{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,28]],"date-time":"2026-08-28T01:14:30Z","timestamp":1787879670044,"version":"build-2784847793"},"reference-count":42,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2021,1,18]],"date-time":"2021-01-18T00:00:00Z","timestamp":1610928000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Kai Wei","award":["Grant Nos. 51978583"],"award-info":[{"award-number":["Grant Nos. 51978583"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>The purpose of this research was to investigate and improve the accuracy of the existing slab-track mat (STM) specifications in the evaluation of the vibration reduction effect. The static nonlinearity and dynamic mechanical characteristics of three types of STMs were tested, and then a modified fractional derivative Poynting\u2013Thomson (FDPT) model was used to characterize the preload and frequency dependence. A modified vehicle\u2013floating slab track (FST) coupled dynamic model was established to analyze the actual insertion loss. The insertion loss error evaluated by the frequency-dependent tangent stiffness increased with the increase in STM nonlinearity, and the error obtained by the third preload tangent stiffness was usually greater than that of the second preload. Compared with the secant stiffness, the second preload frequency-dependent tangent stiffness was more suitable for evaluating STMs with high-static\u2013low-dynamics (HSLD) stiffness. In order to reflect the frequency dependence effect and facilitate engineering applications, it is recommended that second preload tangent stiffness corresponding to the natural frequency of the FST be used for evaluation. Furthermore, the insertion loss of the STMs with monotonically increased stiffness decreased as the axle load increased, and the opposite was true for the STMs with monotonically decreased stiffness. The vibration isolation efficiency of the STMs with HSLD stiffness was both stable and better than that of the STMs with monotonic stiffness.<\/jats:p>","DOI":"10.3390\/ma14020452","type":"journal-article","created":{"date-parts":[[2021,1,19]],"date-time":"2021-01-19T11:39:55Z","timestamp":1611056395000},"page":"452","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":18,"title":["Evaluation Method of the Vibration Reduction Effect Considering the Real Load- and Frequency-Dependent Stiffness of Slab-Track Mats"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0782-9092","authenticated-orcid":false,"given":"Zeming","family":"Zhao","sequence":"first","affiliation":[{"name":"Ministry of Education Key Laboratory of High-Speed Railway Engineering, Southwest Jiaotong University, 4th Floor, Civil Engineering Building, Chengdu 610031, China"},{"name":"School of Civil Engineering, Southwest Jiaotong University, St No. 111, Beiyi Section, Erhuan Road, Chengdu 610031, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kai","family":"Wei","sequence":"additional","affiliation":[{"name":"Ministry of Education Key Laboratory of High-Speed Railway Engineering, Southwest Jiaotong University, 4th Floor, Civil Engineering Building, Chengdu 610031, China"},{"name":"School of Civil Engineering, Southwest Jiaotong University, St No. 111, Beiyi Section, Erhuan Road, Chengdu 610031, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenhao","family":"Ding","sequence":"additional","affiliation":[{"name":"Ministry of Education Key Laboratory of High-Speed Railway Engineering, Southwest Jiaotong University, 4th Floor, Civil Engineering Building, Chengdu 610031, China"},{"name":"School of Civil Engineering, Southwest Jiaotong University, St No. 111, Beiyi Section, Erhuan Road, Chengdu 610031, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fang","family":"Cheng","sequence":"additional","affiliation":[{"name":"Ministry of Education Key Laboratory of High-Speed Railway Engineering, Southwest Jiaotong University, 4th Floor, Civil Engineering Building, Chengdu 610031, China"},{"name":"School of Civil Engineering, Southwest Jiaotong University, St No. 111, Beiyi Section, Erhuan Road, Chengdu 610031, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ping","family":"Wang","sequence":"additional","affiliation":[{"name":"Ministry of Education Key Laboratory of High-Speed Railway Engineering, Southwest Jiaotong University, 4th Floor, Civil Engineering Building, Chengdu 610031, China"},{"name":"School of Civil Engineering, Southwest Jiaotong University, St No. 111, Beiyi Section, Erhuan Road, Chengdu 610031, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,1,18]]},"reference":[{"key":"ref_1","first-page":"107754632093091","article-title":"Prediction of building vibration induced by metro trains running in a curved tunnel","volume":"2","author":"Ma","year":"2020","journal-title":"J. Vib. Control"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1016\/j.conbuildmat.2014.11.027","article-title":"The use of elastic elements in railway tracks: A state of the art review","volume":"75","year":"2015","journal-title":"Constr. Build. Mater."