Modal Participation Estimated from the Response Correlation Matrix

Rune Brincker, Sandro D. R. Amador*, Martin Juul, Manuel Lopez-Aenelle

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review

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Abstract

In this paper, we are considering the case of estimating the moda participation vectors from the operating response of a structure. Normally, this is done using a fitting technique either in the time domain using the correlation function matrix or in the frequency domain using the spectral density matrix. In this paper, a more simple approach is proposed based on estimating the modal participation from the correlation matrix of the operating responses. For the case of general damping, it is shown how the response correlation matrix is formed by the mode shape matrix and two transformation matrices T1 and T1 that contain information about the modal parameters, the generalized modal masses, and the input load spectral density matrix Gx. For the case of real mode shapes, it is shown how the response correlation matrix can be given a simple analytical form where the corresponding real modal participation vectors can be obtained in a simple way. Finally, it is shown how the real version of the modal participation vectors can be used to synthesize empirical spectral density functions.
Original languageEnglish
Article number 9347075
JournalShock and Vibration
Volume2019
Number of pages10
ISSN1070-9622
DOIs
Publication statusPublished - 2019

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