Abstract
The cable-stayed bridge is widely used due to its strong spanning capacity and navigability. However, flexible cables parametrically resonated by external excitation may result in instability or even damage to the bridge. To prevent such undesirable resonance, this paper discusses an in-plane modal interaction-induced parametric resonance of the stayed cable excited by the bridge deck vibration via nonlinear dynamic analysis. Based on the nonlinear distributed model, two modal governing equations of the cable are established via the Galerkin method. A certain working condition, when the external excitation frequency is close to the second-order natural frequency of the stay cable while nearly twice the first-order natural frequency, is theoretically and experimentally investigated. Specifically, the frequency response equations are obtained by the multiscale method, and the stability of solutions is examined through the Routh Hurwitz criterion. Theoretical and experimental results show that bridge deck vibration can induce not only the primary and superharmonic resonance of the cable but also the principal parametric resonance. Parametric resonance-induced bifurcations are also observed in the system. Particularly, the energy exchange from second-order primary resonance to first-order principal parametric resonance is found, which can induce the parametric resonance with the response amplitude one to three times higher than that of the primary resonance. This paper also validates the superiority of the present modal interaction model over the traditional single-mode model in practical engineering applications.
Highlights
Academic Editor: Francesca Di Puccio e cable-stayed bridge is widely used due to its strong spanning capacity and navigability
To prevent such undesirable resonance, this paper discusses an in-plane modal interaction-induced parametric resonance of the stayed cable excited by the bridge deck vibration via nonlinear dynamic analysis
The frequency response equations are obtained by the multiscale method, and the stability of solutions is examined through the Routh Hurwitz criterion. eoretical and experimental results show that bridge deck vibration can induce the primary and superharmonic resonance of the cable and the principal parametric resonance
Summary
Modal Interaction-Induced Parametric Resonance of Stayed Cable: A Combined Theoretical and Experimental Investigation. Flexible cables parametrically resonated by external excitation may result in instability or even damage to the bridge. Liu et al [17] discussed a single mode in-plane vibration of the stay cable under axial excitation based on sag curve. Macdonald et al [23] used the scaling and averaging method to calculate the steady-state amplitude of the cable under nonlinear modal interaction when the excitation frequency is close to any order natural frequency of the in-plane and out-plane models. The mechanism of energy exchange between modes of a stay cable under 2 : 1 internal resonance is revealed, and the bifurcation parameter characteristics of the system are theoretically calculated and experimentally studied.
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