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Shock and Vibration
Volume 15, Issue 3-4, Pages 435-445

Measurement of FRFs and Modal Identification in Case of Correlated Multi-Point Excitation

U. Fuellekrug, M. Boeswald, D. Goege, and Y. Govers

Institute of Aeroelasticity, German Aerospace Center, DLR Goettingen, Bunsenstrasse 10, 37073 Goettingen, Germany

Received 29 April 2007; Revised 29 April 2007

Copyright © 2008 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The modal identification of large and dynamically complex structures often requires a multi-point excitation. Sine sweep excitation runs are applied when it is necessary to concentrate more energy on each line of the frequency spectrum. The conventional estimation of FRFs from multi-point excitation requires uncorrelated excitation signals. In case of multi-point (correlated) sine sweep excitation, several sweep runs with altered excitation force patterns have to be performed to estimate the FRFs. An alternative way, which offers several advantages, is to process each sine sweep run separately. The paper first describes the conventional method for FRF estimation in case of multi-point excitation, followed by two alternative methods applicable in case of correlated excitation signals. Both methods generate a virtual single-point excitation from a single run with multi-point excitation. In the first method, an arbitrary structural point is defined as a virtual driving point. This approach requires a correction of the modal masses obtained from modal analysis. The second method utilizes the equality of complex power to generate virtual FRFs along with a single virtual driving point. The computation of FRFs and the modal identification using virtual single-point excitation are explained. It is shown that the correct set of modal parameters can be identified. The application of the methods is elucidated by an illustrative analytical example. It could be shown that the separate evaluation of symmetric and anti-symmetric multi-point excitation runs yield obviously better and more reliable results compared to the conventional method. In addition, the modal analysis of the separate symmetric and anti-symmetric excitation runs is easier, since the stabilization diagrams are easier to interpret. The described methods were successfully applied during the Ground Vibration Tests on Airbus A380 and delivered excellent results. The methods are highly advantageous and may thus be established as a new standard procedure for testing aerospace structures.