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Cable has strong nonlinear characteristics under the static or dynamic force, and if the frequency ratio of the boundary excitation meet some conditions, cable under force will perform a vibration amplitude much more than the initial value. The sling of a long-span suspension bridge may perform a parametric vibration with the vibration ratio of 1:1 or 2:1 under the vibrating of bridge deck. This paper, on the problem, considering the first order modal, build a parametric modal that is a sling under bridge deck as the boundary vibration, which is considering the coupling effect between sling and main girder, then deduced the parametric vibration differential equation set which is considering the sling's damping and the coupling effect between the sling and the main girder.

Analysis of nonlinear parametric vibration of sling considering sling-girder coupling effect