Stochastic non-linear response of a flexible rotor with local non-linearities

Abstract

The effects of uncertainties on the non-linear dynamics response remain misunderstood and most of the classical stochastic methods used in the linear case fail to deal with a non-linear problem. So we propose to take into account of uncertainties into non-linear models, by coupling the Harmonic Balance Method (HBM) and the Polynomial Chaos Expansion (PCE). The proposed method called the Stochastic Harmonic Balance Method (Stochastic-HBM) is based on a new formulation of the non-linear dynamic problem in which not only the approximated non-linear responses but also the non-linear forces and the excitation pulsation are considered as stochastic parameters. Expansions on the PCE basis are performed by passing via an Alternate Frequency Time method with Probabilistic Collocation (AFTPC) for estimating the stochastic non-linear forces in the stochastic domain and the frequency domain. In the present paper, the Stochastic Harmonic Balance Method (Stochastic-HBM) that is applied to a flexible non-linear rotor system, with random parameters modeled as random fields, is presented. The Stochastic-HBM combined with an Alternate Frequency-Time method with Probabilistic Collocation (AFTPC) allows us to solve dynamical problems with non-regular non-linearities in presence of uncertainties. In this study, the procedure is developed for the estimation of stochastic non-linear responses of the rotor system with different regular and non-regular non-linearities. The finite element rotor system is composed of a shaft with two disks and two flexible bearing supports where the non-linearities are due to a radial clearance or a cubic stiffness. A numerical analysis is performed to analyze the effect of uncertainties on the non-linear behavior of this rotor system by using the Stochastic-HBM. Furthermore, the results are compared with those obtained by applying a classical Monte-Carlo simulation to demonstrate the efficiency of the proposed methodology.