Solvability of a Model for the Vibration of a Beam with a Damping Tip Body
We consider a model for the vibration of a beam with a damping tip body that appeared in a previous article. In this paper we derive a variational form for the motion of the beam and use it to prove that the model problem has a unique solution. The proofs are based on existence results for a general...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/298092 |
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| author | M. Basson M. de Villiers N. F. J. van Rensburg |
| author_facet | M. Basson M. de Villiers N. F. J. van Rensburg |
| author_sort | M. Basson |
| collection | DOAJ |
| description | We consider a model for the vibration of a beam with a damping tip body that appeared in a previous article. In this paper we derive a variational form for the motion of the beam and use it to prove that the model problem has a unique solution. The proofs are based on existence results for a general linear vibration model problem, in variational form. Finite element approximation of the solution is discussed briefly. |
| format | Article |
| id | doaj-art-711fd36d5a564f729a5fc0f89bcbe6ff |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-711fd36d5a564f729a5fc0f89bcbe6ff2025-02-03T01:32:05ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/298092298092Solvability of a Model for the Vibration of a Beam with a Damping Tip BodyM. Basson0M. de Villiers1N. F. J. van Rensburg2Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South AfricaDepartment of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South AfricaDepartment of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South AfricaWe consider a model for the vibration of a beam with a damping tip body that appeared in a previous article. In this paper we derive a variational form for the motion of the beam and use it to prove that the model problem has a unique solution. The proofs are based on existence results for a general linear vibration model problem, in variational form. Finite element approximation of the solution is discussed briefly.http://dx.doi.org/10.1155/2014/298092 |
| spellingShingle | M. Basson M. de Villiers N. F. J. van Rensburg Solvability of a Model for the Vibration of a Beam with a Damping Tip Body Journal of Applied Mathematics |
| title | Solvability of a Model for the Vibration of a Beam with a Damping Tip Body |
| title_full | Solvability of a Model for the Vibration of a Beam with a Damping Tip Body |
| title_fullStr | Solvability of a Model for the Vibration of a Beam with a Damping Tip Body |
| title_full_unstemmed | Solvability of a Model for the Vibration of a Beam with a Damping Tip Body |
| title_short | Solvability of a Model for the Vibration of a Beam with a Damping Tip Body |
| title_sort | solvability of a model for the vibration of a beam with a damping tip body |
| url | http://dx.doi.org/10.1155/2014/298092 |
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