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Uniform stabilization of a one-dimensional hybrid thermo-elastic structure

✍ Scribed by Marié Grobbelaar-Van Dalsen

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 160 KB
Volume: 26
Category: Article
ISSN: 0170-4214
DOI: 10.1002/mma.415

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✦ Synopsis

Abstract

This paper is concerned with the stabilization of a one‐dimensional hybrid thermo‐elastic structure consisting of an extensible thermo‐elastic beam which is hinged at one end with a rigid body attached to its free end. The model takes account of the effect of stretching on bending and rotational inertia. The property of uniform stability of the energy associated with the model is asserted by constructing an appropriate Lyapunov functional for an abstract second order evolution problem. Critical use is made of a multiplier of an operator theoretic nature, which involves the fractional power A^−1/2^ of the bi‐harmonic operator pair A acting in the abstract evolution problem. An explicit decay rate of the energy is obtained. Copyright © 2003 John Wiley & Sons, Ltd.

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