{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:17:16Z","timestamp":1760145436804,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2024,7,25]],"date-time":"2024-07-25T00:00:00Z","timestamp":1721865600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["2021.08011.BD","UIDB\/04708\/2020","UIDP\/04708\/2020","UIDB\/50022\/2020","UIDP\/50022\/2020","C645644454-00000065"],"award-info":[{"award-number":["2021.08011.BD","UIDB\/04708\/2020","UIDP\/04708\/2020","UIDB\/50022\/2020","UIDP\/50022\/2020","C645644454-00000065"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Instituto de I&amp;D em Estruturas e Constru\u00e7\u00f5es","award":["2021.08011.BD","UIDB\/04708\/2020","UIDP\/04708\/2020","UIDB\/50022\/2020","UIDP\/50022\/2020","C645644454-00000065"],"award-info":[{"award-number":["2021.08011.BD","UIDB\/04708\/2020","UIDP\/04708\/2020","UIDB\/50022\/2020","UIDP\/50022\/2020","C645644454-00000065"]}]},{"name":"FCT\/MCTES (PIDDAC)","award":["2021.08011.BD","UIDB\/04708\/2020","UIDP\/04708\/2020","UIDB\/50022\/2020","UIDP\/50022\/2020","C645644454-00000065"],"award-info":[{"award-number":["2021.08011.BD","UIDB\/04708\/2020","UIDP\/04708\/2020","UIDB\/50022\/2020","UIDP\/50022\/2020","C645644454-00000065"]}]},{"name":"Recovery and Resilience Plan (PRR)","award":["2021.08011.BD","UIDB\/04708\/2020","UIDP\/04708\/2020","UIDB\/50022\/2020","UIDP\/50022\/2020","C645644454-00000065"],"award-info":[{"award-number":["2021.08011.BD","UIDB\/04708\/2020","UIDP\/04708\/2020","UIDB\/50022\/2020","UIDP\/50022\/2020","C645644454-00000065"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Applied Sciences"],"abstract":"<jats:p>A novel modeling solution (MS) was created that can provide realistically accurate results on the natural frequencies of a railway subgrade layer in the context of a railway infrastructure numerical simulation. This MS was specifically developed for implementation in a multibody simulation (MBS) model, which constitutes a step forward in relation to the state-of-art of this specific topic. The main obstacle was to find a criterion to define the geometry and dimensions of the subgrade elements inside the numerical model, so that the resulting resonance frequencies would be realistically accurate and representative. The proposed MS combines four theoretical models to create a set of equations that enables a deterministic relationship between the height and the diameter of a cylindrically shaped subgrade layer element to be implemented in the MBS model. This MS is dedicated to simulating scenarios involving railway infrastructure and a railway vehicle. However, its background theoretical models are adaptable to simulating other model configurations. This article details the MS and a sensitivity analysis that was performed to assess it. These tests were performed using the MBS software Simpack\u00ae (version 2021x). The results obtained from these tests support the selected theoretical equations and the overall validity of the proposed MS.<\/jats:p>","DOI":"10.3390\/app14156510","type":"journal-article","created":{"date-parts":[[2024,7,25]],"date-time":"2024-07-25T14:31:07Z","timestamp":1721917867000},"page":"6510","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Railway Substructure Modeling Approach for Modal Analysis Using Multibody Simulation"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9589-6185","authenticated-orcid":false,"given":"Jo\u00e3o","family":"Morais","sequence":"first","affiliation":[{"name":"Scientific Instrumentation Centre, National Laboratory for Civil Engineering, 1700-066 Lisbon, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9968-0821","authenticated-orcid":false,"given":"Eduardo","family":"Fortunato","sequence":"additional","affiliation":[{"name":"Transportation Department, National Laboratory for Civil Engineering, 1700-066 Lisbon, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8624-9904","authenticated-orcid":false,"given":"Diogo","family":"Ribeiro","sequence":"additional","affiliation":[{"name":"CONSTRUCT-LESE, School of Engineering, Polytechnic of Porto, 4249-015 Porto, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4254-1879","authenticated-orcid":false,"given":"Joaquim","family":"Mendes","sequence":"additional","affiliation":[{"name":"INEGI, Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2024,7,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Azimi, M., Eslamlou, A., and Pekcan, G. (2020). Data-Driven Structural Health Monitoring and Damage Detection through Deep Learning: State-of-the-Art Review. Sensors, 20.","DOI":"10.3390\/s20102778"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"107077","DOI":"10.1016\/j.ymssp.2020.107077","article-title":"A review of vibration-based damage detection in civil structures: From traditional methods to Machine Learning and Deep Learning applications","volume":"147","author":"Avci","year":"2021","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_3","unstructured":"INNOTRACK (2019, March 03). Methods of Track Stiffness Measurements. Thematic Priority 6: Sustainable Development, Global Change and Ecosystems Project No. TIP5-CT-2006-031415O, Co-Funded by the European Commission within the Sixth Framework Programme (2002\u20132006). . Available online: https:\/\/insitutek.com\/documents\/methods-of-track-stiffness-measurements-innotrack-guideline-project-no-tip5-ct-2006-031415-pdf\/."