Many rooms struggle with the absorption of low-frequency sound due to its long wavelengths. The integration of existing solutions into these spaces is often challenging due to their intricate installations and large depths. To address this problem, a new type of resonance absorber has been developed: the Distributed Mode Absorber (DMA). It consists of a thin vibrating front panel and a volume of enclosed air behind it. This straightforward structure can be utilized to create acoustically functional furniture that can be seamlessly incorporated into rooms. This article is devoted to the structural optimization of the DMA front panel, using the Acoustic Black Hole (ABH) effect known within structural dynamics. A numerical model is constructed using a Finite Element Analysis (FEA) and examined numerically. Several geometric parameters of the ABH are studied with regard to their influence on the vibrations of the front panel. Prototypes are developed and manufactured based on these insights. The quality of the numerical model is verified during the subsequent validation. Finally, the sound absorption of the improved DMA is compared with that of the reference DMA.