{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T15:40:43Z","timestamp":1762443643453,"version":"build-2065373602"},"reference-count":30,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,8,31]],"date-time":"2019-08-31T00:00:00Z","timestamp":1567209600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100014440","name":"Ministerio de Ciencia, Innovaci\u00f3n y Universidades","doi-asserted-by":"publisher","award":["PGC2018-096696-B-I00"],"award-info":[{"award-number":["PGC2018-096696-B-I00"]}],"id":[{"id":"10.13039\/100014440","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100008425","name":"Conseller\u00eda de Cultura, Educaci\u00f3n e Ordenaci\u00f3n Universitaria, Xunta de Galicia","doi-asserted-by":"publisher","award":["ED481A-2019\/230"],"award-info":[{"award-number":["ED481A-2019\/230"]}],"id":[{"id":"10.13039\/501100008425","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we present the optimization of a vibration mitigation system for railway bridges. These structures are subjected to significant moving loads, whose dynamic characteristics may produce resonance effects, compromising the integrity of the bridge and the security of the passengers if the speed or the load of the train is not controlled. The study focuses on the Auxiliary Beam system. It consists of a beam located under the bridge and connected to the slab by viscous dampers. The symmetry of the problem allowed for the use of a 2D Finite Element model of the system. This model was used together with a genetic algorithm in order to evaluate the behaviour of different candidates and to optimize the design parameters: the inertia of the beam and the damper coefficient. The goal of the optimization process is to minimize the acceleration of the bridge while adding the lightest mitigation system possible. The combination of a Finite Element Model and Genetic Algorithm helps to address the complex problem and to find an optimized set of structural parameters. The system finally shows good behaviour for optimal parameters.<\/jats:p>","DOI":"10.3390\/sym11091089","type":"journal-article","created":{"date-parts":[[2019,9,2]],"date-time":"2019-09-02T03:16:12Z","timestamp":1567394172000},"page":"1089","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Optimization of the Auxiliary-Beam System in Railway Bridge Vibration Mitigation Using FEM Simulation and Genetic Algorithms"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0377-7208","authenticated-orcid":false,"given":"Jacobo","family":"Baldonedo","sequence":"first","affiliation":[{"name":"Departamento de Ingenier\u00eda Mec\u00e1nica, M\u00e1quinas y Motores T\u00e9rmicos y Flu\u00eddos, Escola de Enxe\u00f1ar\u00eda Industrial, Campus As Lagoas Marcosende s\/n, 36310 Vigo, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0391-7661","authenticated-orcid":false,"given":"Jos\u00e9 A.","family":"L\u00f3pez-Campos","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda Mec\u00e1nica, M\u00e1quinas y Motores T\u00e9rmicos y Flu\u00eddos, Escola de Enxe\u00f1ar\u00eda Industrial, Campus As Lagoas Marcosende s\/n, 36310 Vigo, Spain"}]},{"given":"Marcos","family":"L\u00f3pez","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda Mec\u00e1nica, M\u00e1quinas y Motores T\u00e9rmicos y Flu\u00eddos, Escola de Enxe\u00f1ar\u00eda Industrial, Campus As Lagoas Marcosende s\/n, 36310 Vigo, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5066-3644","authenticated-orcid":false,"given":"Enrique","family":"Casarejos","sequence":"additional","affiliation":[{"name":"Departamento de Ingenier\u00eda Mec\u00e1nica, M\u00e1quinas y Motores T\u00e9rmicos y Flu\u00eddos, Escola de Enxe\u00f1ar\u00eda Industrial, Campus As Lagoas Marcosende s\/n, 36310 Vigo, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8533-1858","authenticated-orcid":false,"given":"Jos\u00e9 R.","family":"Fern\u00e1ndez","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada I, Universidade de Vigo, ETSI Telecomunicaci\u00f3n, Campus As Lagoas Marcosende s\/n, 36310 Vigo, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2019,8,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1016\/S0376-0421(02)00029-5","article-title":"Aerodynamics of high-speed railway train","volume":"38","author":"Raghunathan","year":"2002","journal-title":"Prog. Aerosp. Sci."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"936","DOI":"10.1016\/S0141-0296(97)00001-1","article-title":"Vibration of simple beams due to trains moving at high speeds","volume":"19","author":"Yang","year":"1997","journal-title":"Eng. Struct."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1891","DOI":"10.1016\/j.compstruc.2005.02.014","article-title":"Dynamic analysis of railway bridge under high-speed trains","volume":"83","author":"Xia","year":"2005","journal-title":"Comput. Struct."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"724","DOI":"10.1016\/j.engstruct.2007.05.009","article-title":"Vibrations of railway bridges for high speed trains under moving loads varying in time","volume":"30","author":"Garinei","year":"2008","journal-title":"Eng. Struct."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"240","DOI":"10.1016\/j.jsv.2009.03.021","article-title":"The effect of dynamic train\u2013bridge interaction on the bridge response during a train passage","volume":"325","author":"Liu","year":"2009","journal-title":"J. Sound Vib."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"5125","DOI":"10.1016\/j.jsv.2012.07.005","article-title":"Dynamic response of underpasses for high-speed train lines","volume":"331","author":"Vega","year":"2012","journal-title":"J. Sound Vib."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"810","DOI":"10.1016\/j.jsv.2006.04.022","article-title":"Analysis of resonance mechanism and conditions of train\u2013bridge system","volume":"297","author":"Xia","year":"2006","journal-title":"J. Sound Vib."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/S0141-0296(97)00078-3","article-title":"Parametric study and simplified design of tuned mass dampers","volume":"20","author":"Rana","year":"1998","journal-title":"Eng. Struct."