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On boundary feedback stabilisability of a viscoelastic beam

Published online by Cambridge University Press:  14 November 2011

Guenter Leugering
Guenter Leugering
Affiliation:
Fachbereich Mathematik, Technische Hochschule Darmstadt, Schlossgartenstrasse 7, D-6100 Darmstadt, West Germany
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Synopsis

It is shown that a cantilevered beam with weak viscoelastic damping of Boltzmann-type can be uniformly stabilised by velocity feedback applied as a shearing force at the free end of the beam. Estimates for the viscoelastic energy are derived using the energy multiplier method. The energy decay is related to the decay of the relaxation modulus associated with the viscoelastic material.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 114 , Issue 1-2 , 1990 , pp. 57 - 69
Copyright
Copyright © Royal Society of Edinburgh 1990

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