Calcul des Valeurs Propres Pour des Structures Lineaires par la Methode de Kuhn

  • M. C. Delfour
  • G. Peyre
  • P. Rideau
Conference paper
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 83)


We present two algorithms to compute the eigenvalues of a clam of closed loop linear hyperbolic contrai systems describing the vibrations of a linear structure made up of interconnected beams. They are based on an extension to analytic functions of the H. Kuhn’s method ta find the zeros of polynomials. These algorithms are very selective and accurate even for eigenvalues of large moduli. In fact this method is particularily well suited for asymptetic studies of the spectrum. Equivalent results by a finite element method vould require an extremely fine finite element approximation which vould result in unusually large matrices and unmanageable computations.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. L. Elaratehart [1] communication personnelle.Google Scholar
  2. G. Chen, H.C. Delfeur A. Krall and G. Pagre [1] Modeling, Stabilization and Contrai of Serially Connected Beams, SIAM J. on Control and Optimization, accepted.Google Scholar
  3. H.C. Delfour, G. Pagre and P. Rideau [1] Nutnerical Computation of Eigenvalues for Lineat- Structures by Kuhris flethod, accepted for presentation at the 4th IFAC Symp. an Control of Dist. Par. Syst., Los Angeles, June 30-July 3, 1986.Google Scholar
  4. H. Kuhn [1] A nevr proof of the fundamental theorem of algebra, Math. Prog. Studies 1 (1974), 148–158.CrossRefGoogle Scholar
  5. R.E. Langer [1] On the zends of exponentiel sums and integrals, Bulletin af American Mathematical Society (1931), 213–239.CrossRefGoogle Scholar
  6. A. M’Inities, H. Trait, G. Peyre and R. Roy [1] Computation of Eigenvaluss associated vith Functional Differential Equations, RPI Repart, May 19134.Google Scholar
  7. P. Rideau [1], Conirble d’un assemblage de poutres flexibles par des capteurs-actionneuns ponctuels: étude du spectre MI systerne, Tbese de docteur ingénieur, Ecole Nationale Supérieure des Mines de Paris, Paris 1905.Google Scholar
  8. L. Tanguag and R. Vaillancuort [1] Numerical solution of the dielectric equation coaxial line, IEEE Trans. On Instrumentation and Measurements IM-31 (1984), 88–90.CrossRefGoogle Scholar
  9. JI. Rowland and R. Vaillancourt [1] Attractive cycles in the iteration of meromorphic futictions, Numerische Mathetnatics, to appear.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 1986

Authors and Affiliations

  • M. C. Delfour
    • 1
  • G. Peyre
    • 2
  • P. Rideau
    • 3
  1. 1.Centre de recherches mathématiques et département de Mathématiques et StatistiqueUniversité de MontréalCanada
  2. 2.Département de Génie MécaniqueUniversité de SherbrookeSherbrookeCanada
  3. 3.100 Boul. du MidiAéroespatiale CannesCannes La Bocca CédesFrance

Personalised recommendations