# Time Domain Damage Identification Approach of the Newly Hollow Floor Structure with TRMD
## 4 Experimental Validation  
A single-story frame with the damping device TRMD at the top of the frame is conducted in the laboratory to verify the proposed method, as shown in Figure 8. The two stainless steel sheets and one aluminum alloy plate are rigidly connected as the model structure. Two stainless steel sheets, which are modeled as the frame columns, are 500 mm high, 100 mm wide, and 1 mm thick, and the aluminum alloy plate, which is modeled as the frame beam, is 300 mm long, 100 mm wide, and 10 mm thick. The natural vibration frequency of the model is measured as 1.465 Hz, and the damping ratio is 0.057. The specific parameters of the experiment model are shown in Table 3. The arched path  
The model was fixed on the shaking table made by Canada Quanser company. Two accelerometers were mounted at the top of the frame and on the shaking table to record the acceleration response. Furthermore, two laser displacement meters were also mounted at the top of the frame and the shaking table to record the displacement response. The model was excited by the El-Centro wave with a peak acceleration of 0.2 g.  
The structure was tested in three states: the uncontrolled intact state (Case 1), the controlled intact state (Case 2), and the controlled damaged state (Case 3), which are given in Table 5. The uncontrolled structure and controlled structure with TRMD were first tested comparatively without any damage. Afterward, the frame column was cut at the middle of the two stainless steel sheets with a depth of \(d\) = 15 mm in Case 3. The width of the cuts is \(b\) = 100 mm in this damage case. One typical cut is demonstrated in Figure 9.  
Figure 10 shows the displacement response comparison between the uncontrolled and the controlled structure in the intact state. It is shown that the displacement response can be obviously reduced, especially in the latter part of the earthquake wave for the controlled structure with TRMD.  
In Case 3, structural damage identification is performed by the dynamic response sensitivity-based model updating method. The displacement response difference at the top of the structure is selected as the objective function. The local damage is identified by iteratively calculating the acceleration response difference and the response sensitivity. The equivalent stiffness reduction of the frame column is identified as about 8.3% in Case 3 when the depth of the cut equals 15 mm. Based on the displacement-based finite element method, the theoretical equivalent stiffness reduction of the damaged frame column is derived as 5% in the case of cut depth \(d\) = 15 mm. It is illustrated that the location and  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Case 1** & **Case 2** & **Case 3** \\ \hline \multirow{2}{*}{**Configuration**} & \multirow{2}{*}{Uncontrolled} & Controlled with & Controlled with \\  & & TRMD & TRMD \\ \multirow{2}{*}{} & \multirow{2}{*}{Intact} & \multirow{2}{*}{Intact} & \(d\) = 15 mm \\  & & & \(b\) = 100 mm \\ \hline \hline \end{tabular}
\end{table}
Table 5: Configuration of the different cases.  
Figure 9: A typical cut in the test.  
extent of the damage can be identified accurately for the laboratory-controlled frame by the proposed method.