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Applicable Analysis
An International Journal
Volume 86, 2007 - Issue 12
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Original Articles

Asymptotic behavior of some elastic planar networks of Bernoulli–Euler beams

Pages 1529-1548 | Received 08 Jan 2007, Accepted 03 Oct 2007, Published online: 21 Nov 2007
 

Abstract

We study the energy decay of a network of elastic Bernoulli–Euler beams in star-shaped and tree-shaped network configurations. We show that the vibrations of star-shaped or tree-shaped network of beams are not exponentially stable in the energy space. So, we give explicit polynomial decay estimates valid for regular initial data. These estimates depend on the diophantine approximations properties.

AMS 2000 Subject Classifications::

Acknowledgement

The author would like to thank V. Komornik for assistance in the proof of Lemma 4.1.

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