Skip to main content
SpringerLink
Log in

Exact internal controllability of a one-dimensional aeroelastic plate

  • Published:
Applied Mathematics and Optimization Submit manuscript

Abstract

This paper considers a control problem associated with a one-dimensional elastic plate with self-induced aerodynamic pressure. When the support of control lies in a prescribed subinterval, exact controllability is established by deriving a key energy estimate. By means of this estimate, it is also proved that the energy of a beam with partial damping decays exponentially fast.

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. Bardos, C., Lebeau, G., and Rauch, J., Contrôle et stabilisation dans les problèmes hyperboliques, Appendix 2 in [9] below.

  2. Chen, G., Fulling, S. A., Narcowich, F. J., and Sun, S., Exponential decay of energy of evolution equations with locally distributed damping, SIAM J. Appl. Math., Vol. 51, No. 1, pp. 266–301, 1991.

    Google Scholar 

  3. Dowell, E. H., Aeroelasticity of Plates and Shells, Noordhoff, Amsterdam, 1975.

    Google Scholar 

  4. Haraux, A., Séries lacunaires et contrôle semi-interne des vibrations d'une plaque rectangulaire, J. Math. Pures Appl., t. 68, fasc. 4, pp. 457–465, 1989.

    Google Scholar 

  5. Jaffard, S., Contrôle interne exact des vibrations d'une plaque carrée, C. R. Acad. Sci. Paris Sér. I, Vol. 307, pp. 759–762, 1988.

    Google Scholar 

  6. Lagnese, J., Boundary Stabilization of Thin Plates, Studies in Applied Mathematics, Vol. 10, SIAM, Philadelphia, PA, 1989.

    Google Scholar 

  7. Lasiecka, I., and Triggiani, R., Exact controllability of the Euler-Bernoulli equation with controls in the Dirichlet and Neumann boundary conditions: a nonconservative case, SIAM J. Control Optim., Vol. 27, No. 27, pp. 330–373, 1989.

    Google Scholar 

  8. Lasiecka, I., and Triggiani, R., Exact controllability of the Euler-Bernoulli equation with boundary controls for displacement and moment, J. Math. Anal. Appl., to appear.

  9. Lions, J. L., Contrôlabilité exacte perturbations et stabilisation de systèmes distribués, Vol. 1, Masson, Paris, 1988.

    Google Scholar 

  10. Lions, J. L., Exact controllability, stabilization and perturbations for distributed systems, SIAM Rev., Vol. 30, No. 1, pp. 1–68, 1988.

    Google Scholar 

  11. You, Y., Controllability and stabilizability of vibrating simply supported plate with pointwise control, Adv. in Appl. Math., Vol. 10, pp. 324–343, 1989.

    Google Scholar 

  12. Zuazua, E., Contrôlabilité exacte en un temps arbitrairement petit de quelques modèles de plaques, Appendix 1 of [9] above.

  13. Zuazua, E., Unpublished.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Virginia Polytechnic Institute & State University, 24061, Blacksburg, VA, USA

    Jong Uhn Kim

Authors
  1. Jong Uhn Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by R. Triggiani

This research was supported by AFOSR-89-0268.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kim, J.U. Exact internal controllability of a one-dimensional aeroelastic plate. Appl Math Optim 24, 99–111 (1991). https://doi.org/10.1007/BF01447737

Download citation

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01447737

Keywords

Search

Navigation