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On the analysis and control of hyperbolic systems associated with vibrating networks

Published online by Cambridge University Press:  14 November 2011

J. E. Lagnese ,
G. Leugering  and
E. J. P. G. Schmidt
J. E. Lagnese
Affiliation:
Department of Mathematics, Georgetown University, Washington DC 20057, U.S.A.
G. Leugering
Affiliation:
Department of Mathematics, Georgetown University, Washington DC 20057, U.S.A.
E. J. P. G. Schmidt
Affiliation:
Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, Quebec, Canada, H3A2K6
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Abstract

In this paper a general linear model for vibrating networks of one-dimensional elements is derived. This is applied to various situations including nonplanar networks of beams modelled by a three-dimensional variant on the Timoshenko beam, described for the first time in this paper. The existence and regularity of solutions is established for all the networks under consideration. The methods of first-order hyperbolic systems are used to obtain estimates from which exact controllability follows for networks containing no closed loops.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 124 , Issue 1 , 1994 , pp. 77 - 104
Copyright
Copyright © Royal Society of Edinburgh 1994

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