# Improving Low-Frequency Panel Absorbers with Two-Dimensional Acoustic Black Hole
## 1 Introduction  
Appropriate room acoustics has increased in importance in daily life. A suitable reverberation time must be ensured for speech intelligibility or the appropriate sound reinforcement of the room. Recommended reverberation times are defined in standards such as DIN 18041 [1]. These reverberation times can be adjusted by treating rooms with various absorbers, e.g., porous or resonant absorbers [2]. In addition, combinations of porous and resonant absorbers can also be used for improving transmission loss for noise suppression [3]. Low-frequency sound poses unique challenges when it comes to noise control and acoustic treatment. Unlike higher frequencies, low-frequency sound waves possess longer wavelengths and greater energy, making them more difficult to effectively absorb and attenuate. This leads, for porous materials, to a requirement for very thick absorbing structures which is not practical for many applications. To overcome this issue, the commonly preferred absorber types for low-frequency sound absorption are resonant absorbers. Specifically, panel absorbers are a possibility to achieve low-frequency absorption, while keeping the installation space low. To work efficiently, panel absorbers usually need to have a significant surface area to achieve low-frequency sound absorption [4]. Its principle is based on using resonant frequencies of the vibrating membrane or panel for dissipating the incident sound energy [5]. For this reason, resonance absorbers are effective at a narrow frequency bandwidth in the vicinity of small numbers of modes (mostly, first mode). To further improve panel absorbers, its possible to make use of the multimodal structural vibrations a panel shows under pressure excitation. Concepts for this kind of absorber have been studied for several years, such as VPRs (Verbund Platten Resonators) [4]and DMAs (Distributed Mode Absorbers) [6; 7; 8; 9]. It has been shown theoretically [4] and practically [9] that increasing the number of excitable modes leads to an increase in the sound absorption. This study is devoted to the inclusion of Acoustic Black Holes to panel absorbers for improving the low-frequency sound absorption performance. The Acoustic Black Hole (ABH) is a moderately recent phenomenon to control the vibrational behavior of plates and beams. It is based on the theoretical findings of [PERSON] [10]. When structure-borne sound is propagating in a flexural wave, a power-law-shaped profile (wedges) improves the damping behaviour significantly. The waves are entering the indentation, and successively slow down due to decreasing material thickness. For an infinitesimally thin material, this ultimately results in a fully absorptive system. However, there always needs to be a truncation in practice. The use of thin damping layers on this wedge has been suggested to increase the effectiveness of ABH designs for damping flexural vibrations [11; 12]. It is also possible to extend the power-law profile to generate two-dimensional tapered indentations, which are also referred to as 2D ABH in circular [13; 14] or elliptical forms [15]. Coupled systems consisting of ABH embedded panels and air back cavities have recently been studied numerically and experimentally [16; 17; 18]. ABH has been successfully applied for vibration and noise reduction in structures [19; 20]. ABH can be designed to perform better for selected frequency ranges. Local ABH modes have been found to be dominant in the low-frequency performance of absorption in the structural response [21; 22; 23]. Below the first mode of ABH, the structural response has been claimed to be similar to a plate of uniform thickness, and thus, the first mode of ABH is considered to be the cut-on frequency [19; 24; 25]. At higher frequencies, the effectiveness of ABH increases due to the increase in the modal density and overlaps [21]. In order to tune the cut-on frequency, adjusting the size of the Acoustic Black Hole is the basic design option.