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1 theoretical and numerical analysis:

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Document pages: 10 pages

Abstract: For the main parameter resonance problem of 1:   1 cable bridge coupling vibration, the main parameter resonance model considering cable beam coupling is established, and the dimensionless parameter resonance differential equation is derived. The resonance characteristics of the main parameters are discussed by using the multi-scale approximate solution method. Taking the actual stay cable of a cable-stayed bridge as the research object, this paper expounds the numerical simulation analysis under various working conditions. The results show that when the coupling system causes 1   1 parameter resonance, the nonlinear principal parameter resonance in the response is independent of the initial displacement of the cable, but with the increase of the vertical initial displacement of the beam end of the bridge deck, it is considerede “beat” vibration. When the vertical initial displacement of deck beam end is 10−6 m order of magnitude or even smaller, “beat” vibration phenomenon of cable and beam appears. Displacement amplitude of the cable is small and considerable amplitude vibration may not occur at this time, only making a slight stable “beat” vibration in the vicinity of the equilibrium position, which is different from 2 : 1 parametric resonance condition of cable-bridge coupling system. Therefore, it is necessary to limit the initial displacement excitation amplitude of beam end and prevent the occurrence of amplitude main parametric excitation resonances.

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