MODELING AND INHERENT CHARACTERISTICS OF SAGGED-CABLE-CROSSTIE SYSTEM

Crosstie is a promising mean for vibration mitigation of long inclined cables. In order to study the inherent characteristics of the system with crosstie and its variation with key parameters, a model for the sagged-cable-crosstie system composed of N vertical cables and of M crossties was established. The dimensionless equation of motion was obtained and then solved by introducing boundary, continuity, and equilibrium conditions. The general model was reduced to a double-cable-crosstie system, and its dimensionless frequency equation was obtained. The effects of key parameters on the frequencies and modes of the system were studied by numerical analysis, such as Irvine parameter λ², stiffness and location of crossties, and wave velocity ratio η. The results show that the sag only affects the out-of-phase frequency when the parameters of the two cables are the same, so the ω-λ² curves of in-phase vibration and out-of-phase vibration show cross-over phenomenon and veering phenomenon, respectively. When λ² is a certain value, the first order out-of-phase vibration frequency under any crosstie stiffnesses is equal to the first order in-phase frequency, thusly the frequency curves pass through the first cross-over point. If the parameters of the two sagged cables are the same, increasing the stiffness of the crosstie only increases the out-of-phase vibration frequency of the system, but the increase is not more than 1. If the wave velocities of the two sagged cables are different, all the frequencies of the system will be “jumping” to higher orders with the increase of the wave velocity difference, and the higher the frequency order, the more the number of “jumping”.