# Stabilization of Berger–Timoshenko’s equation as limit of the uniform stabilization of the von Kármán system of beams and plates

G. Perla Menzala; Ademir F. Pazoto; Enrique Zuazua

- Volume: 36, Issue: 4, page 657-691
- ISSN: 0764-583X

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topMenzala, G. Perla, Pazoto, Ademir F., and Zuazua, Enrique. "Stabilization of Berger–Timoshenko’s equation as limit of the uniform stabilization of the von Kármán system of beams and plates." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 36.4 (2002): 657-691. <http://eudml.org/doc/244980>.

@article{Menzala2002,

abstract = {We consider a dynamical one-dimensional nonlinear von Kármán model for beams depending on a parameter $\{\varepsilon \}> 0$ and study its asymptotic behavior for $t$ large, as $\{\varepsilon \}\rightarrow 0$. Introducing appropriate damping mechanisms we show that the energy of solutions of the corresponding damped models decay exponentially uniformly with respect to the parameter $\{\varepsilon \}$. In order for this to be true the damping mechanism has to have the appropriate scale with respect to $\{\varepsilon \}$. In the limit as $\{\varepsilon \}\rightarrow 0$ we obtain damped Berger–Timoshenko beam models for which the energy tends to zero exponentially as well. This is done both in the case of internal and boundary damping. We address the same problem for plates with internal damping.},

author = {Menzala, G. Perla, Pazoto, Ademir F., Zuazua, Enrique},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {uniform stabilization; singular limit; von kármán system; beams; plates},

language = {eng},

number = {4},

pages = {657-691},

publisher = {EDP-Sciences},

title = {Stabilization of Berger–Timoshenko’s equation as limit of the uniform stabilization of the von Kármán system of beams and plates},

url = {http://eudml.org/doc/244980},

volume = {36},

year = {2002},

}

TY - JOUR

AU - Menzala, G. Perla

AU - Pazoto, Ademir F.

AU - Zuazua, Enrique

TI - Stabilization of Berger–Timoshenko’s equation as limit of the uniform stabilization of the von Kármán system of beams and plates

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2002

PB - EDP-Sciences

VL - 36

IS - 4

SP - 657

EP - 691

AB - We consider a dynamical one-dimensional nonlinear von Kármán model for beams depending on a parameter ${\varepsilon }> 0$ and study its asymptotic behavior for $t$ large, as ${\varepsilon }\rightarrow 0$. Introducing appropriate damping mechanisms we show that the energy of solutions of the corresponding damped models decay exponentially uniformly with respect to the parameter ${\varepsilon }$. In order for this to be true the damping mechanism has to have the appropriate scale with respect to ${\varepsilon }$. In the limit as ${\varepsilon }\rightarrow 0$ we obtain damped Berger–Timoshenko beam models for which the energy tends to zero exponentially as well. This is done both in the case of internal and boundary damping. We address the same problem for plates with internal damping.

LA - eng

KW - uniform stabilization; singular limit; von kármán system; beams; plates

UR - http://eudml.org/doc/244980

ER -

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