Reduced order modeling for multi-stage bladed disks with friction contacts at the flange joint

Most aircraft turbojet engine consist of multiple stages coupled by means of bolted flange joints which potentially represent source of nonlinearities due to friction contacts. The methods aimed at predicting the forced response of a multi-stage bladed disk have to take into account such nonlinear behavior and its effect in damping the blades vibration. In this paper, a novel reduced order modeling method is proposed for studying nonlinear vibration problems of multi-stage bladed disk. The methodology exploits the shape of the single stage normal modes at the inter-stage boundary that are approximated by few spatial Fourier coefficients. Most of the Fourier coefficients refers to the dominant kinematics of the mode shapes of a cyclic symmetric structure (standard harmonics), while the others corresponds to new higher frequency phenomena detectable at the inter-stage boundary (extra harmonics). Under the hypothesis of the Single Harmonic Balance Method the relative displacement field at the inter-stage boundary can be rebuilt and the contact forces calculated by employing the classic Jenkins contact element. The method is here applied to a simple multi-stage bladed disk and its performances are tested using as a benchmark the multi-stage reduced order model obtained by the Craig-Bampton reduction of each single-stages