International Journal of Differential Equations

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

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 $t\to \infty$ 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.

Article information

Source
Int. J. Differ. Equ., Volume 2013, Special Issue (2013), Article ID 435456, 6 pages.

Dates
Accepted: 21 February 2013
First available in Project Euclid: 24 January 2017

https://projecteuclid.org/euclid.ijde/1485226923

Digital Object Identifier
doi:10.1155/2013/435456

Mathematical Reviews number (MathSciNet)
MR3038082

Zentralblatt MATH identifier
1270.35298

Citation

Kobayashi, Kusuo; Yoshida, Norio. Unboundedness of Solutions of Timoshenko Beam Equations with Damping and Forcing Terms. Int. J. Differ. Equ. 2013, Special Issue (2013), Article ID 435456, 6 pages. doi:10.1155/2013/435456. https://projecteuclid.org/euclid.ijde/1485226923

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