Dynamics of Laminated Timoshenko Beams

Abstract

This paper is concerned with long-time dynamics of laminated beams modeled from the well established Timoshenko system. Of particular interest is a model of two-layered beam proposed by Hansen and Spies which describes the slip effect produced by a thin adhesive layer uniting the structure. In a more general setting, involving a nonlinear foundation, we establish the existence of smooth finite dimensional global attractors for the corresponding solution semigroup.

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Acknowledgements

The authors thank the referee for his/her constructive remarks on a previous version of the paper. They also thank the partial support of CNPq (Brazil).

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Correspondence to R. N. Monteiro.

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Feng, B., Ma, T.F., Monteiro, R.N. et al. Dynamics of Laminated Timoshenko Beams. J Dyn Diff Equat 30, 1489–1507 (2018). https://doi.org/10.1007/s10884-017-9604-4

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Keywords

  • Timoshenko system
  • Laminated beam
  • Interfacial slip
  • Global attractor
  • Superlinear damping
  • Quasi-stable systems

Mathematics Subject Classification

  • 35B41
  • 35L53
  • 74K10