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...