Effects of Supporting Member on the Nonlinear Parametric Resonance of a Cable

The cables in cable-supported structures are commonly subjected to potentially damaging large amplitude motions mainly arising from parametric vibrations of the cables. This paper presents an analysis of the effects of supporting member on the nonlinear parametric vibration of a cable using a coupled cable-beam model. The proposed model considers the parameters of the beam and geometric nonlinearities of the cable. First, the multiple scales method is applied directly to the model, and by using the first-order equation, the frequency response and stability conditions are obtained. The effects of the mass ratio, stiffness ratio, and inclined angle of the coupled model are then evaluated. Then, the effects of these parameters on the parametric vibration characteristics of cable are investigated in terms of the maximum mid-span displacement and dynamic amplification factor. The results obtained represent an extension of the previous studies, which provide some useful insights into the design of cable-supported structures.