Uncertainty quantification in modal characteristics of viscoelastic damping structures by using integration approach of adaptive dimension reduction method and stochastic collocation method

The adaptive dimension reduction method is combined with a stochastic collocation method to quantitatively estimate the variability of modal characteristics in viscoelastic damping structures. For the deterministic solver, the layer-wise finite element is employed to model the viscoelastic damping structures and the shift-invert iteration method is used to solve nonlinear eigenvalue problem. In the uncertainty quantification phase, the high-dimensional model is first decomposed into several low-dimensional component models by the adaptive dimension reduction method. Then, in each component model, the stochastic collocation method (SC) is used for constructing the approximate model with minimal model evaluations. The integration approach is illustrated on two examples. It is shown that the integration approach has efficiency and accuracy advantages over Monte Carlo Simulation and SC method.