Model reduction of a cyclic symmetric structure exhibiting geometric nonlinearity with a normal form approach

Abstract

This papers deals with the computationally costly simulation of the frequency response function of geometrically nonlinear structures exhibiting cyclic symmetry. Its objective is to propose a reduction method that extends the model of a single sector reduced via the direct normal form to a full cyclically symmetric system. After validation on simple structures, the methodology is applied on a 3D meshed blade, representative component of the new generation of high bypass ratio turbofans. Based on both the proposed reduction methodology and theoretical conditions that predict the possible appearance of internal resonances as a function of the number of sectors and the engine order of the excitation, the complex nonlinear dynamics of a finely meshed full fan cyclic system is then investigated. This could not have been achieved without an appropriate reduction method. Branch switching algorithm, stability analysis, and bifurcation tracking compose the numerical tools employed along the harmonic balance method to simulate the forced response of the structure.