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1016\/S0020-7683(02)00589-9","article-title":"Vibration suppression for high-speed railway bridges using tuned mass dampers","volume":"40","author":"Wang","year":"2003","journal-title":"Int. J. Solids Struct."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1061\/(ASCE)1084-0702(2005)10:4(398)","article-title":"Train-Induced Vibration Control of High-Speed Railway Bridges Equipped with Multiple Tuned Mass Dampers","volume":"10","author":"Lin","year":"2005","journal-title":"J. Bridge Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"55","DOI":"10.12989\/sem.2017.62.1.055","article-title":"Optimization and application of multiple tuned mass dampers in the vibration control of pedestrian bridges","volume":"62","author":"Lu","year":"2017","journal-title":"Struct. Eng. Mech."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"453","DOI":"10.12989\/sem.2017.61.4.453","article-title":"Series tuned mass dampers in train-induced vibration control of railway bridges","volume":"61","author":"Kahya","year":"2017","journal-title":"Struct. Eng. Mech."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"292","DOI":"10.1016\/j.jsv.2006.08.007","article-title":"Vibration control of simply supported beams under moving loads using fluid viscous dampers","volume":"300","author":"Museros","year":"2007","journal-title":"J. Sound Vib."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1016\/j.jsv.2012.08.008","article-title":"Free vibrations of simply-supported beam bridges under moving loads: Maximum resonance, cancellation and resonant vertical acceleration","volume":"332","author":"Museros","year":"2013","journal-title":"J. Sound Vib."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"355","DOI":"10.1016\/j.engstruct.2013.10.038","article-title":"Dynamic performance of existing high-speed railway bridges under resonant conditions following a retrofit with fluid viscous dampers supported on clamped auxiliary beams","volume":"59","author":"Lavado","year":"2014","journal-title":"Eng. Struct."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1016\/j.engstruct.2012.03.016","article-title":"Retrofit of existing railway bridges of short to medium spans for high-speed traffic using viscoelastic dampers","volume":"40","author":"Moliner","year":"2012","journal-title":"Eng. Struct."},{"key":"ref_17","unstructured":"Goldberg, D.E. (1989). Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley Professional."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1162\/evco.1995.3.1.1","article-title":"An Overview of Evolutionary Algorithms in Multiobjective Optimization","volume":"3","author":"Fonseca","year":"1995","journal-title":"Evolut. Comput."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"529","DOI":"10.12989\/sem.2006.24.5.529","article-title":"Genetic optimization of vibrating stiffened plates","volume":"24","author":"Marcelin","year":"2006","journal-title":"Struct. Eng. Mech."},{"key":"ref_20","unstructured":"(2007). Instrucci\u00f3n de Acciones a Considerar en Puentes de Ferrocarril."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"277","DOI":"10.1016\/0045-7949(94)00611-6","article-title":"Formulation of Rayleigh damping and its extensions","volume":"57","author":"Liu","year":"1995","journal-title":"Comput. Struct."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"744","DOI":"10.1080\/14786442108636264","article-title":"LXVI. On the correction for shear of the differential equation for transverse vibrations of prismatic bars","volume":"41","author":"Timoshenko","year":"1921","journal-title":"Lond. Edinb. Dublin Philos. Mag. J. Sci."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"2421","DOI":"10.1016\/j.jsv.2013.12.030","article-title":"H\u221e optimization of fluid viscous dampers for reducing vibrations of high-speed railway bridges","volume":"333","author":"Luu","year":"2014","journal-title":"J. Sound Vib."},{"key":"ref_24","unstructured":"Clough, R.W. (1993). Dynamics of Structures, McGraw-Hill College."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Gendreau, M., and Potvin, J.Y. (2010). Genetic Algorithms. Handbook of Metaheuristics (International Series in Operations Research & Management Science), Springer. Chapter 5.","DOI":"10.1007\/978-1-4419-1665-5"},{"key":"ref_26","first-page":"239","article-title":"A genetic algorithm for the characterization of hyperelastic materials","volume":"329","author":"Segade","year":"2018","journal-title":"Appl. Math. Comput."},{"key":"ref_27","first-page":"239","article-title":"A Comparison of Three Methods for Selecting Values of Input Variables in the Analysis of Output from a Computer Code","volume":"21","author":"McKay","year":"1979","journal-title":"Technometrics"},{"key":"ref_28","unstructured":"Baker, J.E. (1987, January 28\u201331). Reducing Bias and Inefficiency in the Selection Algorithm. Proceedings of the Second International Conference on Genetic Algorithms and Their Application, Cambridge, MA, USA."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/0952-1976(94)00064-T","article-title":"Least median squares curve fitting using a genetic algorithm","volume":"8","author":"Karr","year":"1995","journal-title":"Eng. Appl. Artif. Intell."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1007\/s005000000042","article-title":"Adaptive mutation in genetic algorithms","volume":"4","author":"Alba","year":"2000","journal-title":"Soft Comput."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/9\/1089\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T13:15:34Z","timestamp":1760188534000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/11\/9\/1089"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,8,31]]},"references-count":30,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2019,9]]}},"alternative-id":["sym11091089"],"URL":"https:\/\/doi.org\/10.3390\/sym11091089","relation":{},"ISSN":["2073-8994"],"issn-type":[{"type":"electronic","value":"2073-8994"}],"subject":[],"published":{"date-parts":[[2019,8,31]]}}}