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- Title
Asymptotics and stabilization for dynamic models of nonlinear beams.
- Authors
Araruna, Fágner D.; e Silva, Pablo Braz; Zuazua, Enrique
- Abstract
We prove that the von Kármán model for vibrating beams can be obtained as a singular limit of a modified Mindlin-Timoshenko system when the modulus of elasticity in shear κ tends to infinity, provided a regularizing term through a fourth-order dispersive operator is added. We also show that the energy of solutions for this modified Mindlin-Timoshenko system decays exponentially, uniformly with respect to the parameter κ, when suitable damping terms are added. As κ → ∞, one deduces the uniform exponential decay of the energy of the von Kármán model.
- Subjects
ELASTICITY; EXPONENTIAL functions; GIRDER vibration; NONLINEAR statistical models; DAMPING (Mechanics); NONLINEAR theories
- Publication
Proceedings of the Estonian Academy of Sciences, 2010, Vol 59, Issue 2, p150
- ISSN
1736-6046
- Publication type
Article
- DOI
10.3176/proc.2010.2.14