{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,10]],"date-time":"2026-06-10T11:14:52Z","timestamp":1781090092226,"version":"3.54.1"},"reference-count":32,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2021,11,8]],"date-time":"2021-11-08T00:00:00Z","timestamp":1636329600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In order to research train derailment law under ship impact, the spatial vibration calculation model of a freight train-track-bridge (FTTB) system is used to establish the vibration model of the FTTB system under ship impact. Meanwhile, the calculation method of a train derailment process under ship impact is proposed based on the random analysis method of train derailment energy. Further, the train derailment process on a bridge under ship impact is calculated, and the variation law of the FTTB system spatial vibration response under different impact loads and speeds is analyzed. The results show that the ship impact load has a great influence on wheel lift value. When the impact load is greater than 15 MN, the wheel derails more easily. With the increase of impact load, the derailment coefficient, wheel load reduction rate, and lateral relative displacement of bogie and rail, the lateral displacement of the bridge increases significantly, but the limits of them make it difficult to determine whether the wheel has derailed. The lateral relative displacement of the bogie and rail considering the safety factor is calculated at the moment of derailment, which is taken as the early warning threshold of train derailment. The above conclusions can provide a reference for controlling train safety under ship impact.<\/jats:p>","DOI":"10.3390\/sym13112122","type":"journal-article","created":{"date-parts":[[2021,11,8]],"date-time":"2021-11-08T22:08:41Z","timestamp":1636409321000},"page":"2122","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Train Derailment Process Analysis on Heavy Haul Railway Bridge under Ship Impact"],"prefix":"10.3390","volume":"13","author":[{"given":"Kai","family":"Gong","sequence":"first","affiliation":[{"name":"Engineering Research Center of Railway Environmental Vibration and Noise Ministry of Education, East China Jiaotong University, Nanchang 330013, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Linya","family":"Liu","sequence":"additional","affiliation":[{"name":"Engineering Research Center of Railway Environmental Vibration and Noise Ministry of Education, East China Jiaotong University, Nanchang 330013, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Cuiying","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Science, East China Jiaotong University, Nanchang 330013, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chen","family":"Wang","sequence":"additional","affiliation":[{"name":"Engineering Research Center of Railway Environmental Vibration and Noise Ministry of Education, East China Jiaotong University, Nanchang 330013, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,11,8]]},"reference":[{"key":"ref_1","unstructured":"Larry, D., and Olson, P.E. 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