Nonlinear dynamics of a cable-stayed beam driven by sub-harmonic and principal parametric resonance

The nonlinear dynamics of a cable-stayed beam driven by the subharmonic resonance of the beam and the principal parametric resonance of the cable are investigated. Considering the combined effects of the nonlinear terms caused by the geometry of the cable and the coupled behavior between the modes of the beam and cable, a spatial discrete model of the cable-stayed beam is developed. The frequency response curves are determined by applying the method of multiple time scales to the model. The effects of some key parameters of the cable-stayed beam, namely the mass, stiffness, and sag-to-span ratios and the initial tension force, are discussed. The bifurcation and chaos of cable-stayed beams with different parameters are also studied to understand the effects of external excitation. The results show that these parameters have a considerable effect on the dynamic behavior of the cable-stayed beam, particularly that of the cable. Changes in the stiffness ratio and initial tension force also lead to more complex dynamics.