Existence and stability of large scale nonlinear oscillations in suspension bridges

  • J. Glover
  • A. C. Lazer
  • P. J. McKenna
Original Papers
Received:

Abstract

A nonlinear model of a suspension bridge is considered in which large-scale, stable oscillatory motions can be produced by constant loading and a small-scale, external oscillatory force. Loud's implicit-function theoretic method for determining existence and stability of periodic solutions or nonlinear differential equations is extended to a case of a non-differentiable nonlinearity.

Keywords

Differential Equation Periodic Solution Mathematical Method Nonlinear Model Theoretic Method 
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References

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    O. H. Amann, T. von Karman, and G. B. Woodruff,The failure of the Tacoma Narrows Bridge, Federal Works Agency 1941.Google Scholar
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    S. N. Chow and J. K. Hale,Methods of bifurcation theory, Springer-Verlag, New York 1982.Google Scholar
  3. [3]
    A. C. Lazer and P. J. McKenna,Large scale oscillatory behaviour in loaded asymmetric systems, Ann. Inst. Henri Poincaré, Analyse non linéaire,4, 244–274 (1987).Google Scholar
  4. [4]
    W. S. Loud,Periodic solutions of x″+cx′+g(x)=εf(t), Mem. Amer. Math. Soc.,31, 55 pp. 1959.Google Scholar
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    S. Solimini,Some remarks on the number of solutions of some nonlinear elliptic equations, Ann. Inst. Henri Poincaré, Analyse non linéaire,2, 143–156 (1985).Google Scholar

Copyright information

© Birkhäuser Verlag 1989

Authors and Affiliations

  • J. Glover
    • 1
  • A. C. Lazer
    • 2
  • P. J. McKenna
    • 3
  1. 1.Dept. of MathematicsUniversity of FloridaGainesville
  2. 2.Dept. of Mathematics and Computer ScienceUniversity of MiamiCoral Gables
  3. 3.Dept. of MathematicsUniversity of ConnecticutStorrsUSA

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