An interpolation scheme for the approximation of dynamical systems

Abstract

The demand of many industries for highly accurate predictions of the structural response of dynamical systems leads to a rapidly growing complexity of the established numerical models. Due to the thereby arising large computational efforts, the use of model reduction techniques becomes an essential task. Model reduction procedures in the context of deterministic structural analysis are already well developed and widely used, such as Guyan reduction and component mode synthesis techniques. However, the assumption of deterministically known structural properties is in most cases not realistic. Hence, the rational propagation of uncertainties becomes an indispensable task in the robust prediction of the structural response. The associated multiple simulation runs of complex models bring the topic of model reduction to the foreground of technical and scientific interest. In this work, a novel method which approximates eigenfrequencies and mode shape vectors needed for the evaluation of frequency response functions, will be presented. This meta-model of structural matrices is established by employing interpolation between the matrices evaluated at some supporting points. The technique has no difficulties with closely spaced eigenfrequencies and mode switching and it can be employed over the entire frequency range on the full model, but also on the substructures and it is hence applicable together with deterministic model reduction techniques.