正交多项式在不确定转子动态响应计算中的应用及对比分析

In order to quantify the influence of interval uncertainties on the dynamic response of a rotor system, a non-intrusive interval analysis procedure was proposed using orthogonal polynomials, so the strict requirements of probabilistic distribution in stochastic methods were met. The deterministic model and equations of motion were established via the finite element method. The surrogate models of the uncertain response were derived by using Chebyshev polynomials and Legendre polynomials and the general solution procedure was illustrated. The classic Monte Carlo simulation was used to demonstrate the accuracy and efficiency of the two series based interval methods. Compared with the results of Monte Carlo simulation with 500 samples, the errors in the interval methods were less than 1% and the computing time were 2.5% and 5.4%, respectively. In the problem under study, the Chebyshev polynomials based method was more efficient. Then the dynamic response curves of the rotor under different uncertain parameters with different uncertain degrees were given. The results show that the orthogonal polynomials can be successfully applied to uncertain rotordynamics with high efficiency and accuracy. Uncertainty has significant effects on the dynamics of the rotor system and multiple uncertainties propagation may lead to heavy vibration.