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Uniform Stabilization of an Axially Moving Kirchhoff String by a Boundary Control of Memory Type

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Abstract

In this paper, we study the stabilization of solutions of an axially moving string of kirchhoff type by a viscoelastic boundary control. We prove that the dissipation produced by the viscoelastic term is sufficient to suppress the transversal vibrations that occur during the axial motion of the string, and we also show that the string displacement decays in an arbitrary rate. When comparing with immobile strings, we conclude that the movement of the string itself produces enough extra damping ensuring the stabilization.

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Acknowledgments

The second author would like to express his gratitude for the financial support and the facilities provided by King Fahd University of Petroleum and Minerals through the Project no.: IP151-MATH-143.

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Authors and Affiliations

  1. Faculté des Mathématiques, Université des Sciences et de la Technologie Houari Boumediene, BP 32, EL-Alia 16111, Bab Ezzouar, Alger, Algeria

    Abdelkarim Kelleche & Ammar Khemmoudj

  2. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Nasser-eddine Tatar

Authors
  1. Abdelkarim Kelleche
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  2. Nasser-eddine Tatar
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  3. Ammar Khemmoudj
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Correspondence to Abdelkarim Kelleche.

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Kelleche, A., Tatar, Ne. & Khemmoudj, A. Uniform Stabilization of an Axially Moving Kirchhoff String by a Boundary Control of Memory Type. J Dyn Control Syst 23, 237–247 (2017). https://doi.org/10.1007/s10883-016-9310-2

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  • DOI: https://doi.org/10.1007/s10883-016-9310-2

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