Discussion of the Improved Methods for Analyzing a Cantilever Beam Carrying a Tip-Mass under Base Excitation
Two improved analytical methods of calculations for natural frequencies and mode shapes of a uniform cantilever beam carrying a tip-mass under base excitation are presented based on forced vibration theory and the method of separation of variables, respectively. The cantilever model is simplified in...
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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/10.1155/2014/981053 |
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| author | Wang Hongjin Meng Qingfeng Feng Wuwei |
| author_facet | Wang Hongjin Meng Qingfeng Feng Wuwei |
| author_sort | Wang Hongjin |
| collection | DOAJ |
| description | Two improved analytical methods of calculations for natural frequencies and mode shapes of a uniform cantilever beam carrying a tip-mass under base excitation are presented based on forced vibration theory and the method of separation of variables, respectively. The cantilever model is simplified in detail by replacing the tip-mass with an equivalent inertial force and inertial moment acting at the free end of the cantilever based on D’Alembert’s principle. The concentrated equivalent inertial force and inertial moment are further represented as distributed loads using Dirac Delta Function. In this case, some typical natural frequencies and mode shapes of the cantilever model are calculated by the improved and unimproved analytical methods. The comparing results show that, after improvement, these two methods are in extremely good agreement with each other even the offset distance between the gravity center of the tip-mass and the attachment point is large. As further verification, the transient and steady displacement responses of the cantilever system under a sine base excitation are presented in which two improved methods are separately utilized. Finally, an experimental cantilever system is fabricated and the theoretical displacement responses are validated by the experimental measurements successfully. |
| format | Article |
| id | doaj-art-18d01dca63454a168a944ce0601508fb |
| 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-18d01dca63454a168a944ce0601508fb2025-02-03T06:05:20ZengWileyShock and Vibration1070-96221875-92032014-01-01201410.1155/2014/981053981053Discussion of the Improved Methods for Analyzing a Cantilever Beam Carrying a Tip-Mass under Base ExcitationWang Hongjin0Meng Qingfeng1Feng Wuwei2Theory of Lubrication and Bearing Institute, Xi’an Jiaotong University, No. 28 Xianning West Road, Xi’an, Shaanxi 710049, ChinaTheory of Lubrication and Bearing Institute, Xi’an Jiaotong University, No. 28 Xianning West Road, Xi’an, Shaanxi 710049, ChinaSchool of Ship and Ocean Engineering, Zhejiang Ocean University, No. 18 Haiyuan Road, Zhoushan, Zhejiang 316000, ChinaTwo improved analytical methods of calculations for natural frequencies and mode shapes of a uniform cantilever beam carrying a tip-mass under base excitation are presented based on forced vibration theory and the method of separation of variables, respectively. The cantilever model is simplified in detail by replacing the tip-mass with an equivalent inertial force and inertial moment acting at the free end of the cantilever based on D’Alembert’s principle. The concentrated equivalent inertial force and inertial moment are further represented as distributed loads using Dirac Delta Function. In this case, some typical natural frequencies and mode shapes of the cantilever model are calculated by the improved and unimproved analytical methods. The comparing results show that, after improvement, these two methods are in extremely good agreement with each other even the offset distance between the gravity center of the tip-mass and the attachment point is large. As further verification, the transient and steady displacement responses of the cantilever system under a sine base excitation are presented in which two improved methods are separately utilized. Finally, an experimental cantilever system is fabricated and the theoretical displacement responses are validated by the experimental measurements successfully.http://dx.doi.org/10.1155/2014/981053 |
| spellingShingle | Wang Hongjin Meng Qingfeng Feng Wuwei Discussion of the Improved Methods for Analyzing a Cantilever Beam Carrying a Tip-Mass under Base Excitation Shock and Vibration |
| title | Discussion of the Improved Methods for Analyzing a Cantilever Beam Carrying a Tip-Mass under Base Excitation |
| title_full | Discussion of the Improved Methods for Analyzing a Cantilever Beam Carrying a Tip-Mass under Base Excitation |
| title_fullStr | Discussion of the Improved Methods for Analyzing a Cantilever Beam Carrying a Tip-Mass under Base Excitation |
| title_full_unstemmed | Discussion of the Improved Methods for Analyzing a Cantilever Beam Carrying a Tip-Mass under Base Excitation |
| title_short | Discussion of the Improved Methods for Analyzing a Cantilever Beam Carrying a Tip-Mass under Base Excitation |
| title_sort | discussion of the improved methods for analyzing a cantilever beam carrying a tip mass under base excitation |
| url | http://dx.doi.org/10.1155/2014/981053 |
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