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Journal of Dynamical and Control Systems

Erschienen in:

19.04.2016

Stability of an Axially Moving Viscoelastic Beam

verfasst von: Abdelkarim Kelleche, Nasser-eddine Tatar, Ammar Khemmoudj

Erschienen in: Journal of Dynamical and Control Systems | Ausgabe 2/2017

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Abstract

In this paper, we consider a viscoelastic flexible structure modeled as an Euler-Bernoulli beam. The beam is moving in the direction of its axis. This is one of the main features of this work. We will be dealing with variable intervals of integration and therefore the standard computation using differentiation under the integral sign is no longer valid. The boundary conditions are of ‘cantilever’ type: there is no displacement at one end and the other end is free. In fact, it is subject to a nonlinear force acting there. We prove that when the velocity of the beam is smaller than a critical value, the dissipation produced by the viscoelastic material is sufficient to suppress the transversal vibrations that occur during the axial motion of the beam. The rate of decay is shown to be exponential.

Vorheriger Artikel Remarks on Fractional Discrete Cone Control Systems with n-Orders and Their Stability

Nächster Artikel Uniform Stability of the Solution for a Memory-Type Elasticity System with Nonhomogeneous Boundary Control Condition

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Titel: Stability of an Axially Moving Viscoelastic Beam
verfasst von: Abdelkarim Kelleche
Nasser-eddine Tatar
Ammar Khemmoudj
Publikationsdatum: 19.04.2016
Verlag: Springer US
Erschienen in: Journal of Dynamical and Control Systems / Ausgabe 2/2017
Print ISSN: 1079-2724
Elektronische ISSN: 1573-8698
DOI: https://doi.org/10.1007/s10883-016-9317-8

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