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International Journal of Differential Equations
Volume 2013 (2013), Article ID 435456, 6 pages
http://dx.doi.org/10.1155/2013/435456
Research Article

Unboundedness of Solutions of Timoshenko Beam Equations with Damping and Forcing Terms

Department of Mathematics, University of Toyama, Toyama 930-8555, Japan

Received 15 January 2013; Accepted 21 February 2013

Academic Editor: Jaroslav Jaros

Copyright © 2013 Kusuo Kobayashi and Norio Yoshida. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

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.