Structural vibration has long been a critical factor constraining the performance and service life of equipment systems, leading to mechanical component fatigue damage and precision degradation. The Acoustic Black Hole (ABH), as an innovative flexural wave manipulation technique, achieves energy dissipation by concentrating wave energy through additional damping layers. When employed as Dynamic Vibration Absorbers (DVA), ABH structures enable broadband vibration suppression without compromising primary structural integrity. However, conventional thickness power-law ABH suffers from structural strength reduction at the truncation region and only functions above a threshold frequency (where the ABH radius is comparable to the wave length). To address these limitations, this study proposes a stiffness power-law ABH-DVA. Through theoretical analysis of modal loss factors, a predictive formula for the threshold frequency of stiffness power-law ABH was established, based on which a cantilever beam system integrated with stiffness power-law ABH-DVA was designed. The reduced multibody systems transfer matrix method (RMSTMM) was employed to develop the system dynamic model and calculate the natural frequencies and steady-state responses. Comparative validation with Finite Element Method (FEM) results confirmed both the accuracy and computational efficiency of RMSTMM. Results demonstrate that the proposed stiffness power-law ABH-DVA enhances low-frequency broadband damping and dynamic vibration absorption, providing novel insights for lightweight solutions in low-frequency, broadband vibration suppression.