## 4 Engineering Example Analysis
### Vibration-Reduction Effect  
Figure 16 shows \(f_{d}\) and \(f_{E}\) of the CLNVD under the circumstance of fortification earthquakes and rare earthquakes. From Figure 17, it can be seen as follows: Scheme 1 is the most optimal, Scheme 2 is the second optimal one, and Scheme 3 is the poorest. Meanwhile, for Scheme 1, \(f_{d}>3.5\) and \(f_{E}>30\). Therefore, Scheme 1 satisfies the goals. By comparing Scheme 2 and Scheme 1, we can see that the CLNVD has the highest efficiency when the CLNVD is designed at the middle span. Through comparing Scheme 3 and Scheme 2, we can see that the CLNVD has the highest efficiency when the CLNVD is designed at the middle span. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Scheme** & **Story** & \(\beta\) & **Beam Section** & **Column Section** & \(\chi\) & \(c\) & \(k_{N}\) \\ \hline \multirow{4}{*}{Scheme 1} & \multirow{4}{*}{5–8} & \multirow{4}{*}{0.5} & **(mm\(\times\)mm)** & **(mm\(\times\)mm)** & & \((\text{kN}\)\(\cdot\)(s/mm)\({}^{0.5}\)) & (kN/mm) \\  & & & **(mm\(\times\)mm)** & & & \((\text{kN}\)\(\cdot\)(s/mm)\({}^{0.5}\)) & (kN/mm) \\ \hline \multirow{4}{*}{Scheme 2} & 5–8 & 0.5 & 400 \(\times\) 800 & 1700 \(\times\) 350 & 4 & 8 & \(-\)2 \\  & 2–4 & 0.5 & 400 \(\times\) 800 & 1700 \(\times\) 350 & 4 & 12 & \(-\)2 \\  & 5–8 & 0.2 & 400 \(\times\) 800 & 1700 \(\times\) 350 & 4 & 8 & \(-\)2 \\  & 2–4 Scheme 2, we can see that the CLNVD's stiffness \(k_{N}\) greatly increases the energy dissipation capacity of the damper. Figure 17a reveals the NVD's hysteresis curve of B (1-2) axis on the 5 th floor under the rare earthquake's Big Bear waves. As is shown in Figure 17a, NSD causes the hysteresis curve of NVD to become inclined, and the damper's hysteretic curve area in scheme 1 is larger. Scheme 1 is obtained after optimizing and designing in Section 3.2. Therefore, \(k_{N}/k\) and \(k_{d}^{\prime\prime}/k\) are located within the target region presented in Figure 11d (See Figure 17b). The damping ratio provided by CLNVDs is determined according to the strain energy method specified in Chinese code [50]. According to Table 5, the damping ratios of Scheme 1, Scheme 2, and Scheme 3 are 20.5%, 14.2%, and 8.5%, respectively. Scheme 1 can satisfy the set goals. In addition to the additional damping ratio, the ratio of the cumulative energy dissipation of the damper to the seismic input energy can also be employed as an indicator to measure the performance of CLNVD. As per Table 6, under the circumstance of rare earthquakes, the cumulative energy ratios of dampers from Scheme 1, Scheme 2, and Scheme 3 are 77.9%, 70.8%, and 57.4%, respectively. The internal plastic cumulative damage energy ratios from Scheme 1 to Scheme 3 are 0.8%, 2.1%, and 6.1%, respectively. From this, it can be seen that all three proposed schemes in this paper can significantly reduce  
Figure 16: The CLNVD’s \(f_{d}\) and \(f_{E}\) under fortification earthquakes and rare earthquakes: (**a**) \(f_{d}\); (**b**) \(f_{E}\). Figure 17: NVD’s hysteresis curves of various schemes and combinations of \(k_{N}/k\) and \(k_{d}^{\prime\prime}/k\) in Scheme 1: (**a**) NVD’s hysteresis curves; (**b**) values of \(k_{N}/k\) and \(k_{d}^{\prime\prime}/k\) in Scheme 1.  
structural damage, while Scheme 1's CLNVD system has the strongest energy dissipation capacity and the optimal control effect on structural damage. Figures 18 and 19 reveal the structure's inter-story displacement as well as story shear force under three different schemes. As shown in Figure 18, the CLNVD of Scheme 1 reduces the maximum of the structure's inter-story displacement angle from 1/200 to 1/400 under fortification earthquakes, and from 1/100 to 1/200 under rare earthquakes, meeting the set goals. The inter-story displacement of all floors except for the ground floor has been reduced by almost 50%. From Figure 19, we can draw a conclusion that the shear force of each floor falls to a certain extent, while the magnitude of the decrease is different from the magnitude of the decrease in inter-story displacement.