## 3 Parameter Analysis and Optimization Design
### CLNVD's Optimum Design
#### 3.2.2 Optimum Design for Structures with the CLNVD  
With the aim to evaluate the damping contribution of dampers to the overall structure and control the structure's deformation, the current vibration-reduction design methods mostly utilize additional damping ratios as well as the maximum inter-story displacement angle as control objectives. For additional CLNVD structures, this paper proposes a seismic design method with coefficient \(f_{d}\), coefficient \(f_{E}\), maximum inter-story displacement angle, and additional damping ratio as control objectives. In contrast to the structure without the CLNVD, the stiffness and damping properties of the multi-story structures with the CLNVD vary greatly, and such changes are difficult to predict before the actual calculation. Therefore, for the vibration-reduction design of the additional multi-story CLNVD structures, the current design method is to conduct trial calculations, while ensuring that CLNVD has a high energy consumption, until the proposed design goals are met. During the trial calculation process, it is necessary to utilize the optimization strategy in Section 3.2.1 to optimize CLNVD. Subsequently, the design is conducted according to the vibration-reduction design process in Section 3.2.2. Figure 13 illustrates the vibration-reduction design flowchart. The specific design steps are as follows:  
1. The target values are set for \(f_{E}\), \(f_{d}\), maximum inter-story displacement angle, and additional damping ratio.
2. The stiffness ratio damping \(C_{k}\) of the structure, the seismic response of structures without CLNVD, and the seismic response of structures with additional expected damping ratios are calculated. The floors with the CLNVD layout based on the seismic response of the structure without the CLNVD are selected, and the number of CLNVDs based on the building area (a ratio of building area to number of dampers between 100 and 200 is more reasonable) is selected. The number of CLNVDs for each floor based on the total number of CLNVDs and the layout floor is set. The parameters of CLNVD are set, and CLNVD is optimized according to Section 3.2.1.
3. The time history analysis is conducted under the circumstance of frequent or fortification earthquakes, and it is judged whether \(f_{d}\), \(f_{E}\), damping ratio, and displacement angle satisfy the goals. If not, we should increase the quantity of the CLNVDs or return to Step (2) for optimum strategies.
4. The time history analysis is conducted under the circumstance of rare earthquakes, and it is judged if the displacement angle satisfies the goals. If the goals are not satisfied, we should raise the quantity of the CLNVDs and return to Step (3).  
When the viscous damper is linear, the loss stiffness of the damper does not change with the displacement of the damper, thus avoiding the usage of iterative programs. When the viscous damper is nonlinear, if no iteration is carried out, the approximate formula for the damper loss stiffness provided in the reference [53] can be used for relevant calculations, while the accuracy of the approximate formula is not ideal. The relevant parameters of CLNVD are selected in the target region in Figure 11d, which will enable CLNVD to have a large displacement amplification factor and avoid providing a large negative stiffness to the structure. Hence, for single-story structures and linear viscous dampers, relevant parameters can be directly selected in the target area of Figure 11d for ideal CLNVD design. For nonlinear viscous dampers and multi-story structures, the damping design of additional CLNVD structures needs to follow the design process in Section 3.2.2.