## 5 Laboratory Test Verification  
The test uses steel beams to simulate the bridge, and the design frequency of steel beams is about 7 Hz. The design drawing of the steel beam is shown in Figure 8. The steel beam is made of 3-mm thick steel plate, which is 3 m long and 30 cm wide. The steel plate is equipped with 2 longitudinal ribs and 5 transverse ribs The ribs are made of iron slats with a width of 3 cm and a thickness of 3 mm. Two longitudinal ribs are arranged symmetrically with an interval of 15 cm, and 5 transverse ribs are respectively arranged at the end, 1/4 span, and mid-span of the beam. Dimensions of the support is shown in Figure 8 The finite element model of the steel beam is established by using shell elements. The first three vertical frequencies of the steel beam are 7.00 Hz, 25.24 Hz, and 55.05 Hz, and the corresponding vibration modes are shown in Figure 9. During the test, the beam body adopts single-piece steel beam and double-piece steel beam to simulate the increase of bridge mass. The first three tested vertical frequencies of the single-piece steel beam are 6.39 Hz, 25.45 Hz, and 54.33 Hz. The first three vertical frequencies of the double-piece steel beam are 6.29 Hz, 25.17 Hz, and 55.32 Hz. The time history curve and frequency spectrum of the test are shown in Figures 10 and 11 and the structural parameters of the single-piece steel beam are shown in Table 3. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & & \(\mu_{1}\) \textless{} 1 & & & \(\mu_{1}\) \textgreater{} 1 & \\  & \(\mu_{1}\) & \(\alpha_{mv}\) & \(\alpha_{v}\) & \(\mu_{1}\) & \(\alpha_{mv}\) & \(\alpha_{v}\) \\ \hline \(\mu\) & 5.650 \(\times\) 10\({}^{-1}\) & 4.258 \(\times\) 10\({}^{-1}\) & 5.417 \(\times\)10\({}^{-1}\) & 5.333 \(\times\) 10\({}^{-2}\) & 6.200 \(\times\) 10\({}^{-1}\) & 3.625 \(\times\) 10\({}^{-1}\) \\ \(\sigma\) & 3.180 \(\times\) 10\({-1}\) & 5.106 \(\times\) 10\({}^{-1}\) & 4.010 \(\times\) 10\({}^{-1}\) & 3.409 \(\times\) 10\({}^{-3}\) & 2.378 \(\times\) 10\({}^{-1}\) & 2.251 \(\times\) 10\({}^{-2}\) \\ \hline \end{tabular}
\end{table} 
Table 2: Parameters’ sensitivity analysis results. Figure 8: Design drawing of the steel beam: (**a**) main view and (**b**) side view. Figure 10: Vertical acceleration response of free vibration at \(1/4\) span: (**a**) single-piece and (**b**) double-piece steel beam. Figure 9: The first three vertical modes of the steel beam: (**a**) 7.00 Hz, (**b**) 25.24 Hz, and (**c**) 55.05 Hz. The main structure of the test vehicle is also made of 3-mm thick steel plates, the length and width are 35 cm and 25 cm, respectively. As shown in Figure 12, the test vehicle is a double-layer structure, with 4 springs symmetrically arranged between the upper and lower layers. Steel plates with dimensions 35 cm \(\times\) 25 cm \(\times\) 3 mm are used as the counterweight above the springs in the upper layer of the vehicle. The frequency of the vehicle itself can be altered by adjusting the mass of the upper structure, which is the number of steel plates, and the stiffness of the spring. The vehicle mass is differentiated into the light and heavy categories. Light vehicles have no upper structure, and their frequency is much higher than the bridge frequency. Heavy vehicles have an upper layer mass of 6.18 kg. The vehicle frequency is tested to be 9.33 Hz. The time history curve and frequency spectrum of the test are shown in Figure 13. In the case of light and heavy vehicles, the vehicle passes through single- and double-steel beams at different speeds, respectively. Specific conditions of the four testing scenarios are listed in Table 4. As shown in Figure 12, the test vehicle is symmetrical. Due to the limitation of the vertical rod, the upper layer of the vehicle is mainly vertical movement, and there is almost no front and rear rocking movement. When the test vehicle is simplified to a one degree-of-freedom oscillator, the front and rear springs of the test vehicle are simplified to a single spring element in parallel.