Analysis and Physical Interpretation of the Uncertainty Effect in Structural Dynamics

AbstractIn order to determine the steady-state response of random dynamical systems, the polynomial chaos expansion (PCE) approach appears to be the most suitable, but its convergence is weak around the eigenfrequencies. Indeed, increasing the order of the polynomial creates a side effect, which decreases the convergence of the expansion. Previous studies used convergence accelerating methods to reduce this side effect and the main aim of this study is to present an original approach to obtain a closed-form solution for a class of random dynamical system. The analytical developments are based on the introduction of a new class of modes called eigenmodes of perturbation and on the resolution of periodic systems. This approach gives a physical interpretation of the damping effect observed on the mean response of linear random dynamical systems by referring to the propagation of waves in a fictitious semiperiodic system associated with the eigenmodes of perturbation. The dynamic models used to expose the method are simple but the study is extended to complex structures using modal synthesis.