Unboundedness of Solutions of Timoshenko Beam Equations with Damping and Forcing Terms
Timoshenko beam equations with external damping and internal damping terms and forcing terms are investigated, and boundary conditions (end conditions) to be considered are hinged ends (pinned ends), hinged-sliding ends, and sliding ends. Unboundedness of solutions of boundary value problems for Ti...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | International Journal of Differential Equations |
| Online Access: | http://dx.doi.org/10.1155/2013/435456 |
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| _version_ | 1832551821685555200 |
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| author | Kusuo Kobayashi Norio Yoshida |
| author_facet | Kusuo Kobayashi Norio Yoshida |
| author_sort | Kusuo Kobayashi |
| collection | DOAJ |
| description | Timoshenko beam equations with external damping and internal damping terms and forcing terms are investigated, and boundary conditions (end conditions) to be considered are hinged ends (pinned ends), hinged-sliding ends, and sliding ends. Unboundedness of solutions of boundary value problems for Timoshenko beam equations is studied, and it is shown that the magnitude of the displacement of the beam grows up to ∞ as under some assumptions on the forcing term. Our approach is to reduce the multidimensional problems to one-dimensional problems for fourth-order ordinary differential inequalities. |
| format | Article |
| id | doaj-art-98a8243a75f54935abcbb38367bd3877 |
| institution | Kabale University |
| issn | 1687-9643 1687-9651 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Differential Equations |
| spelling | doaj-art-98a8243a75f54935abcbb38367bd38772025-02-03T06:00:23ZengWileyInternational Journal of Differential Equations1687-96431687-96512013-01-01201310.1155/2013/435456435456Unboundedness of Solutions of Timoshenko Beam Equations with Damping and Forcing TermsKusuo Kobayashi0Norio Yoshida1Department of Mathematics, University of Toyama, Toyama 930-8555, JapanDepartment of Mathematics, University of Toyama, Toyama 930-8555, JapanTimoshenko beam equations with external damping and internal damping terms and forcing terms are investigated, and boundary conditions (end conditions) to be considered are hinged ends (pinned ends), hinged-sliding ends, and sliding ends. Unboundedness of solutions of boundary value problems for Timoshenko beam equations is studied, and it is shown that the magnitude of the displacement of the beam grows up to ∞ as under some assumptions on the forcing term. Our approach is to reduce the multidimensional problems to one-dimensional problems for fourth-order ordinary differential inequalities.http://dx.doi.org/10.1155/2013/435456 |
| spellingShingle | Kusuo Kobayashi Norio Yoshida Unboundedness of Solutions of Timoshenko Beam Equations with Damping and Forcing Terms International Journal of Differential Equations |
| title | Unboundedness of Solutions of Timoshenko Beam Equations with Damping and Forcing Terms |
| title_full | Unboundedness of Solutions of Timoshenko Beam Equations with Damping and Forcing Terms |
| title_fullStr | Unboundedness of Solutions of Timoshenko Beam Equations with Damping and Forcing Terms |
| title_full_unstemmed | Unboundedness of Solutions of Timoshenko Beam Equations with Damping and Forcing Terms |
| title_short | Unboundedness of Solutions of Timoshenko Beam Equations with Damping and Forcing Terms |
| title_sort | unboundedness of solutions of timoshenko beam equations with damping and forcing terms |
| url | http://dx.doi.org/10.1155/2013/435456 |
| work_keys_str_mv | AT kusuokobayashi unboundednessofsolutionsoftimoshenkobeamequationswithdampingandforcingterms AT norioyoshida unboundednessofsolutionsoftimoshenkobeamequationswithdampingandforcingterms |