Mitigation of three-dimensional vibration of inclined sag cable using discrete oil dampers - I. Formulation

Three-dimensional small-amplitude free and forced vibration problems of an inclined sag cable equipped with discrete oil dampers are formulated in this paper using a hybrid method. The hybrid method can readily consider cable sag, cable inclination, cable internal damping, damper direction, damper stiffness and others. Multi-pairs of oil dampers with either symmetric or unsymmetric arrangement can also be dealt with. From complex vibration analyses, the damping ratios of a cable, attributed to the installed oil dampers, in both in-plane and out-of-plane modes of vibration can be estimated. The dynamic in-plane and out-of-plane responses of the cable under harmonic excitation can also be determined in the frequency domain. The application of the derived formulae to sag cables in a real cable-stayed bridge is presented in part II of this paper with extensive parametric studies.