# Seismic Response Study of L-Shaped Frame Structure with Magnetorheological Dampers
## 5 Analysis and Interpretation of Results
### Results Analysis on Multi-Dimensional Vibration Reduction of the Structure  
Throughout the duration of seismic waves, contrasts on the dynamic displacement response of Node 154 of the L-shaped frame structure with and without MRDs are plotted in Figure 9. As seen in Figure 9, during the action time of the Taft wave, in contrast with the structure without MRDs, the three-directional displacement responses of Node 154 of the structure with MRDs are decreased significantly. The three-directional maximum displacements of Node 154 of the structure without MRDs are 71.79, 48.27, and 1.51 mm, respectively, and those with MRDs are 42.36, 38.42, and 1.25 mm, which are decreased by 41.01%, 20.41%, and 17.36%, respectively [42]. During the action time of the Kobe wave, the three-directional maximum displacements of Node 154 of the structure without MRDs are 89.56, 64.13, and 2.20 mm, and those with MRDs are 57.41, 53.87, and 1.68 mm, which are decreased by 35.90%, 16.01%, and 23.58%, respectively. Under the excitation of seismic waves, contrasts on the dynamic acceleration response of Node 154 of the L-shaped frame structure with and without MRDs are plotted in Figure 10. As shown in Figure 10, during the action time of the Taft wave, in contrast with the structure without MRDs, the three-directional acceleration responses of Node 154 of the structure without MRDs are 154 of the structure with MRDs are significantly decreased [43]. The three-directional maximum accelerations of Node 154 of the structure without MRDs are 3.29, 3.35, and 0.13 m/s\({}^{2}\), respectively, and those with MRDs are 2.77, 2.91, and 0.12 m/s\({}^{2}\), which are decreased by 15.87%, 13.03%, and 5.31%, respectively. During the action time of the Kobe wave, the three-directional maximum accelerations of Node 154 of the structure without MRDs are 3.56, 3.70, and 0.13 m/s\({}^{2}\), decreased by 19.35%, 13.29%, and 12.32%, respectively. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & **Floor (Node)** & **10 (154)** & **10 (148)** & **10 (141)** & **9 (140)** & **9 (134)** & **9 (127)** & **8 (126)** & **8 (120)** & **8 (113)** \\ \hline \multirow{3}{*}{X direction} & ANSYS (m/s\({}^{2}\)) & 2.32 & 1.47 & 1.17 & 2.19 & 1.39 & 1.14 & 2.05 & 1.29 & 1.09 \\  & Self-compiled (m/s\({}^{2}\)) & 2.22 & 1.43 & 1.18 & 2.11 & 1.37 & 1.135 & 1.98 & 1.27 & 1.088 \\  & Relative error (\%) & 4.47 & 2.45 & \(-0.95\) & 3.52 & 1.52 & 0.43 & 3.41 & 1.89 & 0.12 \\ \hline \multirow{3}{*}{Y direction} & ANSYS (m/s\({}^{2}\)) & 1.53 & 2.01 & 1.19 & 1.49 & 1.96 & 1.17 & 1.43 & 1.87 & 1.13 \\  & Self-compiled (m/s\({}^{2}\)) & 1.50 & 1.93 & 1.20 & 1.46 & 1.87 & 1.165 & 1.39 & 1.79 & 1.11 \\ \cline{1-1}  & Relative error (\%) & 2.16 & 3.96 & \(-0.52\) & 2.24 & 4.51 & 0.38 & 2.70 & 4.52 & 1.36 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Contrasts of the maximum acceleration of the nodes between the self-compiled program and the ANSYS model. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & **Floor (Node)** & **10 (154)** & **10 (148)** & **10 (141)** & **9 (140)** & **9 (134)** & **9 (127)** & **8 (126)** & **8 (120)** & **8 (113)** \\ \hline \multirow{3}{*}{X direction} & ANSYS (mm) & 44.10 & 24.11 & 22.73 & 42.48 & 23.42 & 22.06 & 40.50 & 22.48 & 21.10 \\  & Self-compiled (mm) & 42.34 & 23.34 & 22.20 & 40.94 & 22.71 & 21.57 & 38.89 & 21.75 & 20.64 \\  & Relative error (\%) & 3.97 & 3.20 & 2.33 & 3.63 & 3.05 & 2.22 & 3.96 & 3.26 & 2.18 \\ \hline \multirow{3}{*}{Y direction} & ANSYS (mm) & 22.78 & 32.91 & 19.38 & 22.17 & 31.93 & 18.91 & 21.20 & 30.54 & 18.18 \\  & Self-compiled (mm) & 21.97 & 31.65 & 18.93 & 21.41 & 30.76 & 18.47 & 20.50 & 29.45 & 17.74 \\ \cline{1-1}  & Relative error (\%) & 3.54 & 3.84 & 2.32 & 3.44 & 3.65 & 2.34 & 3.31 & 3.56 & 2.45 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Contrasts of the maximum displacement of the nodes between the self-compiled program and the ANSYS model. Figure 9: Contrasts of displacement response of Node 154 of the structure with and without MRDs.