An Exact Method for Calculating the Eigenvector Sensitivities
Eigenvector sensitivities are often used in many engineering problems such as structural vibration control, optimization design, model updating and damage identification. So far, modal superposition method and Nelson’s method are the two main methods for exactly calculating eigenvector sensitivities...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-04-01
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| Series: | Applied Sciences |
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| Online Access: | https://www.mdpi.com/2076-3417/10/7/2577 |
| _version_ | 1797571139365502976 |
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| author | Qiuwei Yang Xi Peng |
| author_facet | Qiuwei Yang Xi Peng |
| author_sort | Qiuwei Yang |
| collection | DOAJ |
| description | Eigenvector sensitivities are often used in many engineering problems such as structural vibration control, optimization design, model updating and damage identification. So far, modal superposition method and Nelson’s method are the two main methods for exactly calculating eigenvector sensitivities. However, modal superposition method has a great limitation in applications because it needs all the eigenvectors in its calculation. Although Nelson’s method does not need to use all the eigenvectors, there is no unified sensitivity calculation formula for each eigenvector. In this paper, a new exact method for calculating the eigenvector sensitivity is proposed. The explicit expressions for the first-order and second-order sensitivities of eigenvectors are derived, and strict proof is given. The developed eigenvector sensitivity formulas are simple and convenient in programming. The proposed method is as powerful as Nelson’s method, but much more easy to use. Two numerical examples are used to demonstrate the proposed method and the results show that the developed eigenvector sensitivity formulas are exact and reliable. |
| first_indexed | 2024-03-10T20:35:17Z |
| format | Article |
| id | doaj.art-987b23b8da1242b1877088b11533d571 |
| institution | Directory Open Access Journal |
| issn | 2076-3417 |
| language | English |
| last_indexed | 2024-03-10T20:35:17Z |
| publishDate | 2020-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Applied Sciences |
| spelling | doaj.art-987b23b8da1242b1877088b11533d5712023-11-19T21:06:14ZengMDPI AGApplied Sciences2076-34172020-04-01107257710.3390/app10072577An Exact Method for Calculating the Eigenvector SensitivitiesQiuwei Yang0Xi Peng1School of Civil and Transportation Engineering, Ningbo University of Technology, Ningbo 315211, ChinaSchool of Civil and Transportation Engineering, Ningbo University of Technology, Ningbo 315211, ChinaEigenvector sensitivities are often used in many engineering problems such as structural vibration control, optimization design, model updating and damage identification. So far, modal superposition method and Nelson’s method are the two main methods for exactly calculating eigenvector sensitivities. However, modal superposition method has a great limitation in applications because it needs all the eigenvectors in its calculation. Although Nelson’s method does not need to use all the eigenvectors, there is no unified sensitivity calculation formula for each eigenvector. In this paper, a new exact method for calculating the eigenvector sensitivity is proposed. The explicit expressions for the first-order and second-order sensitivities of eigenvectors are derived, and strict proof is given. The developed eigenvector sensitivity formulas are simple and convenient in programming. The proposed method is as powerful as Nelson’s method, but much more easy to use. Two numerical examples are used to demonstrate the proposed method and the results show that the developed eigenvector sensitivity formulas are exact and reliable.https://www.mdpi.com/2076-3417/10/7/2577eigenvectorsensitivitymodal superposition methodNelson’s method |
| spellingShingle | Qiuwei Yang Xi Peng An Exact Method for Calculating the Eigenvector Sensitivities Applied Sciences eigenvector sensitivity modal superposition method Nelson’s method |
| title | An Exact Method for Calculating the Eigenvector Sensitivities |
| title_full | An Exact Method for Calculating the Eigenvector Sensitivities |
| title_fullStr | An Exact Method for Calculating the Eigenvector Sensitivities |
| title_full_unstemmed | An Exact Method for Calculating the Eigenvector Sensitivities |
| title_short | An Exact Method for Calculating the Eigenvector Sensitivities |
| title_sort | exact method for calculating the eigenvector sensitivities |
| topic | eigenvector sensitivity modal superposition method Nelson’s method |
| url | https://www.mdpi.com/2076-3417/10/7/2577 |
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