Riesz basis property of Timoshenko beams with boundary feedback control.
Feng, De-Xing, Xu, Gen-Qi, Yung, Siu-Pang (2003)
International Journal of Mathematics and Mathematical Sciences
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Feng, De-Xing, Xu, Gen-Qi, Yung, Siu-Pang (2003)
International Journal of Mathematics and Mathematical Sciences
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Jun-Min Wang, Bao-Zhu Guo, Boumediène Chentouf (2006)
ESAIM: Control, Optimisation and Calculus of Variations
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In this paper, we consider the boundary stabilization of a sandwich beam which consists of two outer stiff layers and a compliant middle layer. Using Riesz basis approach, we show that there is a sequence of generalized eigenfunctions, which forms a Riesz basis in the state space. As a consequence, the spectrum-determined growth condition as well as the exponential stability of the closed-loop system are concluded. Finally, the well-posedness and regularity in the sense of Salamon-Weiss...
Jun-Min Wang, Bao-Zhu Guo, Boumediène Chentouf (2005)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
In this paper, we consider the boundary stabilization of a sandwich beam which consists of two outer stiff layers and a compliant middle layer. Using Riesz basis approach, we show that there is a sequence of generalized eigenfunctions, which forms a Riesz basis in the state space. As a consequence, the spectrum-determined growth condition as well as the exponential stability of the closed-loop system are concluded. Finally, the well-posedness and regularity in the sense of Salamon-Weiss...
Vojislav G. Avakumović (1955)
Publications de l'Institut Mathématique
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Robert E. Dressler, Louis Pigno (1974)
Colloquium Mathematicae
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Gen-Qi Xu, Siu Pang Yung (2003)
ESAIM: Control, Optimisation and Calculus of Variations
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We intend to conduct a fairly complete study on Timoshenko beams with pointwise feedback controls and seek to obtain information about the eigenvalues, eigenfunctions, Riesz-Basis-Property, spectrum-determined-growth-condition, energy decay rate and various stabilities for the beams. One major difficulty of the present problem is the non-simplicity of the eigenvalues. In fact, we shall indicate in this paper situations where the multiplicity of the eigenvalues is at least two. We build...
Tomica Divnić, Zlata Đurić (2000)
Kragujevac Journal of Mathematics
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