## 5 Conclusions  
To study the riding comfort of a straddle-type monorail considering the influence of the bridge structure, a model of a coupled straddle-type monorail system based on SIMPACK and ANSYS was established in this study. Since the vehicle model with 35 DOFs was established directly in SIMPACK, complicated programming was avoided, and the simulation of a moving vehicle load was more convenient. Dynamic analyses were carried out to study the influencing factors of riding comfort, and measures to improve the riding comfort from the perspective of the bridge structure were explored. For the 3 m \(\times\) 22 m double-track beam bridge and the four straddle-type monorail trains studied in this study, the following main conclusions could be drawn:  
1. The bridge acceleration was positively correlated with speed, whereas the bridge deflection had little correlation with speed. The acceleration and Sperling indices of the vehicle increased with increasing speed, which meant that the riding comfort became worse. Speeds below 75 km/h could ensure good operation conditions. In all cases, the maximum vertical and lateral Sperling indices were 2.512 and 0.933, respectively; the lateral comfort of the vehicle was better due to the symmetrical horizontal wheels.
2. Taking the linear stiffness of the pier as the index of the bridge pier height, the influence of different pier heights on riding comfort is analyzed. The results showed that the vehicle-bridge response generally decreased as the linear stiffness of the pier increased; when the stiffness of the pier was low, the flexibility of the bridge was high. The lateral dynamic responses of the vehicle and bridge were very sensitive to changes in the linear stiffness of the pier.
3. When the amplitude of the irregularity reached the Chinese national B-level road roughness, the vertical Sperling index was 2.906, which indicated poor riding comfort. In practice, the surface roughness of the track beam should be strictly controlled. It should be smoother than Chinese national A-level road roughness, and the range should be between \(-\)8 mm and 8 mm. Based on a large number of actual measurements on the track beam surface roughness of straddle-type monorails, a roughness index similar to the International Roughness Index (IRI) could be proposed, and its threshold could be specified to provide guidance for related projects.
4. The proposed measures that increased the stiffness of the track beam were effective for the improvement of riding comfort, such as increasing the thickness of the inner cross-beams and increasing the height of the track beams.  
The authors contributed equally to this work. [PERSON] and [PERSON] conceived and prepared the original draft. [PERSON] and [PERSON] provided analysis tools. [PERSON] and [PERSON] analyzed the data. [PERSON] and [PERSON] reviewed the manuscript. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by the National Natural Science Foundation of China (grant No. 51778194), the China Postdoctoral Science Foundation (grant No. 2017M621282), and the Fundamental Research Funds for the Central Universities (grant No. HIT. NSRIF. 2019056).  
**Conflicts of Interest:** The authors declare no conflicts of interest regarding the publication of this manuscript.