A novel concept for the passive mitigation of forced, resonant vibrations is presented. The key to this concept is an absorption phenomenon which relies on the energy conversion from low to high frequencies by means of nonlinearity. The vibration energy of a resonantly driven substructure is transferred to an internally resonant substructure within the system. Compared with the well-known linear tuned vibration absorber (LTVA), the main advantage of the proposed concept is that no separate absorber is required, but instead the existing modal structure is properly tuned and inherent nonlinearities are utilized. Just like the former concept, however, the proposed concept is limited to a narrow frequency bandwidth, which represents its main drawback of the approach. The concept is exemplified for a system of two beams connected via a nonlinear joint with a soft, unilateral-elastic characteristic. It is demonstrated that when the system is appropriately tuned, its vibration level is reduced by 60–80%, i.e., by a factor of 2.5–5. Moreover, it is shown how the efficacy and robustness of the concept can be optimized.