Stability and Dynamics Analysis of In-Plane Parametric Vibration of Stay Cables in a Cable-Stayed Bridge with Superlong Spans Subjected to Axial Excitation

Stay cables are prone to parametric vibrations, which might severely affect the serviceability and safety of cable-stayed bridges. This paper investigates the stability and dynamic characteristics of in-plane parametric vibrations for stay cables in cable-stayed bridges with superlong span under axial excitations. First, the nonlinear motion equation of a stay cable under axial harmonic excitation is derived on the basis of an established cable sag curve equation with the chord component of cable self-weight considered. Next, the equation is solved theoretically using a multiscale method, which reveals the conditions for the existence of the constant solution in parametric resonances. Subsequently, the sufficient conditions for the existence of the asymptotic steady solution are further obtained according to the Lyapunov’s first approximate stability criterion. Moreover, a numerical analysis is performed to assess the influences of the cable’s damping ratio, excitation frequency, and amplitude on the cable vibration using the longest cable, S36, in the Hutong Yangtze River Railway Bridge. The results show that the minimum external excitation amplitude exists for parametrical vibrations of stay cables, while the damping does not effectively suppress the amplitude of large-scale parametrical vibrations. Therefore, controlling the excitation amplitude may be an effective way to inhibit the parametrical vibrations of stay cables.