Influence of Cable Attachment on the Spectrum of Transverse Eigenvibrations

Abstract

Studies of the cables of the Lover’s pedestrian bridge in the city of Tyumen were conducted using the previously developed method, which takes into account the bending stiffness of steel cables during their transverse vibrations. The obtained values of tension forces and bending stiffness were in the expected range. The high variability in the values of bending stiffness prompted attention to the accuracy of the initial cable length values, which were obtained from a photograph. To refine the cable length, a method of recording nodal harmonics was proposed, but the results obtained by this method turned out to be higher than those obtained from the photograph. The error analysis of the measurements could not explain this overestimation, leading to the need to reconsider the solution of the differential equation for transverse vibrations. It was found that only its particular solution, assuming a hinged support for the cable, had been considered earlier, while in reality, it is cantilevered and has a bending response. Accounting for this feature by introducing an additional boundary condition allowed the improvement of the calculation model and explained the overestimation of the cable length in the nodal harmonics method. Taking into account the type of cable attachment allowed the introduction of a generalized parameter \(s\) that takes a value of zero for a rigid cantilever attachment and a value of one for a hinged attachment. In this case, a reduction in stiffness within the attachment manifests itself as an increase in the parameter \(s\), which can be detected through the vibration spectrum recording results.