Statistical moment analysis of nonlinear rotor system with multi uncertain variables

The statistical moments of the dynamical system models with uncertainties are analyzed in this paper. The analytical and numerical cases of the polynomial dimensional decomposition to solve the dynamical responses are provided. First, the polynomial dimensional decomposition method is applied to study a two-degree-of-freedom spring system model with stiffness uncertainty. Second, a linear rotor system model with eight random variables is discussed in the cases of different polynomial orders. Third, a rotor system model supported by cubically nonlinear stiffness is established by the Newton's second law. The amplitude-frequency responses of nine and twelve uncertain variables are calculated by combining the harmonic balance method and the polynomial dimensional decomposition method. The accuracy of the polynomial dimensional decomposition method is verified via comparing with the Monte Carlo Simulation method. The applications of the polynomial dimensional decomposition method in the nonlinear rotor systems can provide theoretical guidance to study complex rotor-bearing systems in the future.