Vibration Amplitudes Caused by Parametric Excitation of Cable Stayed Structures

Abstract There are very impressive projects today for very long free span bridges, both for suspended (the Great Belt in Denmark—free span of 1624 m, Akashi Kaikyo in Japan—1990 m) and stayed bridges (the Pont de Normandie in Frances—free span of 856 m). Numerous wind and aerodynamic aspects have been taken into account [1]. However, this is not the case for the dynamics of cables. This paper deals with one kind of cable vibrations: the ones caused by parametric excitation (i.e., a dynamic instability of the cables due to small periodic movements of the girder and/or the masts). The approach is oriented to calculating the amplitudes and the mechanical tension oscillations. Amplitude formulae for transient as well as for steady state regimes are reviewed and/or deduced. Several time history simulations from the finite element code are presented (displacement and cable tension) and discussed. Practical cases are also discussed. The analysis leads to large amplitude (15 m) oscillation of an inclined 440 m stay (the longer stay of the Pont de Normandie), causing tension oscillation close to 80% around the initial value when the girder and/or the mast produce a 10 cm excitation upon the chord line. In large span stayed bridges, parametric excitation will be very probable due to the presence of many low frequencies in the girder and in the cable stays. This implies new trends in the design of very large stayed bridges.