Eigenvalue and eigenvector derivatives of fractional vibration systems
Dynamic characterizations of fractional vibration systems have recently attracted significant research interest. Increasingly, successful applications of fractional derivatives have been found to the modeling of mechanical damping, vibration transmissions, improved fractional vibration controls and...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
2021
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| Online Access: | https://hdl.handle.net/10356/147831 |
| _version_ | 1811685852063989760 |
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| author | Lin, Rongming Ng, Teng Yong |
| author2 | School of Mechanical and Aerospace Engineering |
| author_facet | School of Mechanical and Aerospace Engineering Lin, Rongming Ng, Teng Yong |
| author_sort | Lin, Rongming |
| collection | NTU |
| description | Dynamic characterizations of fractional vibration systems have recently attracted significant research interest. Increasingly, successful applications of fractional derivatives have been found to the modeling of mechanical damping, vibration transmissions, improved fractional vibration controls and nonlinear vibration analyses. To facilitate further development, the eigenvalue problem including its derivatives, which are the central issues of vibration analysis, have to be fully established. This paper examines how eigenvalue and eigenvector derivatives of fractional systems can be derived when system matrices become functions of physical design parameters. First, new important orthonormal constraints are proposed since the modes are no longer orthonormal to the mass matrix, in this case due to its complex and frequency dependent nature. Next, new methods of eigenvector derivatives are developed for distinct eigenvalues for the cases of complete, incomplete and single mode modal data. Realistic and practical FE models incorporating fractional derivatives in the form of viscoelastic supports are employed to demonstrate the numerical accuracy and computational efficiency of the proposed methods. However, when repeated eigenvalues are considered due to structural spatial symmetries, the eigenvector space degenerates and further differentiation of system matrices are required in order to uniquely determine the eigenvector derivatives. Consequently, a new and effective general method is developed which can be applied to compute eigenvector derivatives of repeated eigenvalues with any multiplicity m. A simplified turbine bladed disk vibration model which is known to have repeated eigenvalues due to its cyclic symmetry, is then used to demonstrate the accuracy and salient features of the proposed method. |
| first_indexed | 2024-10-01T04:51:06Z |
| format | Journal Article |
| id | ntu-10356/147831 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T04:51:06Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | ntu-10356/1478312021-04-12T08:20:02Z Eigenvalue and eigenvector derivatives of fractional vibration systems Lin, Rongming Ng, Teng Yong School of Mechanical and Aerospace Engineering Engineering::Mechanical engineering Eigenvalue and Eigenvector Derivatives Fractional Vibration Systems Dynamic characterizations of fractional vibration systems have recently attracted significant research interest. Increasingly, successful applications of fractional derivatives have been found to the modeling of mechanical damping, vibration transmissions, improved fractional vibration controls and nonlinear vibration analyses. To facilitate further development, the eigenvalue problem including its derivatives, which are the central issues of vibration analysis, have to be fully established. This paper examines how eigenvalue and eigenvector derivatives of fractional systems can be derived when system matrices become functions of physical design parameters. First, new important orthonormal constraints are proposed since the modes are no longer orthonormal to the mass matrix, in this case due to its complex and frequency dependent nature. Next, new methods of eigenvector derivatives are developed for distinct eigenvalues for the cases of complete, incomplete and single mode modal data. Realistic and practical FE models incorporating fractional derivatives in the form of viscoelastic supports are employed to demonstrate the numerical accuracy and computational efficiency of the proposed methods. However, when repeated eigenvalues are considered due to structural spatial symmetries, the eigenvector space degenerates and further differentiation of system matrices are required in order to uniquely determine the eigenvector derivatives. Consequently, a new and effective general method is developed which can be applied to compute eigenvector derivatives of repeated eigenvalues with any multiplicity m. A simplified turbine bladed disk vibration model which is known to have repeated eigenvalues due to its cyclic symmetry, is then used to demonstrate the accuracy and salient features of the proposed method. 2021-04-12T08:20:02Z 2021-04-12T08:20:02Z 2019 Journal Article Lin, R. & Ng, T. Y. (2019). Eigenvalue and eigenvector derivatives of fractional vibration systems. Mechanical Systems and Signal Processing, 127, 423-440. https://dx.doi.org/10.1016/j.ymssp.2019.03.014 0888-3270 https://hdl.handle.net/10356/147831 10.1016/j.ymssp.2019.03.014 2-s2.0-85063074322 127 423 440 en Mechanical Systems and Signal Processing © 2019 Elsevier Ltd. All rights reserved. |
| spellingShingle | Engineering::Mechanical engineering Eigenvalue and Eigenvector Derivatives Fractional Vibration Systems Lin, Rongming Ng, Teng Yong Eigenvalue and eigenvector derivatives of fractional vibration systems |
| title | Eigenvalue and eigenvector derivatives of fractional vibration systems |
| title_full | Eigenvalue and eigenvector derivatives of fractional vibration systems |
| title_fullStr | Eigenvalue and eigenvector derivatives of fractional vibration systems |
| title_full_unstemmed | Eigenvalue and eigenvector derivatives of fractional vibration systems |
| title_short | Eigenvalue and eigenvector derivatives of fractional vibration systems |
| title_sort | eigenvalue and eigenvector derivatives of fractional vibration systems |
| topic | Engineering::Mechanical engineering Eigenvalue and Eigenvector Derivatives Fractional Vibration Systems |
| url | https://hdl.handle.net/10356/147831 |
| work_keys_str_mv | AT linrongming eigenvalueandeigenvectorderivativesoffractionalvibrationsystems AT ngtengyong eigenvalueandeigenvectorderivativesoffractionalvibrationsystems |