FREE VIBRATION OF TAUT CABLE WITH TWO SPRINGS

Secondary cables are one of counter-measures for cable vibration mitigation, but the mechanism of vibration mitigation in a cable-net system has not fully understood yet, and the optimal design method of secondary cables is still not well established. In this paper, the stiffness contribution of secondary cables to cable is simplified to be two spring supports attached to a taut cable, and then the free vibration of a taut cable with two springs is investigated. The frequency equation of the taut cable with two springs is obtained by means of displacement compatibility and force equilibrium conditions. An asymptotic solution is given by using the first-order Taylor expansion when locations of springs are close to the cable ends. More detail investigations on lower mode vibration frequencies and mode shapes are studied based on the limiting solutions while the spring stiffness is zero or infinite. The variation pattern of frequencies and mode shapes with the changes of spring locations and stiffness is studied and given. The research results can be used as a reference for the optimal design of secondary cables.