The Numerical Analysis for Parametric Resonance of Multicable System considering Interaction between Adjacent Beam Portions

The investigation aims to propose a refined model to analyze the parametric resonance under multicable systems such as cable-stayed bridges. Considering the interaction between the adjacent beam portions, the shear difference is applied to modify the vibration equations derived from the multi-degree-of-freedom stiffness method. Furthermore, the difference method is adopted to make the equations more accessible for numerical analysis. The comparison results indicate that the refined model exhibits the key character of parametric resonance and also further verified the simulation methods. The consequences show that the cable will resonate at the fundamental frequency under the support excitation. In particular, when resonance occurs, most of the energy in the subsystem is transferred to the cable, resulting in the resonance amplitude of the beam portion being weakened to some certain extent. Moreover, the global resonance will have a sufficient excitation on the local resonance only when the resonance condition is satisfied.