The multilayer sound absorber (MSA) is typically a composite structure that consists of a micro-perforated panel (MPP) with circular perforations, a layer of porous material, and an air gap. This combination enhances the sound absorption coefficient (SAC) across a broad frequency range. However, the sound absorption mechanisms of the MSA when incorporating polygonal cross-section perforations have not been thoroughly investigated. In this paper, the acoustic impedance of MPP with square or equilateral triangular cross-section perforations is simply given based on a complex density function and the radiation impedance in short tubes with square cross-sections. Theoretical acoustic impedance models are established for three configurations: CMSA (circular perforations), SMSA (square perforations), and EMSA (equilateral triangular perforations), using the transfer matrix method (TMM). To validate these models, SAC measurements were conducted via an impedance tube, showing good agreement with theoretical predictions. Further analysis of the acoustic performance revealed that the SMSA configuration exhibits a higher resonance peak and a broader absorption band. Finally, a simple optimization of the hole diameter and air gap was performed using an oppositional Runge Kutta optimizer with cuckoo search (OCRUN). The results demonstrate that the EMSA achieves quasi-perfect sound absorption within specific frequency bands using a smaller air gap compared to both CMSA and SMSA.
Liu et al. (2026) studied this question.