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Discrete energy behavior of a damped Timoshenko system

  • Chebbi Sabrine
  • Hamouda MakramEmail author
Article
  • 15 Downloads

Abstract

In this article, we consider a one-dimensional Timoshenko system subject to different types of dissipation (linear and nonlinear damping). Based on a combination between the finite element and the finite difference methods, we design a discretization scheme for the different Timoshenko systems under consideration. We first come up with a numerical scheme to the free-undamped Timoshenko system. Then we adapt this numerical scheme to the corresponding linear and nonlinear damped systems. Interestingly, this scheme reaches to reproduce the most important properties of the discrete energy, namely we show for the discrete energy the positivity, the energy conservation property and the different decay rate profiles. We numerically reproduce the known analytical results established on the decay rate of the energy associated with each type of dissipation.

Keywords

Finite difference Galerkin approximation Finite element Damped Timoshenko system Hyperbolic equations and systems 

Mathematics Subject Classification

65M60 65M06 35B35 58J45 

Notes

Acknowledgements

A part of this work was performed while the first author was visiting LAMFA CNRS UMR 7352 CNRS UPJV. The first author would like to thank all the LAMFA members for their hospitality and their help with warm thanks to Professor Olivier Goubet for many fruitful discussions.

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Copyright information

© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2019

Authors and Affiliations

  1. 1.UR Analyse Non-Linéaire Et Géometrie, UR13ES32 Department of Mathematics, Faculty of Sciences of TunisUniversity of Tunis El-ManarEl Manar IITunisia
  2. 2.Imam Abdulrahman Bin Faisal UniversityDammamKingdom of Saudi Arabia

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