# Performance of Strengthened Accelerated Oscillator Damper for Vibration Control of Bridges
## 5 Damping Performance of SAOD-LS and SAOD-NSD in an Actual Bridge Example  
To illustrate the profound effect of the SAOD-LS and SAOD-NSD in mitigating vibrations of real bridge structures, in this section, the FE calculation of a six-span continuous beam bridge (i.e., the Puwan 14 th Bridge in the Puwan New Area of Dalian) is taken as Example 5. This bridge is a twin-deck concrete continuous beam bridge that plays a vital role in Puwan New Area's transportation network. Figure 9: Amplitude spectrum in Case 4, Case 5 and Case 6. As shown in Figure 10, Example 5 has a span arrangement of 70 m + 120 m + 120 m + 120 m + 70 m, summing up to a total length of 500 m. The piles, piers, and main girder were constructed using concrete grades C30, C40, and C50, respectively. The seismic fortification intensity for Dalian stands at 8 degrees, with a corresponding design seismic acceleration peak value of 0.2 g [47; 48; 49]. The El Centro wave, scaled to a magnitude of 2.1 times, was selected as the external excitation for our analysis. We conducted a comparative study on the displacement of the main girder in three different cases: the original bridge (labeled as Case 7), the bridge equipped with two identical SAOD-LS devices on both abutments (Case 8), and the bridge equipped with two identical SAOD-NSD devices on both abutments (Case 9). Regarding the SAOD-LS and SAOD-NSD, it can be considered that the main beam of the bridge is the primary structure, while the transmission device can be positioned on the abutment. Additionally, the secondary structure can be located within the bridge's box-grider. This arrangement effectively addresses the challenge of installing the secondary structure of the AOD. The specific parameters chosen for the SAOD-NSD devices in Case 9 on one side of the abutment are presented in Table 5.  
Apart from the \(k_{2}\) of the SAOD-LS in Case 8, which is precisely set to 100 kN/m, all the other parameters for the SAOD-LS in Case 8 are identical to those in Case 9 (i.e., \(m_{2}\) = 180 t, \(c_{2}\) = 0 Ns/m and \(r_{2}\) = 5). We compute the displacement and force results in Section 5 using the FE method. The general FE modeling method (i.e., the finite element analysis) for beam bridges models the Puwan 14 th Bridge part. The modeling methods for the SAOD-LS and SAOD-NSD are similar to Example 4, with the distinction that the main girder of the bridge is treated as the primary structure, including \(m_{1}\), \(c_{1}\), and \(k_{1}\). Figure 11 illustrates a comparison of the main girder's time-history displacement response during the first 10 s for Case 7, Case 8, and Case 9. After researching Figure 11, it is observed that within the first 10 s, the maximum value for \(x_{1}\)-Case 7 reaches 17.93 cm, while \(x_{1}\)-Case 8 is 13.55 cm (reflecting a seismic reduction rate of 24.43%), and \(x_{1}\)-Case 9 is 13.15 cm (showing a seismic reduction rate of 26.66%). This suggests that both SAOD-LS and SAOD-NSD exhibit exceptional shock absorption capabilities for the actual bridge. Note: seismic reduction rate = (maximum structural response without control \(-\) maximum structural response with control)/maximum structural response without control [50]. A vibration reduction system with remarkable robustness implies that, under different types of seismic waves, the system demonstrates superior damping performance. Therefore, in the following study, we selected three near-field and three far-field seismic waves [51; 52; 53; 54], listed in Table 6.  
Figure 10: General layout of half of Example 5 (units: m). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \(m_{2}\) (t) & \(c_{2}\) (Ns/m) & \(r_{2}\) & \(k_{A}\) (kN/m) & \(k_{B}\) (kN/m) & \(l_{1}\) (m) & \(l_{2}\) (m) & \(l_{3}\) (m) \\ \hline \(180\) & 0 & 5 & 81.30 & 81.30 & 0.73 & 0.38 & 0.40 \\ \hline \end{tabular}
\end{table} 
Table 5: Values of one-side-abutment parameters of Case 9 in Example 5.