Multiple Parametric Resonances of Taut Inclined Cables Excited by Deck Vibration

A mechanical model is proposed to describe the vibration of a taut inclined cable excited by a deck. The dynamic system is simplified into a one-degree-of-freedom nonlinear system with non-dimensional parameters by using the Galerkin and non-dimensional analysis methods. The periodicity ratio (PR) method is improved and applied to the parameter analysis for the cable system. The frequency ratio between the natural frequency of the cable and the vibration frequency of the deck and the amplitude of deck vibration are the main variable parameters, and nonlinear motion is diagnosed for a large range of parameters. Several forms of motion are distinguished, and the evolution between the forms is studied. Meanwhile, several types of parametric resonance are revealed in different ranges of parameters. The results indicate that the parametric resonance in the case of a 3:2 frequency ratio is significant and should be given more attention.