A state-of-the-art review on theory and engineering applications of eigenvalue and eigenvector derivatives
Eigenvalue and eigenvector derivatives with respect to system design variables and their applications have been and continue to be one of the core issues in the design, control and identification of practical engineering systems. Many different numerical methods have been developed to compute accura...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://hdl.handle.net/10356/161600 |
| _version_ | 1826128007786397696 |
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| author | Lin, Rongming Mottershead, J. E. Ng, Teng Yong |
| author2 | School of Mechanical and Aerospace Engineering |
| author_facet | School of Mechanical and Aerospace Engineering Lin, Rongming Mottershead, J. E. Ng, Teng Yong |
| author_sort | Lin, Rongming |
| collection | NTU |
| description | Eigenvalue and eigenvector derivatives with respect to system design variables and their applications have been and continue to be one of the core issues in the design, control and identification of practical engineering systems. Many different numerical methods have been developed to compute accurately and efficiently these required derivatives from which, a wide range of successful applications have been established. This paper reviews and examines these methods of computing eigenderivatives for undamped, viscously damped, nonviscously damped, fractional and nonlinear vibration systems, as well as defective systems, for both distinct and repeated eigenvalues. The underlying mathematical relationships among these methods are discussed, together with new theoretical developments. Major important applications of eigenderivatives to finite element model updating, structural design and modification prediction, performance optimization of structures and systems, optimal control system design, damage detection and fault diagnosis, as well as turbine bladed disk vibrations are examined. Existing difficulties are identified and measures are proposed to rectify them. Various examples are given to demonstrate the key theoretical concepts and major practical applications of concern. Potential further research challenges are identified with the purpose of concentrating future research effort in the most fruitful directions. |
| first_indexed | 2024-10-01T07:17:50Z |
| format | Journal Article |
| id | ntu-10356/161600 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T07:17:50Z |
| publishDate | 2022 |
| record_format | dspace |
| spelling | ntu-10356/1616002022-09-09T06:39:53Z A state-of-the-art review on theory and engineering applications of eigenvalue and eigenvector derivatives Lin, Rongming Mottershead, J. E. Ng, Teng Yong School of Mechanical and Aerospace Engineering Engineering::Mechanical engineering Review Eigenvalues Eigenvalue and eigenvector derivatives with respect to system design variables and their applications have been and continue to be one of the core issues in the design, control and identification of practical engineering systems. Many different numerical methods have been developed to compute accurately and efficiently these required derivatives from which, a wide range of successful applications have been established. This paper reviews and examines these methods of computing eigenderivatives for undamped, viscously damped, nonviscously damped, fractional and nonlinear vibration systems, as well as defective systems, for both distinct and repeated eigenvalues. The underlying mathematical relationships among these methods are discussed, together with new theoretical developments. Major important applications of eigenderivatives to finite element model updating, structural design and modification prediction, performance optimization of structures and systems, optimal control system design, damage detection and fault diagnosis, as well as turbine bladed disk vibrations are examined. Existing difficulties are identified and measures are proposed to rectify them. Various examples are given to demonstrate the key theoretical concepts and major practical applications of concern. Potential further research challenges are identified with the purpose of concentrating future research effort in the most fruitful directions. Ministry of Education (MOE) The first and third authors gratefully acknowledge the financial support from the Singapore Ministry of Education through the award of research project grant AcRF Tier 1 RG183/17. 2022-09-09T06:39:53Z 2022-09-09T06:39:53Z 2020 Journal Article Lin, R., Mottershead, J. E. & Ng, T. Y. (2020). A state-of-the-art review on theory and engineering applications of eigenvalue and eigenvector derivatives. Mechanical Systems and Signal Processing, 138, 106536-. https://dx.doi.org/10.1016/j.ymssp.2019.106536 0888-3270 https://hdl.handle.net/10356/161600 10.1016/j.ymssp.2019.106536 2-s2.0-85075973442 138 106536 en RG183/17 Mechanical Systems and Signal Processing © 2019 Elsevier Ltd. All rights reserved. |
| spellingShingle | Engineering::Mechanical engineering Review Eigenvalues Lin, Rongming Mottershead, J. E. Ng, Teng Yong A state-of-the-art review on theory and engineering applications of eigenvalue and eigenvector derivatives |
| title | A state-of-the-art review on theory and engineering applications of eigenvalue and eigenvector derivatives |
| title_full | A state-of-the-art review on theory and engineering applications of eigenvalue and eigenvector derivatives |
| title_fullStr | A state-of-the-art review on theory and engineering applications of eigenvalue and eigenvector derivatives |
| title_full_unstemmed | A state-of-the-art review on theory and engineering applications of eigenvalue and eigenvector derivatives |
| title_short | A state-of-the-art review on theory and engineering applications of eigenvalue and eigenvector derivatives |
| title_sort | state of the art review on theory and engineering applications of eigenvalue and eigenvector derivatives |
| topic | Engineering::Mechanical engineering Review Eigenvalues |
| url | https://hdl.handle.net/10356/161600 |
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