Performance of wire rope damper in vibration reduction of stay cable

•Proposed a wire rope damper system to control high-mode vibrations of stay cables.•Clarified three-direction cyclic behaviors of the wire rope damper by physical tests.•Presented a modified normalized Bouc-Wen model to describe behavior of the wire rope damper.•Proposed an analysis method considering the nonlinear damping behavior instead of the equivalent damping method.•Verified the effectiveness of the wire rope dampers by field monitoring and analysis.