Long-time behaviour of a translational thermoelastic Timoshenko system with second sound

Aissa Guesmia, Mohammad Kafini*, Nasser Eddine Tatar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a Timoshenko system coupled with heat equations modelled by Cattaneo's law. The coupling is through the transverse displacement. Both ends of the beam are dynamic. One end of the beam is fixed to a base in a translational motion and a tip mass is attached to the other end. We design a feedback control acting at the base. It is shown that this feedback control is a reasonable one and is capable of stabilizing the system. We prove an exponential and a polynomial stability result using the multiplier technique. To this end, we introduce new functionals to form a suitable Lyapunov functional.

Original languageEnglish
Pages (from-to)1335-1363
Number of pages29
JournalApplicable Analysis
Volume102
Issue number5
DOIs
StatePublished - 2023

Bibliographical note

Publisher Copyright:
© 2021 Informa UK Limited, trading as Taylor & Francis Group.

Keywords

  • 35B35
  • 35B40
  • 35M13
  • Vibration control
  • exponential decay
  • polynomial decay
  • second sound
  • translational Timoshenko beam

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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