Amplitude-dependent frequency and damping identification of bridge cables with MR dampers in different setups

As the world's first time implementation of MR-based smart damping technique in bridge structures, a total of 312 semi-active magneto-rheological (MR) dampers have recently been installed on the cable-stayed Dongting Lake Bridge for wind-rain-induced cable vibration control. Prior to the full implementation, a comprehensive field vibration test, has been conducted on the longest cable of 150 m to identify and compare damping performance of the cable-damper system under different damper installation setups and under a wide spectrum of voltage inputs to the MR dampers. Forced vibration experiments were carried out for the cable without damper, with single-damper setup, and with twin-damper setup, respectively. One purpose of this in-situ experimental investigation is to determine the optimal input voltage which achieves maximum system damping for the aim of designing a multi-switch control strategy. Due to geometric nonlinearity of cables and hysteretic nonlinearity of MR dampers, the equivalent modal properties of the cable-damper system are deemed to be amplitude-dependent. Keeping this in mind, a Hilbert transform based method is deployed in the present study to identify the amplitude-dependent natural frequencies and modal damping from the sinusoidal-decay response data. The experimental and identification results show that the equivalent modal damping ratios of the system are noticeably dependent on vibration amplitude and the relevance of the natural frequencies to vibration amplitude is negligible. The single-damper setup is competitive with the twin-damper setup in suppressing in-plane vibration of the cables. However, when mitigation of cable out-of-plane vibration is also required, the twin-damper setup performs much better. For both setups, the value of optimal voltage is found to be mode-dependent and amplitude-dependent.