APPLICATIONS OF MATHEMATICS, Vol. 50, No. 6, pp. 503-525, 2005

Instability of oscillations in cable-stayed bridges

Josef Malik

J. Malik, Institute of Geonics, Academy of Sciences of the Czech Republic, Studentska 1768, 708 00 Ostrava, Czech Republic, e-mail:

Abstract: In this paper the stability of two basic types of cable stayed bridges, suspended by one or two rows of cables, is studied. Two linearized models of the center span describing the vertical and torsional oscillations are investigated. After the analysis of these models, a stability criterion is formulated. The criterion expresses a relation between the eigenvalues of the vertical and torsional oscillations of the center span. The continuous dependence of the eigenvalues on some data is studied and a stability problem for the center span is formulated. The existence of a solution to the stability problem is proved. Some other qualitative results concerning the stability/instability of oscillations are studied as well.

Keywords: cable stayed bridge, vertical and torsional oscillations, eigenvalues and eigenfunctions of center span

Classification (MSC 2000): 35P10, 35Q80, 35B27

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