{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,31]],"date-time":"2026-08-31T17:52:14Z","timestamp":1788198734823,"version":"build-2803163510"},"reference-count":23,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,1,1]],"date-time":"2020-01-01T00:00:00Z","timestamp":1577836800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"the National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["51827813"],"award-info":[{"award-number":["51827813"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"the Key Program of National Natural Science Foundation of China","award":["U1734206"],"award-info":[{"award-number":["U1734206"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>The vibration induced by the high-speed railway (HSR) system has been a severe problem during the construction and operation period. To investigate the vibration-energy properties of the China Railways Track System (CRTS)-III track, a vehicle-track-subgrade coupling model is developed, in which the distribution of the tangent force is symmetrical according to the FASTSIM theory, and the power flow method is utilized. What\u2019s more, the corresponding evaluation indexes of the power flow are proposed to analyze the vibration energy of the track structure. The results reveal that the vibration energy decreases from top to bottom of the track structure among the frequency considered, and the decreasing trend is obvious. The vibration energy of the track structure is sensitive to the stiffness of fasteners. Differently, the vibration energy of the composite slab and the base slab is more sensitive to the stiffness of rubber damping pads than that of the rail. To sum up, this paper can provide a new perspective and method to study the vibration-energy properties and select the reasonable stiffness of the fasteners and the rubber damping pads of the CRTS-III track, and the proposed values of the stiffness of the fasteners and the rubber damping pads for the case under this study are 40 kN\/mm and 400 MPa\/m, respectively.<\/jats:p>","DOI":"10.3390\/sym12010069","type":"journal-article","created":{"date-parts":[[2020,1,3]],"date-time":"2020-01-03T11:55:07Z","timestamp":1578052507000},"page":"69","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Study of the Vibration-Energy Properties of the CRTS-III Track Based on the Power Flow Method"],"prefix":"10.3390","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1523-8551","authenticated-orcid":false,"given":"Hanwen","family":"Jiang","sequence":"first","affiliation":[{"name":"School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Liang","family":"Gao","sequence":"additional","affiliation":[{"name":"School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"105841","DOI":"10.1016\/j.soildyn.2019.105841","article-title":"A preliminary investigation of vibration mitigation technique for the high-speed railway in seasonally frozen regions","volume":"127","author":"Tang","year":"2019","journal-title":"Soil Dyn. Earthq. Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1080\/23248378.2016.1209444","article-title":"Application of fluid viscous dampers to mitigate vibrations of high-speed railway bridges","volume":"5","author":"Andersson","year":"2017","journal-title":"Int. J. Rail Transp."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1016\/j.conbuildmat.2014.12.124","article-title":"Numerical modelling of high speed train\/track system for the reduction of vibration levels and maintenance needs of railway tracks","volume":"79","author":"Ferreira","year":"2015","journal-title":"Constr. Build. Mater."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"229","DOI":"10.1080\/23248378.2016.1220844","article-title":"The effect of embankment on high speed rail ground vibrations","volume":"4","author":"Olivier","year":"2016","journal-title":"Int. J. Rail Transp."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3525","DOI":"10.1007\/s12205-019-1947-4","article-title":"Noise and Vibration Mitigation Performance of Damping Pad under CRTS-III Ballastless Track in High Speed Rail Viaduct","volume":"23","author":"Liu","year":"2019","journal-title":"KSCE J. Civ. Eng."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"233","DOI":"10.3151\/jact.16.233","article-title":"Fatigue performance of CRTS III slab ballastless track structure un-der High-speed train load based on concrete fatigue damage constitu-tive law","volume":"16","author":"Yu","year":"2018","journal-title":"J. Adv. Concr. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2237","DOI":"10.1016\/j.jsv.2010.11.023","article-title":"Reducing slab track vibration into bridge using elastic materials in high speed railway","volume":"330","author":"Xin","year":"2011","journal-title":"J. Sound Vib."