Perturbation Methods for the Eigencharacteristics of Symmetric and Asymmetric Systems
Dynamic analysis for a vibratory system typically begins with an evaluation of its eigencharacteristics. However, when design changes are introduced, the eigensolutions of the system change and thus must be recomputed. In this paper, three different methods based on the eigenvalue perturbation theor...
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| Format: | Article |
| Language: | English |
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Wiley
2018-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2018/8609138 |
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| _version_ | 1832558567805157376 |
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| author | Philip D. Cha Austin Shin |
| author_facet | Philip D. Cha Austin Shin |
| author_sort | Philip D. Cha |
| collection | DOAJ |
| description | Dynamic analysis for a vibratory system typically begins with an evaluation of its eigencharacteristics. However, when design changes are introduced, the eigensolutions of the system change and thus must be recomputed. In this paper, three different methods based on the eigenvalue perturbation theory are introduced to analyze the effects of modifications without performing a potentially time-consuming and costly reanalysis. They will be referred to as the straightforward perturbation method, the incremental perturbation method, and the triple product method. In the straightforward perturbation method, the eigenvalue perturbation theory is used to formulate a first-order and a second-order approximation of the eigensolutions of symmetric and asymmetric systems. In the incremental perturbation method, the straightforward approach is extended to analyze systems with large perturbations using an iterative scheme. Finally, in the triple product method, the accuracy of the approximate eigenvalues is significantly improved by exploiting the orthogonality conditions of the perturbed eigenvectors. All three methods require only the eigensolutions of the nominal or unperturbed system, and in application, they involve simple matrix multiplications. Numerical experiments show that the proposed methods achieve accurate results for systems with and without damping and for systems with symmetric and asymmetric system matrices. |
| format | Article |
| id | doaj-art-125d5f8a96d3403faba361e8b899b29a |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-125d5f8a96d3403faba361e8b899b29a2025-02-03T01:31:58ZengWileyShock and Vibration1070-96221875-92032018-01-01201810.1155/2018/86091388609138Perturbation Methods for the Eigencharacteristics of Symmetric and Asymmetric SystemsPhilip D. Cha0Austin Shin1Department of Engineering, Harvey Mudd College, 301 Platt Blvd., Claremont, CA 91711, USADepartment of Engineering, Harvey Mudd College, 301 Platt Blvd., Claremont, CA 91711, USADynamic analysis for a vibratory system typically begins with an evaluation of its eigencharacteristics. However, when design changes are introduced, the eigensolutions of the system change and thus must be recomputed. In this paper, three different methods based on the eigenvalue perturbation theory are introduced to analyze the effects of modifications without performing a potentially time-consuming and costly reanalysis. They will be referred to as the straightforward perturbation method, the incremental perturbation method, and the triple product method. In the straightforward perturbation method, the eigenvalue perturbation theory is used to formulate a first-order and a second-order approximation of the eigensolutions of symmetric and asymmetric systems. In the incremental perturbation method, the straightforward approach is extended to analyze systems with large perturbations using an iterative scheme. Finally, in the triple product method, the accuracy of the approximate eigenvalues is significantly improved by exploiting the orthogonality conditions of the perturbed eigenvectors. All three methods require only the eigensolutions of the nominal or unperturbed system, and in application, they involve simple matrix multiplications. Numerical experiments show that the proposed methods achieve accurate results for systems with and without damping and for systems with symmetric and asymmetric system matrices.http://dx.doi.org/10.1155/2018/8609138 |
| spellingShingle | Philip D. Cha Austin Shin Perturbation Methods for the Eigencharacteristics of Symmetric and Asymmetric Systems Shock and Vibration |
| title | Perturbation Methods for the Eigencharacteristics of Symmetric and Asymmetric Systems |
| title_full | Perturbation Methods for the Eigencharacteristics of Symmetric and Asymmetric Systems |
| title_fullStr | Perturbation Methods for the Eigencharacteristics of Symmetric and Asymmetric Systems |
| title_full_unstemmed | Perturbation Methods for the Eigencharacteristics of Symmetric and Asymmetric Systems |
| title_short | Perturbation Methods for the Eigencharacteristics of Symmetric and Asymmetric Systems |
| title_sort | perturbation methods for the eigencharacteristics of symmetric and asymmetric systems |
| url | http://dx.doi.org/10.1155/2018/8609138 |
| work_keys_str_mv | AT philipdcha perturbationmethodsfortheeigencharacteristicsofsymmetricandasymmetricsystems AT austinshin perturbationmethodsfortheeigencharacteristicsofsymmetricandasymmetricsystems |