Stability and Riesz basis property of a star-shaped network of Euler-Bernoulli beams with joint damping

Gen Qi Xu; Siu Pang Yung

doi:10.3934/nhm.2008.3.723

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2008, Volume 3, Issue 4: 723-747. Doi: 10.3934/nhm.2008.3.723

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Stability and Riesz basis property of a star-shaped network of Euler-Bernoulli beams with joint damping

Gen Qi Xu^1, and
Siu Pang Yung^2,

1.
Department of Mathematics, Tianjin University, Tianjin, 300072
2.
Department of Mathematics, The University of Hong Kong, Hong Kong

Received: January 31, 2008

Revised: June 30, 2008

Published: November 2008

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Abstract

In this paper we study a star-shaped network of Euler-Bernoulli beams, in which a new geometric condition at the common node is imposed. For the network, we give a method to assert whether or not the system is asymptotically stable. In addition, by spectral analysis of the system operator, we prove that there exists a sequence of its root vectors that forms a Riesz basis with parentheses for the Hilbert state space.

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Mathematics Subject Classification: Primary: 35B40, 35C10; Secondary: 93D20, 94C99.

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