Asymptotics and stabilization for dynamic models of nonlinear beams

Proceedings of the Estonian Academy of Sciences

Enrique Zuazua¹  Fágner D. Araruna¹  Pablo Braz e Silva¹ 

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关键词: vibrating beams;    Mindlin–Timoshenko system;    von von Kármán system;    singular limit;    uniform stabilization;   

DOI  :  10.3176/proc.2010.2.14

学科分类：化学（综合）

来源: Teaduste Akadeemia Kirjastus

【 摘 要 】

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 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 â†’ âˆž, one deduces the uniform exponential decay of the energy of the von Kármán model.

【 授权许可】

Unknown