Stability for a boundary contact problem in thermoelastic Timoshenko’s beam

Abstract

We demonstrate the existence of solutions to Signorini’s problem for the Timoshenko’s beam by using a hybrid disturbance. This disturbance enables the use of semigroup theory to show the existence and asymptotic stability. We show that stability is exponential, when the waves speed of propagation is equal. When the waves speed is different, we show that the solution decays polynomially. This result is new. We perform numerical experiments to visualize the asymptotic properties.

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Acknowledgements

The authors would like to express their deepest gratitude to the anonymous referees for their comments and suggestions that have contributed greatly to the improvement of this article.

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Correspondence to C. A. da Costa Baldez.

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Rivera, J.E.M., da Costa Baldez, C.A. Stability for a boundary contact problem in thermoelastic Timoshenko’s beam. Z. Angew. Math. Phys. 72, 8 (2021). https://doi.org/10.1007/s00033-020-01437-y

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Keywords

  • Timoshenko’s beams
  • Thermoelasticity
  • Contact problem
  • Semilinear problem
  • Asymptotic behaviour
  • Numerical solution

Mathematics Subject Classification

  • 35Q74
  • 35Q79
  • 35D40
  • 35D30
  • 65N22