Owing to its broadband and lightweight features, the Acoustic Black Hole (ABH) effect has attracted increasing interests in the structural dynamics and vibration-acoustic communities in recent years. And damping material is essential to achieve effective ABH phenomena. To explore effective vibration and noise control in thin-walled structures such as vehicle body panel using ABH effect, aiming at the plate embedded with two-dimensional ABH array, this paper investigates the coupling between ABH structure and damping material. First, the energy dissipation mechanism of viscoelastic damping material is analyzed to obtain the deformation characteristic that leads to effective energy dissipation. Next, the bending deflection of a plate with a single ABH under harmonic excitation is investigated, and the damping material configuration is optimized to obtain an optimal vibration suppression. Finally, the above-mentioned configuration is applied to a plate embedded with the ABH array and compared with the conventional damping arranging method. And the advantages of this damping material configuration scheme in vibration and noise control are investigated and summarized. This paper provides a reference for the damping material configuration and optimization of the thin plates embedded with ABHs.