Collocation-based Stochastic Modeling of Uncertain Geometric Mistuning in Bladed Rotor

Abstract

In this paper, a collocation–based stochastic model is proposed to analysis mistuned bladed–rotors with geometrical parameter uncertainties. The uncertain parameters are approximated by the Karhunen-Loe‘ve expansion with predefined correlation functions. The generalized polynomial chaos (gPC) expansion possessing random orthogonal basis is served as uncertain dynamic responses. A set of collocation points are generated from the roots of higher order random polynomial basis and the whole FEM model of the rotor is executed on each point to estimate the dynamic responses. These estimations then are used to calculate the coefficients of the gPC expansions. The most attractive feature of the method is that only multiple solutions of the original deterministic FEM model of the rotor are required. A numerical case study is presented in which the geometrical parameters of a blisk are considered as uncertain parameters with spatial variation. The probability distributions of the random natural frequencies are evaluated for rotational and non-rotational blisk. The results show high accuracy compared to the Monte Carlo simulations with 500 realizations. The impact of the parameter uncertainty on the Campbell diagram during the start up and start down are presented.