Influence of Damping on the Vibration of an Inclined Cable Subjected to Support Excitation

The cables used in cable-stayed bridges are known to have low levels of damping and, as a result, their large amplitude vibrations represent a problem for the structure. Therefore, augmenting the natural damping of cables is used as a strategy to decrease their vibration response. Here we investigate how this precaution changes the dynamics of the cable vibration response. We use a four-mode model of an inclined cable specifically, that is fixed at the top, and vertically excited at the base in order to simulate excitation due to the deck motion. This model simulates the internal resonances between in-plane and out-of-plane modes of vibration. The deck motion is taken to be at a frequency close to the natural frequency of the second cable mode in each plane, hence, directly exciting just the second in-plane mode. The objective of this study is to examine how the regions of stability (of the different possible solutions) change with variations in the modal damping value of the cable. The damping ratios of the cables used for bridges being considered is usually about 0.2%; here we investigate increasing ξ up to 1%. Three-parameter analysis shows that 2:1 resonance occurs for damping ratios larger than 0.6%; but it requires higher excitation amplitudes than for damping ratios about 0.2%. The analysis of the damping ratio variation shows us that bifurcations that can lead to sudden change in the cable dynamics still persist for the parameter ranges considered in this study. However, they occur at excitation frequencies that are further from the second natural frequency of the cable.