Discrete Equivalence Principle for Model Order Reduction of Dynamic Structures

Abstract eng:
In dynamic structural analyses, in order to improve the analyses performance, model order reduction methods are applied to mathematical models obtained by computational techniques to reduce the size of the associated problems. There are various techniques for model order reduction with different performance levels applying to complex problems. In this study, model order reduction approaches based on discrete equivalent principle are compared with some methods given in literature. Newly developed discrete equivalent model order reduction approach is based on that the response of the original and reduced order model is equal to each other at discrete time steps. In the proposed model order reduction approach, the degrees-of-freedom (DOFs) that give responses conforming with the original system are the main criteria at the selection of the DOFs which are transferred into the reduced system as the active DOFs. The developed model order reduction method was applied to create some sample structures by using some Matlab codes and the results of the model order reduction analyses are compared with the original system response. In the same Matlab codes, responses of some other model order reduction methods were also compared with the original system responses. Damping characteristics of the systems are taken into account in all these comparisons and the results of analyses with different model orders are evaluated in terms of calculation time and performance. To develop computational models, finite element methods are employed. It is observed that as the damping of the original system decreases, the accuracy of the model order reduction process decreases. In simulation studies, the inputs for the sample systems are selected to be external forces applied to some nodes. If the input force is smooth enough then the performance of model order reduction process based on discrete equivalent methods improves substantially.

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