Advertisement

Exact controllability of a spherical cap: Numerical implementation of HUM

  • G. Marini
  • P. Testa
  • V. Valente
Contributed Papers
  • 41 Downloads

Abstract

This paper deals with the numerical implementation of the exact boundary controllability of the Reissner model for shallow spherical shells (Ref. 1). The problem is attacked by the Hilbert uniqueness method (HUM, Refs. 2–4), and we propose a semidiscrete method for the numerical approximation of the minimization problem associated to the exact controllability problem. The numerical results compare well with the results obtained by a finite difference and conjugate gradient method in Ref. 5.

Key Words

Vibration of shells boundary controllability semidiscrete method 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Reissner, E.,On Axisymmetrical Vibrations of Shallow Spherical Shells, Journal of Applied Physics, Vol. 13, pp. 278–290, 1955.Google Scholar
  2. 2.
    Lions, J. L.,Contrôlabilité Exacte des Systèmes Distribués, Comptes Rendus de l'Academie des Sciences, Paris, Serie I, Vol. 302, pp. 471–475, 1986.Google Scholar
  3. 3.
    Lions, J. L.,Exact Controllability, Stabilization, and Perturbations for Distributed Systems, SIAM Review, Vol. 30, pp. 1–68, 1988.CrossRefGoogle Scholar
  4. 4.
    Lions, J. L.,Contrôlabilité Exacte, Perturbation, et Stabilization des Systèmes Distribués, Vols. 1 et 2, Masson, Paris, France, 1988.Google Scholar
  5. 5.
    Glowinski, R., Li, C. H., andLions, J. L.,A Numerical Approach to the Exact Boundary Controllability of the Wave Equation, Part 1, Dirichlet Controls: Description of the Numerical Methods, Japan Journal of Applied Mathematics, Vol. 7, pp. 1–75, 1990.Google Scholar
  6. 6.
    Geymonat, G., Loreti, P., andValente, V.,Contrôlabilité Exacte d'un Modèle de Coque Mince, Comptes Rendus de l'Académie des Sciences, Paris, Serie I, Vol. 313, pp. 81–86, 1991.Google Scholar
  7. 7.
    Geymonat, G., Loreti, P., andValente, V.,Exact Controllability of a Shallow Shell Model, International Series of Numerical Mathematics, Vol. 107, pp. 85–97, 1992.Google Scholar
  8. 8.
    Lagnese, J. E., andLions, J. L.,Modelling Analysis and Control of Thin Plates, Masson, Paris, France, 1988.Google Scholar
  9. 9.
    Zuazua, E.,Contrôlabilité Exacte d'un Modèle de Plaques Vibrantes en un Temps Arbitrairement Petit, Comptes Rendus de l'Académie des Sciences, Paris, Serie I, Vol. 804, pp. 173–176, 1987.Google Scholar
  10. 10.
    Adams, R. A.,Sobolev Spaces, Academic Press, New York, New York, 1975.Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • G. Marini
    • 1
  • P. Testa
    • 1
  • V. Valente
    • 2
  1. 1.Department of MathematicsUniversity of RomeRomeItaly
  2. 2.CNR-IACRomeItaly

Personalised recommendations