In-plane modal behavior of a single shallow flexible cable with an intermediate transverse elastic support

Abstract

Cross-tie solution has been successfully applied in field to mitigate undesirable bridge stay cable vibrations, especially for cables on modern long-span cable-stayed bridges which typically have long length and relative thick cross section. In evaluating the effectiveness of the cross-tie solution and analyzing dynamic response of the formed cable network, the taut cable assumption has been used in most existing studies. Nevertheless, cable sag and bending stiffness could have non-negligible influence in networks consisting of long cables with relatively large diameter. Since a transverse cross-tie provides an elastic constraint to a vulnerable cable by connecting it with its neighbors, to fully comprehend the impact of cable sag and bending stiffness on the dynamic behavior of shallow-cable networks, it is imperative to scrutinize their effect on the behavior of a shallow cable with a transverse elastic constraint within the span. In the current study, by using the linear theory of shallow cables, an analytical model for the in-plane dynamics of a single flexible low-sag cable with an intermediate transverse elastic support is proposed. The impact of the intermediate support stiffness, location, cable bending stiffness, and sag on the in-plane modal response of the studied cable system are examined. Results show that the presence of an intermediate transverse elastic support breaks the symmetry and anti-symmetry of the original cable mode shapes, which renders the influence of sag extends to all cable modes. Further, the level of such a mode shape distortion would determine whether or not modal cross-over would occur. For any given intermediate support location, it is found that there always exists a specific level of intermediate support stiffness of which the cable sag corresponding to the occurrence of modal cross-over would be independent of cable bending stiffness. By reducing or increasing the intermediate support stiffness to be lower or higher than this specific level, the increase of cable bending stiffness would either delay modal cross-over to occur at a larger cable sag or advance its occurrence at a smaller cable sag. Reducing the intermediate support stiffness would render a local mode to evolve into a global mode, and the presence of cable bending stiffness and sag is found to allow this mode evolution to occur when a more flexible intermediate support is used.