The concept of an Acoustic Black Hole (ABH) has been developed and exploited as an approach for passively attenuating structural vibration. The basic principle of the ABH relies on proper tailoring of the structure geometrical properties in order to produce a gradual reduction of the flexural wave speed, theoretically approaching zero. For practical systems the idealized "zero" wave speed condition cannot be achieved so the structural areas of low wave speed are treated with surface damping layers to allow the ABH to approach the idealized dissipation level. In this work, an investigation was conducted to assess the effects that distributions of ABHs embedded in plate-like structures have on both vibration and structure radiated sound, focusing on characterizing and improving low frequency performance. Finite Element and Boundary Element models were used to assess the vibration response and radiated sound power performance of several plate configurations, comparing baseline uniform plates with embedded periodic ABH designs. The computed modal loss factors showed the importance of the ABH unit cell low order modes in the overall vibration reduction effectiveness of the embedded ABH plates at low frequencies where the free plate bending wavelengths are longer than the scale of the ABH.