# Development of a Self-Powered Magnetorheological Damper System for Cable Vibration Control
## 4 Experimental Results and Discussion
### The Stay Cable with a Self-Povered MR Damper System  
Figures 13 and 14 give the time histories of the acceleration of the cable, the input voltage, and the damping force of the self-powered MR damper in the first and fourth modes, respectively. As expected, the voltage induced by the generator can successfully make the MR damper operate normally, and both the input voltage and damping force increase with the increase of mode order. The shapes of the curves for the acceleration, the input voltage, and the damping force are quite similar. It can be seen that the acceleration amplitudes of the cable decay exponentially, indicating that the damping force of the self-powered MR damper is proportional to the collocated velocity of the cable. In other words, the self-powered MR damper works as a linear viscous damper, and velocity feedback control can be achieved inherently. Moreover, the self-powered MR damper system is always dissipative even at small amplitudes of the cable, in contrast to the passively operated MR damper. In addition, the output voltage signal of the generator seems to be accurate enough to sense the velocity of the cable at the generator's location, demonstrating the good potential of the generator as a velocity sensor for the semi-active control of a self-powered MR damper system. Figure 12: Identified damping coefficients and stiffness coefficients of the DC generator: (**a**) Identified damping coefficients; (**b**) Identified stiffness coefficients. The damping ratios in the first four modes of the cable attached with different kinds of dampers are summarized in Table 4. Except for the first mode, the self-powered MR damper system performs the best among the three control strategies for the left three higher-order modes. The poor performance of the self-powered MR damper in the first mode is mainly due to the sag effect of the model cable [38]. As shown in Table 1, the sag parameter (\(\lambda^{2}\)) of the model cable is 16.28, which is much bigger than practical stay cables. Another reason is that the electrical energy harvested from the cable in the first mode may be too small to have a significant influence on the damping force of the MR damper. The control performance of the system can be further enhanced by decreasing the effective transmission radius of the sprocket or moving the rotary DC generator to a higher location. However, the main purpose of this paper is to demonstrate the feasibility of the self-powered MR damper system in reducing cable vibration, and the system may not show the best performance in the test. Hence, the optimum design of the system should be considered in later research, including the relative  
Figure 14: Time histories of acceleration, input voltage, and damping force for the fourth mode of the cable. Figure 13: Time histories of acceleration, input voltage, and damping force for the first mode of the cable. locations of the generator and the MR damper, the sizes and parameters of both the generator and the MR damper, and the effective transmission radius of the sprocket. The hysteretic loops of the self-powered MR damper are shown in Figure 15. The damping characteristics of the self-powered MR damper are quite similar to a combination of a traditional linear viscous damper and a negative stiffness device in the higher mode. Accordingly, the equivalent damping and stiffness coefficients are identified and shown in Figure 16. The equivalent damping coefficients are almost the same for the first four modes, while the stiffness coefficient jumps from positive to negative values after the second mode. Moreover, the negative stiffness coefficient increases with an increase in the mode order of the cable. Hence, the self-powered MR damper is found to be similar to the generator with respect to the negative stiffness characteristics.