Simulation et analyse d’une structure non-linéaire à symétrie cyclique

Abstract

This paper is intented to study both free and forced vibration of a nonlinear structure with cyclic symmetry, under geometric nonlinearity, through use of the harmonic balance method (HBM). In order to study the influence of nonlinearity due to the large deflection of blades, a simplified model has been developed. After adjusting the model parameters, this approach leads to a system of linearly-coupled, second-order nonlinear differential equations, in which nonlinearity appears via quadratic and cubic terms. Periodic solutions, are sought by applying HBM coupled with an arc length continuation method. In the free case, in addition to featuring similar and nonsimilar nonlinear modes, the unforced system is shown to contain localized nonlinear modes. In the forced case, several cases of excitation have been analyzed (low-engine-order excitation and detuned excitation) and we study the influence of the excitation level on the structure of dynamical response. For a sufficiently-detuned excitation, we show that several solutions can coexist, some of them being represented by closed curves in the frequency-amplitude domain.