The Acoustic Black Hole (ABH) has been developed in recent years as an effective, passive, and lightweight method for attenuating bending wave vibrations in beams and plates. The acoustic black hole effect utilizes a local change in the plate or beam thickness to reduce the bending wave speed and increase the transverse vibration amplitude. Attaching a viscoelastic damping layer to the ABH results in effective energy dissipation and vibration reduction. Surface averaged mobility and radiated sound power measurements were performed on an aluminum plate containing an array of 20 two-dimensional ABHs with damping layers and compared to a similar uniform plate. Detailed laser vibrometer scans of an ABH cell were also performed to analyze the vibratory characteristics of the individual ABHs and compared with mode shapes calculated using Finite Elements. The diameter of the damping layer was reduced in successive steps to experimentally demonstrate the effect of damping layer distribution on the ABH performance. The experimental analysis demonstrated the importance of low order ABH modes in reducing the vibration and radiated sound power of plates with embedded ABHs. The results will be useful for designing the low frequency performance of future ABH systems and describing ABH performance in terms of design parameters.