Acoustic Black Hole effect (ABH) describes a passive vibration mitigation technique used to damp out the flexural vibrations of thin structures such as beams. It relies on a wedge profile where the thickness is gradually decreasing, so that wave velocities slows down, potentially decaying to zero without reflection. The device generally shows very interesting damping properties in the mid and high-frequency range, however its efficiency in the low-frequency range still remains limited. In this contribution, the inclusion of a nonlinearity as a way to improve the low-frequency performance of an ABH is investigated. Indeed, the nonlinearity may be used as a vector to transfer energy from the low to the high frequency range, where the damping properties are much more significant. Two different mechanisms are tested, based respectively on geometric and contact nonlinearity.