## 3 Parameter Analysis and Optimization Design  
The coefficients \(f_{d}\) and \(f_{E}\) of CLNVD are jointly affected by the intermediate column's position \(\beta\), the lever's amplification factor \(\chi\), the bending line stiffness \(i_{b}\) of the beam, negative stiffness \(k_{N}\), and damping coefficient \(c\). For the convenience of parameter analysis, the single-story structure shown in Figure 6 is taken as the analysis object.  
For single-story structures, \(\gamma_{M}=\gamma_{\theta}=\gamma_{\Delta}=0\). Combining Equations (2)-(4), (9), (10), and (18), we obtain the following:  
\[f_{d}=\frac{\chi-3\chi\big{[}6(\beta^{2}-\beta)+1\big{]}\,/\big{[}2(3\rho+2) \big{]}}{\Big{[}(1+k_{N}/k)^{1+\alpha}+(k_{d}^{\prime\prime}/k)^{1+\alpha}\Big{]} ^{1-0.5\kappa}} \tag{20}\]  
\[f_{E}=\frac{\lambda cf_{d}^{1+\alpha}(\omega U_{1})^{\alpha-1}}{\pi C_{k1}} \tag{21}\]  
where \(k\) is calculated by Equation (11), and \(k_{d}^{\prime\prime}\) is calculated by Equation (17); \(U_{1}\) is the inter-story displacement, and \(C_{k1}\) is the structural stiffness proportional damping coefficient. For \(\omega\), we take the first modal frequency of the structure.  
When the damping index \(\alpha<1\), Equation (17) cannot be directly employed since \(u_{do}\) is unknown. However, the following iterative method is applied. This iterative method is as follows:  
1. The damper displacement \(u_{do}\) is assumed to be equal to the inter-story displacement \(U_{1}\).
2. \(u_{do}\) is substituted into Equation (17) for calculation, and Equations (20) and (21) are utilized to calculate \(f_{d}\) and \(f_{E}\).
3. The error \(\varepsilon=u_{do}/(f_{d}U_{1})-1\) is calculated. When \(\varepsilon>1\%\), \(u_{do}\) is made to be equal to \(f_{d}U_{1}\), and steps from 2 to 3 are repeated. When \(\varepsilon<1\%\), the iteration ends.  
For the convenience of discussion, an analysis is conducted on the single-story structure illustrated in Table 1. The material of the lever amplification device is Q235, and the concrete material grade of the structure is C35. The cross-section of the lever box is 230 \(\times\) 140 \(\times\) 25 \(\times\) 25 (unit: mm), with the length of 1000 mm; the box section of slant support is 200 \(\times\) 200 \(\times\) 25 \(\times\) 25 (unit: mm). The structure maintains elasticity, and the modal frequency is \(\omega=8.1\) rad/s; the structure's stiffness proportional damping is \(C_{k1}=1.56\) kN\(/(\)mm\(/\)s\()\), and the inter-story displacement under the circumstance of fortification earthquakes is \(U_{1}=h/400\). The method adopted for parameter analysis in this section is to keep other parameters unchanged and observe the impact of changing a certain parameter on the efficiency of CLNVD.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Column Section** & **Beam Section** & **Intermediate Column Section** & \(\beta\) & \(\chi\) & \(\epsilon\) & \(k_{N}\) \\ \hline (**mm\(\times\)mm**) & (**mm\(\times\)mm**) & (**mm\(\times\)mm**) & & & \((\)**kN\(\cdot\)(s/mm)\()^{0.5}\)** & (**kN/mm**) \\ \hline
600 \(\times\) 600 & 400 \(\times\) 800 & 1600 \(\times\) 250 & 0.5 & 4 & 5 & \(-\)2 \\ \hline \end{tabular}
\end{table}
Table 1: Parameters of the improved TNVD components.  
Figure 6: Schematic diagram of structure with CLNVDs.