Bistable enhanced passive absorber based on integration of nonlinear energy sink with acoustic black hole beam

•A new design is provided to solve the problem of the energy dependence of NES.•The novel NES, named ABH-BNES, has great and robust damping performance at both low and large input energy.•The damping mechanism of this structure is clarified by analytical (Complexification-Averaging Method) and numerical methods (numerical integration).•A parameter optimization scheme of the structure is provided by the slow invariant manifold theory.