A Local Correspondence Principle for Mode Shapes in Structural Dynamics

It is well known that the correlation between experimental and finite element (FE) mode shapes is often relatively low, even for detailed models. The classical way of dealing with this problem is to perform an updating of the FE model to enhance the correlation between the two sets of mode shapes. However this is resource consuming and does not always lead to high quality results. This paper presents a simple way of modeling the experimental modes shapes as a linear combination of the FE mode shapes only including the mode shapes around (in terms of frequency) the corresponding FE mode shape, thus this principle is denoted “local correspondence” (LC). The principle is introduced based on the classical theory of eigenvector derivatives presented by Nelson and further developed by Heylen et al. A criterion is developed for determining the optimal number of modes to be included, and the principle is tested on a simple plate example. The example shows a clear improvement of the correlation between the modeled and the experimental mode shape. The LC principle can be used for accurate expansion of experimental mode shapes and response measurements to all degrees of freedom in the considered FE model, to quantify physical differences between the theoretical model and experiment and to scale experimental mode shapes using the FE model mass matrix.