The mechanism and the characteristics of the cable-deck coupled nonlinear vibration in a cable-stayed bridge are studied using numerical methods. A simple three-degrees-of-freedom (d.f.) model, with one independent d.f. for modeling the bridge deck movement, is proposed for describing the nonlinear interactions between the in-plane/out-of-plane vibration of the cable and the oscillation of the bridge deck. The governing equations are discretized with the Galerkin method and then solved with a numerical time integration algorithm. It is pointed out that the periodic variation of cable tension caused by vibration of a bridge deck will lead to the parametric resonance of the stay cable under certain tuning conditions. Numerical results also confirm that energy transfer between different vibration modes and beating phenomenon of the cable-deck vibration may be exhibited in the case of parametric resonance.

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