Journal Article

Riesz basis property of the generalized eigenvector system of a Timoshenko beam

Gen‐Qi Xu, De‐Xing Feng and Siu Pang Yung

in IMA Journal of Mathematical Control and Information

Published on behalf of Institute of Mathematics and its Applications

Volume 21, issue 1, pages 65-83
Published in print March 2004 | ISSN: 0265-0754
Published online March 2004 | e-ISSN: 1471-6887 | DOI: http://dx.doi.org/10.1093/imamci/21.1.65
Riesz basis property of the generalized eigenvector system of a Timoshenko beam

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The Riesz basis property of the generalized eigenvector system of a Timoshenko beam with boundary feedback controls applied to two ends is studied in this paper. The spectral property of the operator A determined by the closed loop system is investigated. It is shown that operator A has compact resolvent and generates a C<sub>0</sub> semigroup, and its spectrum consists of two branches and has two asymptotes under some conditions. Furthermore it is proved that the sequence of all generalized eigenvectors of the system principal operator forms a Riesz basis for the state Hilbert space.

Keywords: Timoshenko beam; boundary feedback; generalized eigenvector system; Riesz basis

Journal Article.  0 words. 

Subjects: Mathematics

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