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"89","DOI":"10.1007\/s40534-016-0104-8","article-title":"Overview and outlook on railway track stiffness measurement","volume":"24","author":"Wang","year":"2016","journal-title":"J. Mod. Transp."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Sousa, E., Bragan\u00e7a, C., Meixedo, A., Ribeiro, D., Bittencourt, T.N., and Carvalho, H. (2023). Drive-by Methodologies Applied to Railway Infrastructure Subsystems: A Literature Review\u2014Part I: Bridges and Viaducts. Appl. Sci., 13.","DOI":"10.3390\/app13126982"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Kong, X., and Cai, C.S. (2017). The State-of-the-Art on Framework of Vibration-Based Structural Damage Identification for Decision Making. Appl. Sci., 7.","DOI":"10.3390\/app7050497"},{"key":"ref_7","unstructured":"Berggren, E. (2009). Railway Track Stiffness\u2014Dynamic Measurements and Evaluation for Efficient Maintenance. [Ph.D. Dissertation, KTH Royal Institute of Technology]."},{"key":"ref_8","first-page":"3507344","article-title":"Modern Tendencies in Vehicle-based Condition Monitoring of the Railway Track","volume":"72","author":"Martin","year":"2023","journal-title":"IEEE Trans. Instrum. Meas."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"108331","DOI":"10.1016\/j.soildyn.2023.108331","article-title":"On railway track receptance","volume":"177","author":"Connolly","year":"2024","journal-title":"Soil Dyn. Earthq. Eng."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Zhai, W. (2020). Vehicle\u2013Track Coupled Dynamics. Theory and Applications, Springer.","DOI":"10.1007\/978-981-32-9283-3"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"103","DOI":"10.1016\/j.jsv.2004.06.017","article-title":"The excitation of ground vibration by rail traffic: Theory of vehicle\u2013track\u2013soil interaction and measurements on high-speed lines","volume":"284","author":"Auersch","year":"2005","journal-title":"J. Sound Vib."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1080\/00423114.2012.734627","article-title":"Investigating the influence of soil properties on railway traffic vibration using a numerical model","volume":"51","author":"Kouroussis","year":"2012","journal-title":"Veh. Syst. Dyn."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"132715","DOI":"10.1016\/j.conbuildmat.2023.132715","article-title":"A critical review on the vertical stiffness irregularity of railway ballasted track","volume":"400","author":"Shi","year":"2023","journal-title":"Constr. Build. Mater."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"100350","DOI":"10.1016\/j.trgeo.2020.100350","article-title":"Rigorous vehicle-soil-track simulation of high-speed rail through optimization-based model order reduction","volume":"23","author":"Lesgidis","year":"2020","journal-title":"Transp. Geotech."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1080\/15732479.2021.1936569","article-title":"Systems thinking approach for improving maintenance management of discrete rail assets: A review and future perspectives","volume":"19","author":"Shang","year":"2021","journal-title":"Struct. Infrastruct. E"},{"key":"ref_16","first-page":"9","article-title":"Railway track support condition assessment\u2014Initial developments on a vehicle-based monitoring solution through modal analysis","volume":"236","author":"Morais","year":"2021","journal-title":"Proc. Inst. Mech. Eng. Part F J. Rail Rapid Transit."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"107483","DOI":"10.1016\/j.engfailanal.2023.107483","article-title":"Railway track support condition assessment\u2014Methodology validation using numerical simulations","volume":"152","author":"Morais","year":"2023","journal-title":"Eng. Fail. Anal."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1177\/058310249803000201","article-title":"A Summary Review of Vibration-Based Damage Identification Methods","volume":"30","author":"Doebling","year":"1998","journal-title":"Shock Vib. Dig."},{"key":"ref_19","unstructured":"Esveld, C. (2001). Modern Railway Track, MRT-Productions."},{"key":"ref_20","unstructured":"Maia, N., and Silva, J. (1997). Theoretical and Experimental Modal Analysis, Research Studies Press."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Selig, E., and Waters, J. (1994). Track Technology and Substructure Management, Thomas Telford Productions.","DOI":"10.1680\/tgasm.20139"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1002\/eqe.4290140502","article-title":"Approximate Dynamic Model of Embedded Foundation in Time Domain","volume":"14","author":"Wolf","year":"1986","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1080\/00423114.2019.1677920","article-title":"The influence of variation in track level and support system stiffness over longer lengths of track for track performance and vehicle track interaction","volume":"59","author":"Milne","year":"2019","journal-title":"Veh. Syst. 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