ESTONIAN ACADEMY
PUBLISHERS
eesti teaduste
akadeemia kirjastus
PUBLISHED
SINCE 1952
 
Proceeding cover
proceedings
of the estonian academy of sciences
ISSN 1736-7530 (Electronic)
ISSN 1736-6046 (Print)
Impact Factor (2022): 0.9
Asymptotics and stabilization for dynamic models of nonlinear beams; pp. 150–155
PDF | doi: 10.3176/proc.2010.2.14

Authors
Fágner D. Araruna, Pablo Braz e Silva, Enrique Zuazua
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 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 → ∞, one deduces the uniform exponential decay of the energy of the von Kármán model.
References

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