Skip to main content
SpringerLink
Log in

About well-posedness and lack of exponential stability of Shear beam models

  • Published:
ANNALI DELL'UNIVERSITA' DI FERRARA Aims and scope Submit manuscript

Abstract

In this paper, we consider the Shear beam model (no rotary inertia) and we stablished a decay result of the total energy of solutions by taking a feedback law acting on angle rotation. Unlike the dissipative Shear beam model with damping effect acting on vertical displacement, where the exponential decay holds irrespective any relationship between coefficients of the system, here we prove that system is non-exponential stability by using semigroup techniques. Also, the well-posedness is achieved by using semigroup theory.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Han, S.M., Benaroya, H., Wei, Timothy: Dynamics of transversely vibration beams using four engineering theories. J Sound Vibrat 225(5), 935–988 (1999)

    Article  Google Scholar 

  2. Almeida Júnior, D.S., Ramos, A.J.A., Freitas, M.M.: Energy decay for damped Shear beam model and new facts related to the classical Timoshenko system. Appl. Mathemat Lett. 120, 107324 (2021)

    Article  MathSciNet  Google Scholar 

  3. Almeida Júnior, D.S., Ramos, A.J.A.: On the nature of dissipative Timoshenko systems at light of the second spectrum. Z. Angew. Math. Phys. 68(145), 31 (2017)

    MathSciNet  MATH  Google Scholar 

  4. Pazy, A.: Semigroups of linear operators and applications to partial differential equations. Springer, New York (1983)

    Book  Google Scholar 

  5. Liu, Z., Zheng, S.: Semigroups associated with dissipative systems (Chap- man & Hall/CRC Research Notes in Mathematics Series). Chapman and Hall/CRC, London (1999)

    Google Scholar 

Download references

Acknowledgements

The authors would like to thank the anonymous referee for critical review and valuable comments which allowed to improve the paper.

Funding

A. J. A. Ramos thanks the CNPq for support through Grant No. 310729/2019-0.D.S. Almeida Júnior thanks the CNPq for support through Grant No. 314273/2020-4.M. M. Freitas thanks the CNPq for support through Grant No. 313081/2021-2.

Author information

Authors and Affiliations

  1. Faculty of Mathematics, Federal University of Pará, Raimundo Santana Street, s/n, 68721-000, Salinópolis, PA, Brazil

    A. J. A. Ramos & M. M. Freitas

  2. PhD Program in Mathematics, Federal University of Pará, Augusto Corrêa Street, 01, Belém, PA, 66075-110, Brazil

    D. S. Almeida Júnior & L. S. Veras

Authors
  1. A. J. A. Ramos
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. S. Almeida Júnior
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. M. Freitas
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. L. S. Veras
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. J. A. Ramos.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ramos, A.J.A., Almeida Júnior, D.S., Freitas, M.M. et al. About well-posedness and lack of exponential stability of Shear beam models. Ann Univ Ferrara 68, 129–136 (2022). https://doi.org/10.1007/s11565-022-00391-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11565-022-00391-z

Keywords

Mathematics Subject Classification

Search

Navigation