In this paper, we develop a planar curved Acoustic Black Hole (ABH) absorber by modifying the baseline of a straight slender tapered beam into a curvilinear one. The curved ABH, in a compact planar configuration, generates beneficial dynamic properties, which allow it to work as a broadband omnidirectional vibration-suppressing device when added onto a primary structure. Analyses demonstrate that, apart from the widely studied bending wave retarding phenomena, the celerity of torsional waves inside the curved ABH with a rectangular cross section also decreases with the thickness thinning. Owing to the combined wave compression effects and the bending-twisting coupling in the curved ABH beams, the proposed design is less orientation-dependent in terms of dynamics and energy absorption. As a result, the curvilinear ABH tailoring brings along enriched dynamics and enhanced energy trapping and dissipation, thus outperforming the conventional uniform beam and giving rise to the development of a more workable and attractive option for vibration control. Experimental studies also show that the deployment of multiple ABH absorbers can entail effective and robust vibration reduction of a general plate structure. The dual vibration reduction mechanisms, i.e. structural interaction and damping enhancement, are fully played out by the curvilinear ABH design.