# Effect of Tuned Spring on Vibration Control Performance of Modified Liquid Column Ball Damper
## 3 Parameter Optimization
### Response of the Structure Subjected to Seismic Excitation  
Figure 8a-c shows the displacement time history responses of the structure without a damper, and with the TLCBD, TLCBSSD, and TLCBSRD when subjected to the 1940 EI Centro ground motion. The reduction in peak response of the structure attached with dampers was compared with the response of the structure without a damper. It can be observed in Figure 9 that these dampers reduced the peak displacement response of the structure during seismic excitations. The peak response reduction of the structure with the TLCBSSD and TLCBSRD arrangement was better than the TLCBD arrangement with the structure in all three seismic excitations, as shown in Figure 9. Figure 10 presents the root-mean-square (RMS) displacement response reduction of the structure with the TLCBD, TLCBSSD, and TLCBSRD. The TLCBSSD and TLCBSRD significantly reduced the RMS response of the structure compared to the TLCBD in the case of EI Centro and Hachinohe ground motion excitation. The better performance of the structure with the TLCBSSD and TLCBSRD was due to the additional energy dissipation mechanism of the spring-ball system, whereas in the case of the TLCBD the energy was dissipated only due to friction between the ball and fluid, and due to the translational and rotational motion of the ball [43; 44; 45]. However, in the case of the Kobe and Kashmir earthquake ground motion, a slight decrease in the RMS response was observed in the TLCBSSD and TLCBSRD compared to the TLCBD. This can be explained in two ways. First, at a high-frequency, low-amplitude signal, the ball inside the TLCBD can move relatively easily compared to the spring-attached ball arrangement of the TLCBSD. Therefore, the TLCBD dissipates energy efficiently compared to the TLCBSD. Second, at very high frequencies there is no significant difference in the response of the TLCBD and TLCBSD, as can be seen in harmonic loading case in Figure 7. To further explain the slight decrease in the RMS response of the TLCBSD compared to the TLCBD, the Fast Fourier Transform spectrum of Kobe and Hachinohe ground motion was developed, as shown in Figure 11. In the case of Kobe, dominant frequencies lay in the range of 1.4 to 2.5 Hz (Figure 11a), whereas in the case of Hachinohe, the dominant frequencies lay in the range of 0.8 to 1.2 Hz (Figure 11b). Therefore, it can be said that the slight difference in response of the TLCBSD and TLCB under Kobe and Kashmir earthquake ground motion was because of high-frequency, low-amplitude vibrations.  
Figure 8: Time-history responses of the primary structure displacement when subjected to 1940 EI Centro ground motion: (**a**) comparison between a primary structure with and without a TLCBD, (**b**) comparison between a primary structure with and without a TLCBSSD, (**c**) comparison between a primary structure with and without a TLCBSRD.  
Figure 10: The percentage reduction in the RMS displacement value of the primary structure with different dampers when subjected to 1940 EI Centro, 2005 Kashmir earthquake, 1995 Kobe earthquake, and Hachinohe earthquake ground motion.  
Figure 9: The percentage reduction in the peak displacement value of the primary structure with different dampers when subjected to 1940 EI Centro, 2005 Kashmir earthquake, 1995 Kobe earthquake, and Hachinohe earthquake ground motion.