The acoustic black hole (ABH) structures have the potential to achieve structural vibration suppression and noise reduction through the effect of the ABH on the concentration and manipulation of flexural waves. In this paper, a new solution is proposed to embed 2-D ABHs on the support plate to suppress the transmission of compressor vibration to the refrigerator body. The vibration and acoustic measurement experiment of the compressor, the support plate and the refrigerator body, and the coherence analysis of the vibration signals and acoustic signal are carried out to determine the influence of the compressor vibration on the vibration of the refrigerator body and the radiation sound of the back wall. The concentration and manipulation effects of 2-D ABH on flexural waves are verified by numerical simulation of flexural wave propagation in the time domain. FEM models of the original support plate and the damping ABH support plate are established to investigate the comprehensive effect of the 2-D ABHs and the damping layers on the vibration characteristics of the support plate through vibration modal and dynamic response analysis. Numerical simulation results show that the 2-D damping ABHs can suppress the vibrations generated by the compressor at specific frequencies in the middle and high-frequency bands from being transmitted to the refrigerator body through the support plate.