A novel eddy current damper system for multi-mode high-order vibration control of ultra-long stay cables

•The wind-induced vibrations of stay cables can be classified into RWIV, VIV and micro-vibration.•A novel eddy current dampers system is developed to suppress the multi-mode high-order vibration of the ultra-long stay cables.•A new damping coefficient design method for the dampers is proposed, which is verified by lab and field forced vibration tests.•The practical wind-induced vibration control effects of the proposed damper system are verified by field measurement data.