Parametric Vibration Analysis of Stay Cables Using a Super-Thin Elastic Rod Model
The mechanical model of super-thin elastic rod is applied to describe the nonlinear vibration behavior of the cable of long-span cable-stayed bridge.Firstly,considering the geometric nonlinearity,sag and flexural stiffness of the cable,the multimodal nonlinear vibration equation of the cable under axi-al excitation is derived on the basis of assuming that the static configuration of the cable is catenary.Sec-ondly,the vibration equation is solved by multiscale method,and the existence conditions of the con-stant solutions of primary resonance,primary parameter resonance and 3∶1 resonance are obtained.The sufficient conditions for the existence of the asymptotic steady solution are further obtained accord-ing to the Lyapunov's first approximate stability criterion.Finally,the effects of frequency ratio,exci-tation amplitude and cable damping on cable vibration characteristics are studied by comparing the ap-proximate solution with the numerical solution.The results show that the amplitude of the cable based on the elastic rod model is slightly larger than that of the elastic beam model,and the minimum ampli-tude of the main parameter resonance of the cable is reduced.Increasing damping can reduce the vibration of the cable to some extent,but the suppression effect is limited,so controlling the excitation amplitude is an effective method to reduce the vibration of the cable.
Kirchhoff elastic rod equationstay cableaxial excitationparametric vibrationmultiscale method
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