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

Proceedings of the Estonian Academy of Sciences Estonian Academy Publishers

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.

Authors with CRIS profile

Enrique Zuazua Iriondo

Involved external institutions

Universidade Federal da Paraíba BR Brazil (BR) Federal University of Pernambuco / Universidade Federal de Pernambuco BR Brazil (BR) Ikerbasque (Basque Foundation for Science) ES Spain (ES)

How to cite

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://dx.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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