Modal Participation Estimated from the Response Correlation Matrix
In this paper, we are considering the case of estimating the modal 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...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2019/9347075 |
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| _version_ | 1832554487246487552 |
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| author | Rune Brincker Sandro D. R. Amador Martin Juul Manuel Lopez-Aenelle |
| author_facet | Rune Brincker Sandro D. R. Amador Martin Juul Manuel Lopez-Aenelle |
| author_sort | Rune Brincker |
| collection | DOAJ |
| description | In this paper, we are considering the case of estimating the modal 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. |
| format | Article |
| id | doaj-art-3fad2520551f40719f6b7c489416d2c5 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-3fad2520551f40719f6b7c489416d2c52025-02-03T05:51:21ZengWileyShock and Vibration1070-96221875-92032019-01-01201910.1155/2019/93470759347075Modal Participation Estimated from the Response Correlation MatrixRune Brincker0Sandro D. R. Amador1Martin Juul2Manuel Lopez-Aenelle3Full Professor, Technical University of Denmark, Department of Civil Engineering, Brovej, Building, 118, 2800Kgs. Lyngby, DenmarkPost Doctoral Researcher, Technical University of Denmark, Department of Civil Engineering, Brovej, Building 118, 2800 Kgs. Lyngby, DenmarkAssistant Professor, Business Academy Aarhus, School of Applied Sciences, Sønderhøj 30, 8260 Viby J, DenmarkAssociate Professor, University of Oviedo, Department of Construction and Manufacturing Engineering, C/Pedro Puig Adam, s/n, 33204 Gijón, SpainIn this paper, we are considering the case of estimating the modal 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.http://dx.doi.org/10.1155/2019/9347075 |
| spellingShingle | Rune Brincker Sandro D. R. Amador Martin Juul Manuel Lopez-Aenelle Modal Participation Estimated from the Response Correlation Matrix Shock and Vibration |
| title | Modal Participation Estimated from the Response Correlation Matrix |
| title_full | Modal Participation Estimated from the Response Correlation Matrix |
| title_fullStr | Modal Participation Estimated from the Response Correlation Matrix |
| title_full_unstemmed | Modal Participation Estimated from the Response Correlation Matrix |
| title_short | Modal Participation Estimated from the Response Correlation Matrix |
| title_sort | modal participation estimated from the response correlation matrix |
| url | http://dx.doi.org/10.1155/2019/9347075 |
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