},{"key":"ref_8","first-page":"8","article-title":"Experimental study on the vibration damping performance of rubber absorbers for ballastless tracks on viaduct","volume":"34","author":"Zhao","year":"2013","journal-title":"China Railw. Sci."},{"key":"ref_9","first-page":"44","article-title":"Analysis of harmonic response of CRTS III prefabricated slab track with anti-vibration structure","volume":"33","author":"Ren","year":"2016","journal-title":"J. Railw. Eng. Soc."},{"key":"ref_10","first-page":"8","article-title":"Dynamic effect and structure optimization of damping layers of CRTS III slab ballastless track for high speed railway","volume":"37","author":"Xin","year":"2016","journal-title":"China Railw. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1837","DOI":"10.1177\/0954409717752201","article-title":"Effect of elastic rubber mats on the reduction of vibration and noise in high-speed elevated railway systems","volume":"232","author":"Zhao","year":"2018","journal-title":"Proc. Inst. Mech. Eng. Part F J. Rail Rapid Trans."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"59","DOI":"10.1016\/0022-460X(80)90452-6","article-title":"Vibrational power flow from machines into built-up structures, part I: Introduction and approximate analyses of beam and plate-like foundations","volume":"68","author":"Goyder","year":"1980","journal-title":"J. Sound Vib."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/0022-460X(80)90453-8","article-title":"Vibrational power flow from machines into built-up structures, part II: Wave propagation and power flow in beam-stiffened plates","volume":"68","author":"Goyder","year":"1980","journal-title":"J. Sound Vib."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1016\/0022-460X(80)90454-X","article-title":"Vibrational power flow from machines into built-up structures, part III: Power flow through isolation systems","volume":"68","author":"Goyder","year":"1980","journal-title":"J. Sound Vib."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1016\/0022-460X(82)90405-9","article-title":"On effective mobilities in the prediction of structure-borne sound transmission between a source structure and a receiving structure, part I: Theoretical background and basic experimental studies","volume":"82","author":"Petersson","year":"1982","journal-title":"J. Sound Vib."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"667","DOI":"10.1016\/j.jsv.2005.12.012","article-title":"A power flow method for evaluating vibration from underground railways","volume":"293","author":"Hussein","year":"2006","journal-title":"J. Sound Vib."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"4153","DOI":"10.1016\/j.jsv.2013.02.036","article-title":"Analysis of the dominant vibration frequencies of rail bridges for structure-borne noise using a power flow method","volume":"332","author":"Li","year":"2013","journal-title":"J. Sound Vib."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1115\/1.1961875","article-title":"Computational Dynamics of Multibody Systems: History, Formalisms, and Applications","volume":"1","author":"Eberhard","year":"2005","journal-title":"J. Comput. Nonlin Dyn."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"380","DOI":"10.2514\/3.2874","article-title":"Reduction of stiffness and mass matrices","volume":"3","author":"GUYAN","year":"1965","journal-title":"AIAA J."},{"key":"ref_20","unstructured":"Hertz, H. (1882). Verhandlungen des Vereins zur Bef\u00f6rderung des Gewerbefleisses, Duncker."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/00423118208968684","article-title":"A fast algorithm for the simplified theory of rolling contact","volume":"11","author":"Kalker","year":"1982","journal-title":"Veh. Syst. Dyn."},{"key":"ref_22","first-page":"12","article-title":"Dynamic Responses of Vehicle-CRTS III Slab Track System and Vehicle Running Safety Subjected to Uniform Seismic Excitation","volume":"2019","author":"Lou","year":"2019","journal-title":"Shock Vib."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"757","DOI":"10.1006\/jsvi.1999.2207","article-title":"Prediction of power flows through machine vibration isolators","volume":"224","author":"Li","year":"1999","journal-title":"J. Sound Vib."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/1\/69\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:18:41Z","timestamp":1760361521000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/12\/1\/69"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,1]]},"references-count":23,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1]]}},"alternative-id":["sym12010069"],"URL":"https:\/\/doi.org\/10.3390\/sym12010069","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,1,1]]}}}