The ABH effect for acoustic waves in fluids was first explored by [PERSON] and [PERSON] [3]. They proposed a retarding structure consisting of a tapered waveguide segment with a locally compliant metamaterial wall, where the wave speed decreases to zero as the waveguide radius diminishes. As with flexural waves, in practice, it is impossible to reduce the waveguide radius to zero, necessitating the introduction of losses to suppress wave reflection.  
Devices employing the ABH effect are typically referred to as acoustic black holes (ABHs). However, in this work, following [PERSON] and [PERSON] [4], we will distinguish between vibrational black holes (VBHs) for flexural waves and sonic black holes (SBHs) for acoustic waves in fluids. While VBHs have been relatively well studied (see, e.g., review paper [5]), SBHs have received less attention. This paper focuses solely on SBHs.  
SBHs, based on the original concept by [PERSON] and [PERSON] [3], are typically realized as a series of circular discs embedded within a waveguide. These discs feature central holes with radii that gradually decrease toward the waveguide's end, which is terminated by a rigid wall. The discs create ribs and cavities (slits) in between, functioning as a tapered compliant wall with specific acoustic admittance. The fundamental properties of SBHs have been studied both theoretically and experimentally [4; 6; 7; 8; 9; 10; 11; 12].  
Recent studies [13; 14; 15] have demonstrated that the ABH effect is not the sole mechanism responsible for acoustic energy absorption in the structure proposed by [PERSON] and [PERSON] [3]. At higher frequencies, \"local\" resonances within individual slits significantly contribute to acoustic energy absorption. Therefore, strictly speaking, these structures should not be called SBHs. Nevertheless, as this term has become established, we will continue to refer to structures inspired by [PERSON] and [PERSON]'s concept [3] as sonic black holes.  
Several applications inspired by SBHs have also been developed, including open mufflers [16; 17; 18], mufflers based on SBHs combined with micro-perforated plates [19; 20; 21], ducts with embedded periodic SBHs [22], thin SBH-inspired metamaterials [23], and acoustic pressure amplifiers [24].  
All of the aforementioned studies have focused on SBHs with axial symmetry, which are suitable for the anechoic termination of waveguides with a circular cross-section. However, in many applications, waveguides (ductwork) exhibit rectangular symmetry. For these applications, SBHs with a rectangular cross-section would be more appropriate. Recent research using an analytical model [25] has demonstrated the ABH effect in rectangular SBHs. It has been shown that, similar to axisymmetric SBHs, resonances in slits play a crucial role in acoustic energy absorption in rectangular SBHs as well [26]. The performance of rectangular SBHs with slits partially filled with porous material has also been studied [27].  
In this paper, we explore the absorption performance limits of rectangular SBHs and rectangular SBHs equipped with micro-perforated plates (MPP-SBHs) using numerical simulations. Both structures (SBHs and MPP-SBHs) are collectively referred to as sound-absorbing structures (SASs) hereafter. Through the use of a numerical model in conjunction with an optimization algorithm, we conduct an extensive parametric study to determine which geometrical parameters, including the internal profile, maximize their absorption performance. We demonstrate that these structures can serve as efficient and broadband acoustic absorbers.  
This article is a revised and expanded version of a paper [28] entitled \"Acoustic black hole combined with microperforated plate for a rectangular waveguide\", presented at Inter-Noise 2024, Nantes, France, 25-29 August 2024.