Model Reduction and Uncertainties in Structural Dynamics

Model reduction procedures for the purpose of reducing computational efforts in structural analysis are already well developed and widely used to compute the dynamic response of complex structural systems. For example the Guyan reduction might essentially reduce the size of the structural matrices, while component mode synthesis provides a means to consider first simpler substructures and to use its modal properties for deriving a reduced global structural model for computing the dynamic response. Moreover, component mode synthesis allows for an assembly of large finite element models consisting of substructures established by different working groups and hence has significant advantages in the design cycle. The above mentioned, frequently used finite element (FE) reduction procedures assume perfect, i.e. deterministic knowledge of all structural properties. However, the assumption of deterministically known structural properties is in most practical, real world cases, not realistic. Many items (e.g. stiffness, mass and damping parameters, etc.) incorporated in the mathematical FE model of a structure are uncertain, i.e. are either not precisely known or might reveal unpredictable random behavior. This paper will give an overview of the well established deterministic reduction techniques and approaches for the efficient uncertainty propagation. Finally, the recent advances in the combination of these two fields are reviewed and methodologies for the consideration of uncertainty when using model reduction schemes are presented. The model reduction schemes considering uncertainties, which usually involve some simplifying assumptions, similar to their deterministic counterparts, are compared with the reference solution as obtained by direct Monte Carlo simulation (MCS), where the deterministic FE reduction scheme is applied together with randomly generated structural properties.