Skip to main content
SpringerLink
Log in

Energy decay for a weakly nonlinear damped piezoelectric beams with magnetic effects and a nonlinear delay term

  • Published:
Zeitschrift für angewandte Mathematik und Physik Aims and scope Submit manuscript

Abstract

This paper considers a one-dimensional piezoelectric beams with magnetic effect damped with a weakly nonlinear feedback in the presence of a nonlinear delay term. Under appropriate assumptions on the weight of the delay, we establish an energy decay rate, using a perturbed energy method and some properties of a convex functions. Our result generalizes the recent result obtained in Ramos et al. (Z Angew Math Phys 72:26, 2021). https://doi.org/10.1007/s00033-020-01457-8.

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.

Similar content being viewed by others

References

  1. Afilal, M., Soufyane, A., Santos, M.L.: Piezoelectric Beams with Magnetic Effect and Nonlinear Damping: General Stability, preprint

  2. Benaissa, A., Bahlil, M.: Global existence and energy decay of solutions to a nonlinear Timoshenko beam system with a delay term. Taiwan. J. Math. 18(5), 1411–1437 (2014)

    Article  MathSciNet  Google Scholar 

  3. Datko, R., Lagnese, J., Polis, M.P.: An example on the effect of time delays in boundary feedback stabilization of wave equations. SIAM J. Control Optim. 24, 152–156 (1986)

    Article  MathSciNet  Google Scholar 

  4. Morris, K.A., Özer, A. O.: Strong stabilization of piezoelectric beams with magnetic effects. In: Proceedings of the 52nd IEEE Conference on Decision & Control, pp. 3014–3019 (2013)

  5. Morris, K.A., Özer, A.O.: Modeling and stabilizability of voltage-actuated piezoelectric beams with magnetic effects. SIAM J. Control Optim. 52, 2371–2398 (2014)

    Article  MathSciNet  Google Scholar 

  6. Nicaise, S., Pignotti, C.: Stability and instability results of the wave equation with a delay term in the boundary or internal feedbacks. SIAM J. Control Optim. 45, 1561–1585 (2006)

    Article  MathSciNet  Google Scholar 

  7. Pohl, D.W.: Dynamic piezoelectric translation devices. Rev. Sci. Instrum. 41, 54–57 (1987)

    Article  Google Scholar 

  8. Racke, R.: Instability of coupled systems with delay. Commun. Pure Appl. Anal. 11(5), 1753–1773 (2012)

    Article  MathSciNet  Google Scholar 

  9. Ramos, A.J.A., Gonçalves, C.S.L., Neto, S.S.C.: Exponential stability and numerical treatment for piezoelectric beams with magnetic effect. ESAIM M2AN 52, 255–274 (2018)

    Article  MathSciNet  Google Scholar 

  10. Ramos, A.J.A., Özer, A.Ö., Freitas, M.M., et al.: Exponential stabilization of fully dynamic and electrostatic piezoelectric beams with delayed distributed damping feedback. Z. Angew. Math. Phys. 72, 26 (2021). https://doi.org/10.1007/s00033-020-01457-8

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The third author has been partially supported by the CNPq Grant 303026/2018-9.

Author information

Authors and Affiliations

  1. Department of Mathematics, College of Sciences, University of Sharjah, P.O. Box 27272, Sharjah, United Arab Emirates

    A. Soufyane

  2. Département de Mathématiques et Informatique, Faculté Polydisciplinaire de Safi, Université Cadi Ayyad, Marrakesh, Marocco

    M. Afilal

  3. Institute of Exact and Natural Sciences, Doctoral Program in Mathematics, Federal University of Pará, Augusto Corrêa Street, Number 01, Belém, PA, 66075-110, Brazil

    M. L. Santos

Authors
  1. A. Soufyane
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Afilal
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. L. Santos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Soufyane.

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

Soufyane, A., Afilal, M. & Santos, M.L. Energy decay for a weakly nonlinear damped piezoelectric beams with magnetic effects and a nonlinear delay term. Z. Angew. Math. Phys. 72, 166 (2021). https://doi.org/10.1007/s00033-021-01593-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00033-021-01593-9

Keywords

Mathematics Subject Classification

Search

Navigation