On the Dynamic Analysis of a Beam Carrying Multiple Mass-Spring-Mass-Damper System
The exact natural frequencies, mode shapes, and the corresponding orthogonality relations are important in forced vibration analysis via modal expansion. In the present paper, a free vibration analysis is conducted to determine the exact natural frequencies and mode shapes of an axially loaded beam...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2014/485630 |
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| _version_ | 1832566238829608960 |
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| author | O. Barry D. C. D. Oguamanam J. W. Zu |
| author_facet | O. Barry D. C. D. Oguamanam J. W. Zu |
| author_sort | O. Barry |
| collection | DOAJ |
| description | The exact natural frequencies, mode shapes, and the corresponding orthogonality relations are important in forced vibration analysis via modal expansion. In the present paper, a free vibration analysis is conducted to determine the exact natural frequencies and mode shapes of an axially loaded beam carrying several absorbers. An explicit expression is presented for the generalized orthogonality relations. These generalized orthogonality conditions are employed along with the assumed modes method to perform forced vibration analysis. The present approach is compared to other approximate methods in the literature with the classical orthogonality relations and different choice of mode shapes. The results indicate that the use of the generalized orthogonality relation with the exact mode shapes is required for a precise investigation of the dynamic response of a beam with mass-spring-mass-damper system. |
| format | Article |
| id | doaj-art-e6fee42a29d44d12ac5a86992422cd54 |
| institution | Kabale University |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-e6fee42a29d44d12ac5a86992422cd542025-02-03T01:04:43ZengWileyShock and Vibration1070-96221875-92032014-01-01201410.1155/2014/485630485630On the Dynamic Analysis of a Beam Carrying Multiple Mass-Spring-Mass-Damper SystemO. Barry0D. C. D. Oguamanam1J. W. Zu2Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, M5S 3G8, CanadaDepartment of Mechanical and Industrial Engineering, Ryerson University, Toronto, ON, M5B 2K3, CanadaDepartment of Mechanical and Industrial Engineering, University of Toronto, Toronto, ON, M5S 3G8, CanadaThe exact natural frequencies, mode shapes, and the corresponding orthogonality relations are important in forced vibration analysis via modal expansion. In the present paper, a free vibration analysis is conducted to determine the exact natural frequencies and mode shapes of an axially loaded beam carrying several absorbers. An explicit expression is presented for the generalized orthogonality relations. These generalized orthogonality conditions are employed along with the assumed modes method to perform forced vibration analysis. The present approach is compared to other approximate methods in the literature with the classical orthogonality relations and different choice of mode shapes. The results indicate that the use of the generalized orthogonality relation with the exact mode shapes is required for a precise investigation of the dynamic response of a beam with mass-spring-mass-damper system.http://dx.doi.org/10.1155/2014/485630 |
| spellingShingle | O. Barry D. C. D. Oguamanam J. W. Zu On the Dynamic Analysis of a Beam Carrying Multiple Mass-Spring-Mass-Damper System Shock and Vibration |
| title | On the Dynamic Analysis of a Beam Carrying Multiple Mass-Spring-Mass-Damper System |
| title_full | On the Dynamic Analysis of a Beam Carrying Multiple Mass-Spring-Mass-Damper System |
| title_fullStr | On the Dynamic Analysis of a Beam Carrying Multiple Mass-Spring-Mass-Damper System |
| title_full_unstemmed | On the Dynamic Analysis of a Beam Carrying Multiple Mass-Spring-Mass-Damper System |
| title_short | On the Dynamic Analysis of a Beam Carrying Multiple Mass-Spring-Mass-Damper System |
| title_sort | on the dynamic analysis of a beam carrying multiple mass spring mass damper system |
| url | http://dx.doi.org/10.1155/2014/485630 |
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