FE model verification for structural dynamics with vector projection

Abstract

An FE model for structural dynamic analysis might have as many as three kinds of error—parameter errors, discretisation errors, and configuration errors—that make the dynamic properties of the model different from those of the actual structure. A model updating procedure cannot correct all these errors but the parameter errors of the model. If the effects of the configuration and discretisation errors in an FE model cannot be neglected in a frequency range of interest, the model updating procedure undertaken on the model will result in no improvement for the correlation of the dynamic properties between the model and the actual structure. The model verification procedure, as a part of the overall process of model validation for structural dynamics, verifies the initial FE model in order to establish whether the model can be updated or not. This paper describes a study of the FE model verification procedure. A method for making a configuration check is proposed to address the problems of configuration errors in FE models. The concept of vector projection is used in the proposed model verification method. By projecting reference eigenvectors (usually, experimental eigenvectors) onto a subspace spanned by the analytical eigenvectors from an FE model, and comparing the projections with the reference eigenvectors themselves, it is possible to establish whether or not the FE model can be updated in order to generate the same (or close) eigenvectors as the reference eigenvectors. Two case studies, one based on a simple theoretical model and the other on an industrial structure, show that the proposed method is effective at distinguishing parameter errors in an FE model (i.e. those errors which can be corrected by model updating) from discretisation and configuration errors (those which cannot be corrected by model updating).