The Response and Instability of Cross-Rope Suspension Towers Under Harmonic Excitation

The galloping or vortex-induced vibration of transmission lines will lead to a periodic excitations to the masts of the cross-rope suspension tower (CRST). The mast of the CRST is modeled as a straight beam with an elastic support subjected to a pulsating axial force on the top, which will change the stiffness of the mast, thereby resulting in produce harmonic excitation and instability. The dynamic characteristics of the system are investigated, which show that the bending frequency of the CRST decreases linearly with increase in axial static load, while it increases nonlinearly with the increase in boundary stiffness. Then, the method of multiple scales is adopted to analyze the vibration. It is found that the wind load on the mast brings primary resonance, but has no effects on instability. In addition, the steady state solution of the primary resonance is obtained by the polar form of the reduced amplitude modulation equations (RAMEs), with the effects of the following parameters on the vibration amplitude of the mast studied: the prestressing load in the guy, magnitude of the dynamic force, detuning parameter and wind load. Finally, the instability regions of two cases (Ω near ω and Ω near 2ω) are studied by the Cartesian form of the RAMEs, with focus on the influence of the axial harmonic load produced by the galloping of the transmission lines on the instability area. It is observed that the magnitude of excitation frequency of the dynamic force in the range of instability region becomes larger until the spring stiffness is increased up to a certain value.