# Study on Passenger Comfort Based on Human-Bus-Road Coupled Vibration
## 4 Case Study  
### Description of Numerical Example  
A numerical study was conducted to investigate human comfort under different road levels. Road surface roughness is the main excitation of human-bus-road coupled vibration, which has a great impact on human comfort. The parameters of the numerical example: the road is a two-way highway with six lanes, the interlayer friction coefficient of the asphalt pavement is 0.5, the bus speed is 36 km/h, and the weight of the bus is 15.89 t. The influence of four road surface roughness levels, i.e., Levels A, B, C, and D on human-bus-road dynamic response is analyzed. The asphalt road model is established according to the layered method. For the asphalt road with large thickness and high modulus of elasticity, the surface layer, base, and subbase can be regarded as linear elasticity, and the stress-strain relationship meets Hooke's law. The soil foundation is regarded as an elastoplastic body, and its stress-strain relationship follows the Drucker-Prager criterion. Since the elastic modulus of the surface layer, base, and subbase are close, the interlayer contact can be considered as flexible-flexible contact. Assuming that the elastic modulus of the subbase is much higher than that of the soil foundation, the contact between the subbase and the soil foundation can be considered as rigid-flexible contact. Each layer is simulated with the Solid186 element in the ANSYS program. The contact between layers is simulated using a pair of contact elements, i.e., Targe170 (3D) and Conta173 (3D), where the surface with larger stiffness is the target surface [26]. The road model consists of 162,000 elements and 178,006 nodes. The boundary conditions of the road are determined by [PERSON]'s principle. The nodes of the road model are symmetrically constrained in X and Y directions, and the nodes on the bottom surface of the soil foundation are fixed. The finite element model of the asphalt road is shown in Figure 4. The structural parameters of the asphalt road are shown in Table 2.  
The road surface roughness is classified into eight levels, i.e., A-H [27]. B and C levels are the most common road surface conditions, accounting for a large proportion. For demonstration, the road surface roughness of a 100-m road in B and C levels is generated with a sampling distance of 0.05, as shown in Figure 5. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Structure** & **Thickness/cm** & **Elastic** & **Poisson’s** & **Density/(kg/m\({}^{3}\))** & **Damping** \\
**Layer** & **Modelus/MPa** & **Ratio** & **Ratio** & **Ratio** (\(Q\))** \\ \hline Upper layer & 10 & 1400 & 0.25 & 2500 & 0.05 \\ Lower layer & 10 & 1200 & 0.25 & 2500 & 0.05 \\ Base & 20 & 1000 & 0.25 & 2400 & 0.05 \\ Subbase & 20 & 900 & 0.25 & 2300 & 0.05 \\ Soil foundation & 540 & 60 & 0.4 & 1900 & 0.05 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Structural parameters of asphalt road. Figure 4: Finite element model of asphalt road. The PSD of road surface roughness is obtained using the FIT method, as shown in Figure 6. Meanwhile, the PSD using the random sine wave superposition method is also obtained, as shown in Figure 7. It is found that the PSD obtained from the random sine wave superposition method has a large error, especially at high frequencies, while the PSD obtained from the FIT method is consistent with the value calculated from Equation (4). Figure 5: Road roughness curves of B and C levels. Figure 6: C-level roughness power spectral density (PSD) by the Fourier inverse transformation (FIT) method. Figure 7: C-level road surface roughness PSD by random sine wave superposition method. The human-bus model with 13 DOF is shown in Figure 8. The bus has 7 DOF, that is, pitch, roll, vertical motion of the bus body, and vertical motions of the four wheels. Three passengers are considered on the bus with two vertical DOF for each passenger. The bus parameters are based on the intercity bus IK-301 in the literature, and the mass, stiffness, and damping values are shown in Table 3[28].