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Riesz basis property of the generalized eigenvector system of a Timoshenko beam |
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| Authors: | Xu Gen-Qi; Feng De-Xing; Yung Siu Pang |
| Institution: | 1 Mathematics Department of Tianjin University, Tianjin, 300072, People's Republic of China 2 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, People's Republic of China 3 Department of Mathematics, University of Hong Kong, Hong Kong, People's Republic of China |
| Abstract: | The Riesz basis property of the generalized eigenvector system of a Timoshenko beam with boundary feedback controls appliedto 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 generatesa C<sub>0</sub> semigroup, and its spectrum consistsof two branches and has two asymptotes under some conditions.Furthermore it is proved that the sequence of all generalizedeigenvectors of the system principal operator forms a Rieszbasis for the state Hilbert space. |
| Keywords: | Timoshenko beam boundary feedback generalized eigenvector system Riesz basis |
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