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Stability to 1-D thermoelastic Timoshenko beam acting on shear force

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Abstract

In this paper, we study the stabilization of a new coupling to thermoelastic Timoshenko beam. In particular, we consider a thermoelastic coupling on shear force. We prove that this dissipative system is exponentially stable if and only if the velocities of waves propagations are the same, as usually occurs in Timoshenko systems with few dissipations. On the contrary, we show that the system (1.7)–(1.10) with boundary conditions (1.12) is polynomially stable, that is, that the semigroup decay as \({1/\sqrt{t}}\). Additionally, we show that this rate of decay is optimal. For the system (1.7)–(1.10) with boundary conditions (1.11), we show that the semigroup decay as \({1/\sqrt[4]{t}}\).

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Authors and Affiliations

  1. Department of Mathematics, Federal University of Pará, Augusto Corrêa Street, 01, Belém, PA, 66075-110, Brazil

    Dilberto da S. Almeida Júnior & M. L. Santos

  2. National Laboratory for Scientific Computation, Getúlio Vargas Street, Number 333, Petrópolis, RJ, 25651-075, Brazil

    J. E. Muñoz Rivera

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  1. Dilberto da S. Almeida Júnior
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  2. M. L. Santos
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  3. J. E. Muñoz Rivera
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Correspondence to Dilberto da S. Almeida Júnior.

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Almeida Júnior, D.d.S., Santos, M.L. & Muñoz Rivera, J.E. Stability to 1-D thermoelastic Timoshenko beam acting on shear force. Z. Angew. Math. Phys. 65, 1233–1249 (2014). https://doi.org/10.1007/s00033-013-0387-0

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  • DOI: https://doi.org/10.1007/s00033-013-0387-0

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