Most aircraft turbojet engines consist of multiple stages coupled by means of bolted flange joints which potentially represent source of nonlinearities due to friction phenomena. Methods aimed at predicting the forced response of multi-stage bladed disks have to take into account such nonlinear behavior and its effect in damping blades vibration. In this paper a novel reduced order model is proposed for studying nonlinear vibration due to contacts in multi-stage bladed disks. The methodology exploits the shape of the single-stage normal modes at the inter-stage boundary being mathematically described by spatial Fourier coefficients. Most of the Fourier coefficients represent the dominant kinematics in terms of the well-known nodal diameters (standard harmonics), while the others, which are detectable at the inter-stage boundary, correspond to new spatial small wavelength phenomena named as extra harmonics. The number of Fourier coefficients describing the displacement field at the inter-stage boundary only depends on the specific engine order excitation acting on the multi-stage system. This reduced set of coefficients allows the reconstruction of the physical relative displacement field at the interface between stages and, under the hypothesis of the Single Harmonic Balance Method, the evaluation of the contact forces by employing the classic Jenkins contact element. The methodology is here applied to a simple multi-stage bladed disk and its performance is tested using as a benchmark the Craig-Bampton reduced order models of each single-stage.

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