The slow-flow method of identification in nonlinear structural dynamics

G. Kerschen; A. F. Vakakis; Y. S. Lee; D. M. McFarland; L. A. Bergman

doi:10.1117/12.716823

10 April 2007 The slow-flow method of identification in nonlinear structural dynamics

G. Kerschen, A. F. Vakakis, Y. S. Lee, D. M. McFarland, L. A. Bergman

Proceedings Volume 6529, Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2007; 65291M (2007) https://doi.org/10.1117/12.716823
Event: SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring, 2007, San Diego, California, United States

Abstract

The Hilbert-Huang transform (HHT) has been shown to be effective for characterizing a wide range of nonstationary signals in terms of elemental components through what has been called the empirical mode decomposition. The HHT has been utilized extensively despite the absence of a serious analytical foundation, as it provides a concise basis for the analysis of strongly nonlinear systems. In this paper, we attempt to provide the missing link, showing the relationship between the EMD and the slow-flow equations of the system. The slow-flow model is established by performing a partition between slow and fast dynamics using the complexification-averaging technique, and a dynamical system described by slowly-varying amplitudes and phases is obtained. These variables can also be extracted directly from the experimental measurements using the Hilbert transform coupled with the EMD. The comparison between the experimental and analytical results forms the basis of a nonlinear system identification method, termed the slow-flow model identification method, which is demonstrated using numerical examples.

Citation Download Citation

G. Kerschen, A. F. Vakakis, Y. S. Lee, D. M. McFarland, and L. A. Bergman "The slow-flow method of identification in nonlinear structural dynamics", Proc. SPIE 6529, Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2007, 65291M (10 April 2007); https://doi.org/10.1117/12.716823

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