This study presents a multiphysics dynamic model based on the Rayleigh-Ritz method for analyzing the free and forced vibrations of a rotating beam integrated with an Acoustic Black Hole (ABH) and a constrained viscoelastic layer. The thermally-coupled vibrational behavior is formulated by coupling the dissipation of mechanical energy with the evaluation of an effective operating temperature. The simultaneous effects of centrifugal stiffening and spin softening are incorporated into the equations of motion. Validation against finite element analysis (Abaqus) demonstrates high accuracy, with a maximum relative error of 0.369% for out-of-plane bending modes. Parametric sensitivity analysis and multi-objective optimization via Genetic Algorithm reveal that an ABH power profile exponent of m≈3.24yields optimal energy concentration and wave focalization. Thermal-vibrational analyses indicate that while the structure maintains overall thermal and dynamic stability across the evaluated speed range, peak damping performance is confined to a specific operational-thermal window. Furthermore, by implementing an allowable stress constraint, the risk of stress concentration at the thin ABH wedge is effectively mitigated within the model boundaries. The findings offer a computationally efficient preliminary model to predict the coupled thermo-mechanical behavior of rotating ABH beams, serving as a useful tool for initial screening in the early design stages under the defined theoretical assumptions.