Application of Polynomial Chaos Expansion and Model Order Reduction for Dynamic Analysis of Structures with Uncertainties

Structural uncertainties greatly influence the dynamic responses of engineering structures. This work examines the variability in the frequency responses of a simply supported plate with uncertainties in its Young's modulus and damping. The polynomial chaos expansion method is used to model the uncertainties, which transforms the stochastic system equations to a set of deterministic equations. The results obtained from the stochastic model are compared with Monte Carlo simulations. To reduce the model order, the polynomial chaos expansion method is combined with the Arnoldi-based Krylov subspace technique. By reducing the number of equations involved in the numerical model, the computational efficiency is significantly increased.