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 Tim...

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Veröffentlicht in:International Journal of Differential Equations 2013-01, Vol.2013 (2013), p.71-76
Hauptverfasser: Kobayashi, Kusuo, Yoshida, Norio
Format: Artikel
Sprache:eng
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Zusammenfassung: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 t→∞ 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.
ISSN:1687-9643
1687-9651
DOI:10.1155/2013/435456