The use of integrally blisk is becoming popular because of the advantages in aerodynamic efficiency and mass reduction. However, in an integrally blisk, the lack of the contact interface leads to a low structural damping compared to an assembled bladed-disk. One emerging damping technique for the integrally blisk is based on the use of friction ring damper which exploits the contact interfaces at the underneath of the disk. In this paper, three different geometries of the ring dampers are investigated for damping enhancement of a blisk. A full-scale compressor blisk is considered as a case study where a node to node contact model is used to compute the contact forces. The dynamic behaviour of the blisk with the ring damper is investigated by using nonlinear modal analysis which allows a direct estimation of the damping generated by the friction interface. The damping performance for the different ring dampers are evaluated and compared. It appears that the damping efficiency as well as the shift in the resonant frequency for the different geometries are highly related to the nodal diameter and contact pressure/gap distributed within contact interface. The geometry of the ring damper has significant impact on the damping performance.