Stability of a complex network of Euler-Bernoulli beams

Authors:
Kui Ting Zhang;Gen Qi Xu;Nikos E. Mastorakis
Affiliations:
Tianjin University, Department of Mathematics, Tianjin, China;Tianjin University, Department of Mathematics, Tianjin, China;Military Institutes of University Education, Hellenic Naval Academy, Piraeus, Greece
Venue:
WSEAS TRANSACTIONS on SYSTEMS
Year:
2009

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Abstract

A complex network of Euler-Bernoulli beams is studied in this paper. As for this network, the boundary vertices are clamped, the displacements of the structure are continuous but the rotations of different beams are not continuous at the interior vertices. The feedback controller are designed at the interior nodes to stabilize the elastic system. The well-posed-ness of the closed loop system is proved by the semigroup theory. By complete spectral analysis of the system operator, the distribution of spectrum, the completeness and the Riesz basis property of the roots vectors of the system operator are given. As a consequence, the asymptotical stability of the system is derived under certain conditions.