## 4 Seat-Human Body Coupled Dynamics Model of High-Speed Trains  
The multibody dynamics method was used to establish the human body dynamics model. The model considered the human body as a total of 17 rigid masses representing head, neck, chest, abdomen, hips, upper arms, forearms, hands, thighs, calves, and feet. The masses of each part were connected to each other by articulation and force units. The inertia parameters (masses and moment inertia of the X-axis (\(I_{\mathrm{xx}}\)), the Y-axis (\(I_{\mathrm{yy}}\)), and the Z-axis (\(I_{\mathrm{zz}}\))) of each part of the human body were obtained from [18; 19; 20], as shown in Table 1. The abdomen and hips were treated as a mass block and connected to the thighs. The height of the mannequin was set to 175 cm, and the total mass of the human body was 66 kg, which was the same as the experiment. High-speed train seats are composed of two-person seats and three-row seats. The seats can be treated as consisting of multiple single seats, and each single seat is rigidly connected to the bottom seat frame by bolts. The seat frame supports were bolted together with the floor. The multibody dynamics method was used to establish the seat model, and the seat was decomposed into seat frame, seat upholstery, backrest skeleton, backrest upholstery, armrest, bottom frame, and frame bracket. The seat frame and the backrest skeleton were hinged, and the degrees of freedom were constrained to only lateral plane rotation. The seat upholstery and backrest upholstery were connected to the frame by a bushing unit, while rigid connections were applied between the armrests, seat frame, and frame brackets. Table 2 shows the stiffness and damping parameters of the seat, where \(K_{t}\) and \(C_{t}\) represent the translational stiffness and damping, respectively, while \(K_{r}\) and \(C_{r}\) represent the rotational stiffness and damping, respectively. Then, the high-speed train seat-human body coupled dynamics model was established for the three-seat seat-human body coupled dynamics model and the two-seat seat-human body coupled dynamics model, as shown in Figure 7. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Place** & **Mass Distribution Percentage** & **Part Mass (kg)** & \(I_{\mathrm{xx}}\) (kg\(\cdot\)m\({}^{2}\)) & \(I_{yy}\) (kg\(\cdot\)m\({}^{2}\)) & \(I_{zz}\) (kg\(\cdot\)m\({}^{2}\)) \\ \hline Head + neck & 8.62\% & 5.69 & 0.036 & 0.037 & 0.016 \\ torso & 44.05\% & 29.07 & 0.94 & 0.99 & 0.18 \\ Upper arm & 2.43\% & 1.60 & 0.027 & 0.026 & 0.0025 \\ Forearm & 1.25\% & 0.83 & 0.0067 & 0.0066 & 0.0007 \\ Hand & 0.64\% & 0.42 & 0.0010 & 0.0009 & 0.002 \\ Thigh & 14.19\% & 9.37 & 0.14 & 0.14 & 0.017 \\ Calf & 3.67\% & 2.42 & 0.025 & 0.025 & 0.003 \\ Feet & 1.48\% & 0.98 & 0.009 & 0.007 & 0.009 \\ Abdomen and hips & 23.67\% & 15.62 & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Ratio of mass distribution and moment of inertia of various parts of the human body. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Place** & \(K_{t}\) (N/m) & **K\({}_{r}\)** & \(C_{t}\) (N\(\cdot\)m\(\cdot\)s/m) & **(N\(\cdot\)m\(\cdot\)s/rad)** \\ \hline Seat cushion & 10,000 & 350 & 1000 & 35 \\ Seat bracket & 10,000 & 300 & 1000 & 30 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: High-speed train seat parameters. In order to verify the accuracy of the seat-human body coupled dynamics model, 0-20 Hz sweep frequency excitation with intensity of 0.5 m/s\({}^{2}\) r.m.s. was applied at the bolted junction between the seat and the floor, and the duration was 20 s. The experimental results were from the on-site vibration test outlined in Section 2. In the simulation, measuring points were set at the interface between human body and seat cushion.