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In order to ascertain the effects of longitudinal girder vibration on the non-linear cable responses in cable-stayed bridges, this study established a mechanical model of a cable which is subjected to three excitations at each anchorage. Non-linear governing equations were derived by Galerkin method and solved numerically. Three longitudinal girder vibration amplitudes were selected to illustrate their effect on cable non-linear response under primary and sub-harmonic resonance. The numerical results show that partially releasing the longitudinal constraint between the girder and pylons ensures that longitudinal girder vibration eases cable vibrations. This provides scientific basis for designing cable-stayed bridge as floating or half-floating system from a non-linear vibrations of view. Two basic and mutually orthogonal excitation mechanisms were identified under the sub-harmonic resonance: external excitation and parametric excitation. Effects of global excitation amplitude and cable inclined angle on response distribution under sub-harmonic resonance were found.

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