Catenary element approach for cable structure vibration analysis

The accurate modeling of cable behavior is of vital importance in the analysis and design of cable-supported structures. In this paper, an iterative approach of forming the cable element stiffness matrix from the basic catenary relationships was introduced. Meanwhile, an efficient iterative scheme that calculates the elemental free length based on a linear search algorithm was also proposed for a cable element with given tension, which allows efficient calculation of cable structures with different initial conditions. The vibration equations for small oscillation about nonlinear equilibrium were derived. One application to the famous Tsing Ma long span cable suspended bridge was presented, in which the free vibration analyses of both the local cable and the whole tower-cable system as a cable-beam compounded structure were carried out and compared with the in situ measurement.