## 5 Laboratory Test Verification
Therefore, when applying Equations (5) and (6), the position of the center of the test vehicle, which is the same distance as the front and rear wheels, is used as the contact point between the vehicle and bridge. Figure 11: Vertical acceleration spectrum of free vibration at 1/4 span: (**a**) single-piece and (**b**) double-piece steel beam. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & \(L\) & \(m_{b}\) & \(EI\) \\ \hline Value & 3 m & 8.6 kg/m & 1.22\(\times\)10\({}^{4}\) N\(\cdot\)m\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Structural parameters of single-piece steel beam. The layout of laboratory experiment is shown in Figure 14. The acceleration sensors are respectively arranged in the center of the vehicle, 1/4 (3/4) span and mid span of the bridge, respectively. The speed of the vehicle is controlled by an adjustable speed motor. A one-car length of space, which is 35 cm away from the two ends, is set as the entry and exit region. Result data excluding the entry and exit region is used for further analysis. At a distance of 35 cm from the support, a protrusion is set. When the vehicle passes through the protrusion, the acceleration signal will produce a significant fluctuation, which is used as a sign of the vehicle entering and leaving the bridge. A set of vehicle acceleration signals contains four obvious fluctuations, and the data between 0.5 s after the second fluctuation and 0.5 s before the third fluctuation are selected for analysis. This ensures that the front and rear wheels of the vehicle are on the bridge at the same time. Moreover, because the speed of the test vehicle passing through the bridge is different, the red box in Figure 15 is only for illustration. The test parameters and results are dimensionless as shown in Table 4. Partial experimental results and their spectrum are shown in Figure 15. To compare the frequency change pattern and provide references for frequency identification, let \(\Delta_{st}\) denote the frequency deviation rate when the vehicle is stationary in the middle of the span. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Steel Beam** & **Vehicle** & \(\mathbf{\mu_{1}}\) & \(\mathbf{\alpha_{\text{mr}}}\) & \(\mathbf{\Delta_{st}}\) & \(\mathbf{\alpha_{v}}\) & \begin{tabular}{c} **Identified Steel** \\ **Beam Frequency** \\ \end{tabular} & \begin{tabular}{c} **Experimental** \\ \(\mathbf{\Delta_{b}}\) \\ \end{tabular} & \begin{tabular}{c} **Theoretical** \\ \(\mathbf{\Delta_{b}}\) \\ \end{tabular} \\ \hline \multirow{3}{*}{Single-piece} & Light & – & 0.16 & \(-\)14.40\% & \begin{tabular}{c} 0.027 \\ 0.045 \\ 0.066 \\ \end{tabular} & \begin{tabular}{c} 5.67 Hz \\ 5.58 Hz \\ \end{tabular} & \begin{tabular}{c} \(-\)11.27\% \\ \(-\)12.36\% \\ \end{tabular} & \begin{tabular}{c} \(-\)11.22\% \\ \(-\)10.26\% \\ \end{tabular} \\ \cline{2-10}  & Heavy & 1.46 & 0.39 & \(-\)29.26\% & 0.031 & 4.62 Hz & \(-\)27.54\% & \(-\)27.06\% \\ \hline \multirow{3}{*}{Double-piece} & Light & – & 0.08 & \(-\)7.79\% & \begin{tabular}{c} 0.031 \\ 0.050 \\ 0.091 \\ \end{tabular} & \begin{tabular}{c} 5.82 Hz \\ 5.84 Hz \\ 5.90 Hz \\ \end{tabular} & \begin{tabular}{c} \(-\)7.47\% \\ \(-\)7.15\% \\ \(-\)6.20\% \\ \end{tabular} & \begin{tabular}{c} \(-\)5.47\% \\ \(-\)7.15\% \\ \(-\)6.20\% \\ \end{tabular} \\ \cline{2-10}  & Heavy & 1.48 & 0.20 & \(-\)11.76\% & \begin{tabular}{c} 0.030 \\ 0.051 \\ 0.094 \\ \end{tabular} & \begin{tabular}{c} 5.22 Hz \\ 5.17 Hz \\ 5.16 Hz \\ \end{tabular} & \
\begin{tabular}{c} \(-\)17.01\% \\ \(-\)17.81\% \\ \(-\)17.97\% \\ \end{tabular} &
\begin{tabular}{c} \(-\)17.94\% \\ \(-\)16.98\% \\ \(-\)15.54\% \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Test parameters and results. Figure 12: Design drawing of the test vehicle: (**a**) main view and (**b**) top view. Figure 13: Free vibration of heavy vehicle: vertical acceleration (**a**) response and (**b**) spectrum. From Table 4, most of the test results show that the measured frequency deviation is larger than the theoretical simulated value.