the percentage of the membrane present was varied.