Soundproofing performance of flexible polyurethane foams as a fractal object

Noise pollution is one of the most severe environmental concerns due to its damaging effects on human health. This study aimed to evaluate the relationship between the acoustic damping behavior and fractal dimension (D_f) of flexible polyurethane foams (FPUFs) manufactured by different synthesized linear saturated aliphatic polyesters (LSAP) resins, methylene diphenyl diisocyanate (MDI), etc. (isocyanate index = 110 & water content = 5%). Cellular and soundproofing properties of FPUFs were evaluated by an optical microscope and impedance tube device. D_f was calculated by the box-counting method after binarization and image processing of FPUF images. Results indicate that by increasing D_f from 1.5415 to 1.8554, the total sound absorption performance (S) of FPUFs improves by 43.07% and the maximum sound absorption coefficient reaches 0.98. The relation between S and D_f was obtained as follows: Log(S) = 0.4583 D_f + 2.6659, r² = 0.9298. Generally, decreasing the cell size and increasing the cell size distribution and open-cell content, increase D_f and irregularity of FPUFs. The results reveal that FPUFs with an optimum condition of cell size of 180–200 μm, open-cell content of 30%, and density of 110 (Kg.m⁻³) have the highest D_f and can be a promising candidate as sound insulating materials.