{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,13]],"date-time":"2026-01-13T16:51:24Z","timestamp":1768323084620,"version":"3.49.0"},"reference-count":30,"publisher":"MDPI AG","issue":"20","license":[{"start":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T00:00:00Z","timestamp":1697587200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["51708429"],"award-info":[{"award-number":["51708429"]}]},{"name":"National Natural Science Foundation of China","award":["2022009"],"award-info":[{"award-number":["2022009"]}]},{"name":"National Natural Science Foundation of China","award":["2023011"],"award-info":[{"award-number":["2023011"]}]},{"name":"Open Projects Foundation of Engineering Research Center of Disaster Prevention and Mitigation of Southeast Coastal Engineering Structures of Fujian Province University","award":["51708429"],"award-info":[{"award-number":["51708429"]}]},{"name":"Open Projects Foundation of Engineering Research Center of Disaster Prevention and Mitigation of Southeast Coastal Engineering Structures of Fujian Province University","award":["2022009"],"award-info":[{"award-number":["2022009"]}]},{"name":"Open Projects Foundation of Engineering Research Center of Disaster Prevention and Mitigation of Southeast Coastal Engineering Structures of Fujian Province University","award":["2023011"],"award-info":[{"award-number":["2023011"]}]},{"name":"Construction Science and Technology Plan Projects of Hubei Province","award":["51708429"],"award-info":[{"award-number":["51708429"]}]},{"name":"Construction Science and Technology Plan Projects of Hubei Province","award":["2022009"],"award-info":[{"award-number":["2022009"]}]},{"name":"Construction Science and Technology Plan Projects of Hubei Province","award":["2023011"],"award-info":[{"award-number":["2023011"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>This paper introduces an innovative model for heavy-haul train\u2013track\u2013bridge interaction, utilizing a coupling matrix representation based on the virtual work principle. This model establishes the relationship between the wheel\u2013rail contact surface and the bridge\u2013rail interface concerning internal forces and geometric constraints. In this coupled system\u2019s motion equation, the degrees of freedom (DOFs) of the wheelsets in a heavy-haul train lacking primary suspension are interdependent. Additionally, the vertical and nodding DOFs of the bogie frame are linked with the rail element. A practical application, a Yellow River Bridge with a heavy-haul railway line, is used to examine the accuracy of the proposed model with regard to discrepancy between the simulated and measured displacement ranging from 1% to 11%. A comprehensive parametric analysis is conducted, exploring the impacts of track irregularities of varying wavelengths, axle load lifting, and the degradation of bridge stiffness and damping on the dynamic responses of the coupled system. The results reveal that the bridge\u2019s dynamic responses are particularly sensitive to track irregularities within the wavelength range of 1 to 20 m, especially those within 1 to 10 m. The vertical displacement of the bridge demonstrates a nearly linear increase with heavier axle loads of the heavy-haul trains and the reduction in bridge stiffness. However, there is no significant rise in vertical acceleration under these conditions.<\/jats:p>","DOI":"10.3390\/s23208550","type":"journal-article","created":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T10:36:56Z","timestamp":1697625416000},"page":"8550","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Analysis of Train\u2013Track\u2013Bridge Coupling Vibration Characteristics for Heavy-Haul Railway Based on Virtual Work Principle"],"prefix":"10.3390","volume":"23","author":[{"given":"Nanhao","family":"Wu","sequence":"first","affiliation":[{"name":"School of Civil Engineering and Architecture, Wuhan Institute of Technology, Wuhan 430073, China"}]},{"given":"Hongyin","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Civil Engineering and Architecture, Wuhan Institute of Technology, Wuhan 430073, China"},{"name":"National Key Laboratory of Bridge Intelligent and Green Construction, Wuhan 430034, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6232-1131","authenticated-orcid":false,"given":"Haleem","family":"Afsar","sequence":"additional","affiliation":[{"name":"Department of Civil and Airport Engineering, College of Civil Aviation, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China"}]},{"given":"Bo","family":"Wang","sequence":"additional","affiliation":[{"name":"National Key Laboratory of Bridge Intelligent and Green Construction, Wuhan 430034, China"}]},{"given":"Jianfeng","family":"Fan","sequence":"additional","affiliation":[{"name":"Wuhan Mafangshan Engineering Structure Testing Co., Ltd., Wuhan 430070, China"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.conbuildmat.2019.01.184","article-title":"Dynamic behavior and stability of soil foundation in heavy haul railway tracks: A review","volume":"205","author":"Lazorenko","year":"2019","journal-title":"Constr. 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