Stabilization of a nonlinear Euler–Bernoulli beam

In this work, we study the vibration control of a flexible mechanical system. The dynamic of the problem is modeled as a viscoelastic nonlinear Euler–Bernoulli beam. To suppress the undesirable transversal vibrations of the beam, we adopt a control at the right boundary of the beam. This control law...

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Bibliographic Details
Published in:Arabian journal of mathematics 2022-12, Vol.11 (3), p.479-496
Main Authors: Benterki, Djamila, Tatar, Nasser-Eddine
Format: Article
Language:English
Subjects:
Control theory
Euler-Bernoulli beams
Mathematics
Mathematics and Statistics
Mechanical systems
Vibration
Vibration control
Viscoelasticity
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Summary:In this work, we study the vibration control of a flexible mechanical system. The dynamic of the problem is modeled as a viscoelastic nonlinear Euler–Bernoulli beam. To suppress the undesirable transversal vibrations of the beam, we adopt a control at the right boundary of the beam. This control law is simple to implement. We prove uniform stability of the system using a viscoelastic material, the multiplier method and some ideas introduced in [20]. It is shown that a large range of rates of decay of the energy can be achieved through a determined class of kernels. Unlike most of the existing classes in the market, ours are not necessarily strictly decreasing.
ISSN:2193-5343
2193-5351
2193-5351
DOI:10.1007/s40065-022-00368-y