Asymptotic limits and stabilization for the 1D nonlinear Mindlin-Timoshenko system

This paper shows how the so called von Kármán model 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. Introducing damping mechanism...

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Detalles Bibliográficos
Autores: Araruna, F.D., E Silva, P.B., Zuazua, E.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2010
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/491
Acceso en línea:http://hdl.handle.net/20.500.11824/491
Access Level:acceso abierto
Palabra clave:Mindlin-Timoshenko system
Singular limit
Uniform stabilization
Vibrating beams
Von Kármán system
Descripción
Sumario:This paper shows how the so called von Kármán model 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. Introducing damping mechanisms, the authors also show that the energy of solutions for this modified Mindlin-Timoshenko system decays exponentially, uniformly with respect to the parameter k. As k → ∞, the authors obtain the damped von Kármán model with associated energy exponentially decaying to zero as well.