Asymptotics and stabilization for dynamic models of nonlinear beams

Araruna FD, Braz E Silva P, Zuazua E (2010)


Publication Type: Journal article

Publication year: 2010

Journal

Book Volume: 59

Pages Range: 150-155

Journal Issue: 2

DOI: 10.3176/proc.2010.2.14

Abstract

We prove that the von Karman model for vibrating beams can be obtained as a singular limit of a modified Mindlin-Timoshenko system when the modulus of elasticity in shear k 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 k, when suitable damping terms are added. As k -> infinity one deduces the uniform exponential decay of the energy of the von Karman model.

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APA:

Araruna, F.D., Braz E Silva, P., & Zuazua, E. (2010). Asymptotics and stabilization for dynamic models of nonlinear beams. Proceedings of the Estonian Academy of Sciences, 59(2), 150-155. https://doi.org/10.3176/proc.2010.2.14

MLA:

Araruna, Fagner D., Pablo Braz E Silva, and Enrique Zuazua. "Asymptotics and stabilization for dynamic models of nonlinear beams." Proceedings of the Estonian Academy of Sciences 59.2 (2010): 150-155.

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