Modeling, stabilization and control of serially connected beams

Many flexible structures consist of a large number of components coupled end to end in the form of a chain. In this paper, we consider the simplest type of such structures which is formed by $N$ serially connected Euler-Bernoulli beams, with $N$ actuators and sensors co-located at nodal points. When...

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Bibliographic Details
Published in:SIAM journal on control and optimization 1987-05, Vol.25 (3), p.526-546
Main Authors: CHEN, G, DELFOUR, M. C, KRALL, A. M, PAYRE, G
Format: Article
Language:English
Subjects:
Applied mathematics
Banach spaces
Boundary conditions
Euclidean space
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Partial differential equations
Physics
Sensors
Solid mechanics
Static elasticity (thermoelasticity...)
Structural and continuum mechanics
Variables
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Summary:Many flexible structures consist of a large number of components coupled end to end in the form of a chain. In this paper, we consider the simplest type of such structures which is formed by $N$ serially connected Euler-Bernoulli beams, with $N$ actuators and sensors co-located at nodal points. When these $N$ beams are strongly connected at all intermediate nodes and their material coefficients satisfy certain properties, uniform exponential stabilization can be achieved by stabilizing at one end point of the composite beam. We use finite elements to discretize the partial differential equation and compute the spectra of these boundary damped operators. Numericall results are also illustrated.
ISSN:0363-0129
1095-7138
DOI:10.1137/0325029