On the Control of Dissipative Viscoelastic Timoshenko Beams

Abstract

In this paper we consider a Timoshenko system subject to a complementary effect of frictional damping and viscoelastic damping. Under very general assumptions on the relaxation function and the frictional damping term, we establish, for the first time as per our knowledge, explicit and optimal energy decay rates for this system. Our result generalizes and improves earlier related results in the literature.

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Acknowledgements

This work was supported by MASEP Research Group in the Research Institute of Sciences and Engineering at University of Sharjah.

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Correspondence to Muhammad I. Mustafa.

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Mustafa, M.I. On the Control of Dissipative Viscoelastic Timoshenko Beams. Mediterr. J. Math. 18, 49 (2021). https://doi.org/10.1007/s00009-020-01680-7

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Keywords

  • Timoshenko beam
  • energy decay rates
  • viscoelastic damping
  • frictional damping

Mathematics Subject Classification

  • 35B40
  • 74D99
  • 93D15
  • 93D20