Application of the polynomial dimensional decomposition method in a class of random dynamical systems

The polynomial dimensional decomposition (PDD) method is applied to study the amplitude-frequency response behaviors of dynamical system model in this paper. The first two order moments of the steady-state response of a dynamical random system are determined via PDD and Monte Carlo simulation (MCS) method that provides the reference solution. The amplitude-frequency behaviors of the approximately exact solution obtained by MCS method can be retained by PDD method except the interval close to the resonant frequency, where the perturbations may occur. First, the results are shown on the two degrees of freedom (DOFs) spring system with uncertainties; the dynamic behaviors of the uncertainties for mass, damping, stiffness and hybrid cases are respectively studied. The effects of PDD order to amplitude-frequency behaviors are also discussed. Second, a simple rotor system model with four random variables is studied to further verify the accuracy of the PDD method. The results obtained in this paper show that the PDD method is accurate and efficient in the dynamical model, providing the theoretical guidance to complexly nonlinear rotor dynamics models.