Non-linear vibrations of multi-stage bladed disks systems with friction ring dampers

In this paper we study the non-linear dynamics of a multi-stage system of turbomachinery bladed disks with friction dampers. We focus on the quasi-periodic forced response of this system under multi-frequency rotating excitations. The system's equations of the motion are expressed in the multi-frequency domain using a multi-frequency harmonic balance method in combination a multi-stage cyclic symmetry reduction. A Dynamic Lagrangian formulation in alternating frequency/time domains is also used for the calculation of the contact and friction forces. In applications we consider a system of two HP compressor stages of integrally bladed disks with friction ring dampers.