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2023 | OriginalPaper | Chapter

16. Sub-Band Decomposition Based-Linear Normal Mode Identification

Authors : Dalton Stein, He-Wen-Xuan Li, David Chelidze

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Abstract

In the past few decades, matrix decomposition methods have been explored as suitable Operational Modal Analysis algorithms. For a given vibratory mechanical system, one looks for its coherent spatial–temporal structures through the assumption of separation of variables. In practical situations, this separation of variables is done by decomposing a sampled scalar field that contains the underlying continuous field of the structure in time. In mechanical vibrations, this sampled scalar field is usually a trajectory matrix, $$X \in \mathbb {R}^{n \times m}$$, that is composed of n displacement, velocity, or acceleration observations at m distinct spatial points on a structure. Methods such as the Proper Orthogonal Decomposition (POD) and the Smooth Orthogonal Decomposition (SOD) have been used to decompose the trajectory matrix into its modal coordinates and modal matrix. In real-world scenarios, there are practical limitations to these algorithms. First, for the case of POD, the free-response sample covariance matrix must be scaled by the mass matrix to identify the true LNMs of the structure. For complicated structures with nonuniform mass distribution, this is problematic.
Literature
1.
Han, S., Feeny, B.: Application of proper orthogonal decomposition to structural vibration analysis. Mech. Syst. Signal Process. 17, 989–1001 (2003) CrossRef
2.
Kim, B.H., Stubbs, N., Park, T.: A new method to extract modal parameters using output-only responses. J. Sound Vibr. 282, 215–230 (2005) CrossRef
3.
Chelidze, D., Zhou, W.: Smooth orthogonal decomposition based vibration mode identification. J. Sound Vibr. 292, 461–473 (2006) CrossRef