# Evaluation of Ride Comfort under Vortex-Induced Vibration of Long-Span Bridge
## Appendix A Vehicle Dynamics Equations and Related Parameters
\begin{array}{c}0_{5\times 1}\\ k_{11y}q_{1y}+c_{11y}\dot{q}_{1y}\\ k_{1 tz}q_{1z}+c_{1 tz}\dot{q}_{1z}\\ k_{2y}q_{2y}+c_{2y}\dot{q}_{2y}\\ k_{1z}q_{2z}+c_{2 tz}\dot{q}_{2z}\\ k_{13y}q_{3y}+c_{13y}\dot{q}_{3y}\\ k_{3z}q_{3z}+c_{13z}\dot{q}_{3z}\\ k_{4y}q_{4y}+c_{4y}\dot{q}_{4y}\\ k_{4z}q_{4z}+c_{4z}\dot{q}_{4z}\end{array} \right. \tag{11}\]  
\[\left\{ \begin{array}{c}q_{1z}=y_{r1z}+y_{\varphi 1z}\\ q_{2z}=y_{r2z}+y_{\varphi 2z}\\ q_{3z}=y_{r32}+y_{\varphi 3z}\\ q_{4z}=y_{r42}+y_{\varphi 4z}\end{array} \right.\left\{ \begin{array}{c}q_{1y}=y_{r1y}+y_{ \varphi 1y}\\ q_{2y}=y_{r2y}+y_{\varphi 2y}\\ q_{3y}=y_{r3y}+y_{\varphi 3y}\\ q_{4y}=y_{r4y}+y_{\varphi 4y}\end{array} \right. \tag{12}\]  
where \(m_{s}\) is the mass of the vehicle body; \(m_{ti}\) (\(i\) = 1, 2; 3; 4) represents the total mass of the vehicle's suspension devices and tires; \(k_{sij}\) and \(k_{siz}\) represent the lateral and vertical spring stiffness of the vehicle suspension system; \(k_{tiy}\) and \(k_{tiz}\) represent the lateral and vertical spring stiffness of the vehicle tires; \(c_{sij}\) and \(c_{siz}\) represent the lateral and vertical damping of the vehicle suspension system; \(c_{tiy}\) and \(c_{tiz}\) represent the lateral and vertical damping of the vehicle tires; \(\theta_{xz}\), \(\theta_{yz}\), and \(\theta_{xy}\) represent the pitch angle, roll angle, and yaw angle of the vehicle body, respectively; \(y_{y}\) and \(y_{z}\) represent the lateral and vertical displacement of the vehicle body; \(y_{tiy}\) and \(y_{tiz}\) represent the lateral and vertical displacement of the wheel; \(i\) represents the \(i\)-th wheel (\(i\) = 1, 2, 3, 4). \(y_{riy}\) and \(y_{riz}\) represent the lateral and vertical excitation of the wheel when it is excited by road irregularities, and \(y_{viy}\) and \(y_{viz}\) represent the lateral and vertical excitation of the wheel when it is excited by the vibration of the bridge. \(a_{1}\) and \(a_{2}\) represent the distance from the front and rear axes to the center of gravity of the car, and \(b_{1}\) and \(b_{2}\) represent the lateral distances from the left and right wheels to the center of gravity of the vehicle. The related parameters of vehicle are shown as Table 1. The selection of vehicle parameters refers to References [15; 23; 25]. \begin{table}
\begin{tabular}{c c c c c} \hline
**Parameter** & **Sedan Car** & **Light Truck** & **Mini Van** & **Motor Bus** \\ \hline \(m_{s}\)(kg) & 1600 & 6500 & 6000 & 12,190 \\ \(m_{t1}\), \(m_{t2}\)(kg) & 80 & 800 & 800 & 240 \\ \(m_{t3}\), \(m_{t4}\)(kg) & 80 & 800 & 700 & 525 \\ \(J_{xz}\)(kg/m\({}^{2}\)) & 2000 & 9550 & 34,000 & 79,000 \\ \(J_{yz}\)(kg/m\({}^{2}\)) & 560 & 3030 & 2950 & 13,000 \\ \(J_{xy}\)(kg/m\({}^{2}\)) & 32,000 & 100,000 & 12,500 & 53,000 \\ \(k_{1 zz}\), \(k_{s2z}\)(kN/m) & 50 & 250 & 200 & 126 \\ \(k_{3z}\), \(k_{t4z}\)(kN/m) & 50 & 250 & 225 & 225 \\ \(c_{t1z}\), \(c_{t2z}\)(kN/s/m) & 6,229 & 2.5 & 3.85 & 9.15 \\ \(c_{t3z}\), \(c_{s4z}\)(kN/m) & 2 & 2.5 & 2.72 & 18.3 \\ \(k_{t1z}\), \(k_{t2z}\)(kN/m) & 192 & 175 & 363 & 750 \\ \(k_{t3z}\), \(k_{t4z}\)(kN/m) & 192 & 175 & 422 & 1500 \\ \(c_{t1z}\), \(c_{t2z}\)(kN-s/m) & 0.6 & 2.5 & 3 & 2 \\ \(c_{t3z}\), \(c_{t4z}\)(kN-s/m) & 0.6 & 2.5 & 3 & 2 \\ \(k_{s1y}\), \(k_{s2y}\)(kN/m) & 110 & 187.5 & 300 & 50 \\ \(k_{s3y}\), \(k_{s4y}\)(kN/m) & 110 & 187.5 & 300 & 85 \\ \(c_{s1y}\), \(c_{s2y}\)(kN-s/m) & 6,229 & 1 & 3.85 & 6 \\ \(c_{s3y}\), \(c_{s4y}\)(kN-s/m) & 2 & 1 & 2.72 & 6 \\ \hline \end{tabular}
\end{table} 
Table 1: The related parameters of vehicles.