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1016\/j.proeng.2017.05.129","article-title":"Methods of Noise and Vibration Protection on Urban Rail Transport","volume":"289","author":"Dudkin","year":"2017","journal-title":"Procedia Eng."},{"key":"ref_4","unstructured":"Hanson, C., Towers, D., and Meister, L. (2006). Transit Noise and Vibration Impact Assessment."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Zbiciak, A., Kra\u015bkiewicz, C., Sabouni-Zawadzka, A.A., Pe\u0142czy\u0144ski, J., and Dudziak, S. (2020). A Novel Approach to the Analysis of Under Sleeper Pads (USP) Applied in the Ballasted Track Structures. Materials, 13.","DOI":"10.3390\/ma13112438"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"18","DOI":"10.1016\/j.conbuildmat.2016.12.115","article-title":"Numerical and experimental characterization of the mechanical behavior of a new recycled elastomer for vibration isolation in railway applications","volume":"134","author":"Diego","year":"2017","journal-title":"Constr. Build. Mater."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"210","DOI":"10.1016\/j.conbuildmat.2019.03.315","article-title":"Effects of crumb rubber size and percentage on degradation reduction of railway ballast","volume":"212","author":"Guo","year":"2019","journal-title":"Constr. Build. Mater."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"117822","DOI":"10.1016\/j.conbuildmat.2019.117822","article-title":"Properties of rubber under-ballast mat used as ballastless track isolation layer in high-speed railway","volume":"240","author":"Sheng","year":"2020","journal-title":"Constr. Build. Mater."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"095440971775220","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":"J. Rail Rapid Transit."},{"key":"ref_10","first-page":"402","article-title":"Use of rubber mat to improve deformation behaviors of ballastless tracks laid on bridges","volume":"8821","author":"Zheng","year":"2020","journal-title":"Adv. Civ. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1080\/23248378.2015.1076622","article-title":"Prediction and efficient control of vibration mitigation using floating slabs: Practical application at Athens metro lines 2 and 3","volume":"3","author":"Vogiatzis","year":"2015","journal-title":"Int. J. Rail Transp."},{"key":"ref_12","first-page":"533","article-title":"Noise and vibration evaluation of a floating slab in direct fixation turnouts in Haidari & Anthoupoli extensions of Athens metro lines 2 and 3","volume":"67","author":"Carels","year":"2012","journal-title":"Ing. Ferrov."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1214","DOI":"10.21595\/jve.2016.17234","article-title":"Optimization of vibration reduction of the rubber floating-slab tracks","volume":"19","author":"Jin","year":"2017","journal-title":"J. Vibroeng."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"118219","DOI":"10.1016\/j.conbuildmat.2020.118219","article-title":"Application of rubber mats in transition zone between two different slab tracks in high-speed railway","volume":"243","author":"Xin","year":"2020","journal-title":"Constr. Build. Mater."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"106988","DOI":"10.1016\/j.apacoust.2019.07.036","article-title":"Structure-borne noise from long-span steel truss cable-stayed bridge under damping pad floating slab: Experimental and numerical analysis","volume":"157","author":"Liang","year":"2020","journal-title":"Appl. Acoust."},{"key":"ref_16","unstructured":"Koroma, S., Hussein, M., Thompson, D., and Ntotsios, E. (2014, January 13\u201317). The effect of non-linearity of railway tracks on ground-borne vibration. Proceedings of the ICSV 21: International Congress on Sound Vibration, Beijing, China."},{"key":"ref_17","first-page":"107754631881340","article-title":"Influence of static preload on vibration reduction effect of floating slab tracks","volume":"25","author":"Li","year":"2018","journal-title":"J. Vib. Control"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Wei, K., Zhao, Z., Ren, J., Ou, L., and Wang, P. (2019). High-speed vehicle\u2013slab track coupled vibration analysis of the viscoelastic-plastic dynamic properties of rail pads under different preloads and temperatures. Veh. Syst. Dyn., 1\u201332.","DOI":"10.1080\/00423114.2019.1673444"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"992","DOI":"10.1177\/0954409719883552","article-title":"Investigation of the vibration isolation performance of floating slab track with rubber bearings using a stochastic fractional derivative model","volume":"234","author":"Yuan","year":"2019","journal-title":"J. Rail Rapid Transit."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"05002","DOI":"10.1051\/matecconf\/201821905002","article-title":"The influence of selected static and dynamic parameters of resilient mats on vibration reduction of railway tracks","volume":"219","author":"Krakiewicz","year":"2018","journal-title":"MATEC Web Conf."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"557","DOI":"10.1016\/j.jsv.2005.08.042","article-title":"Measurements of the dynamic railpad properties","volume":"293","author":"Maes","year":"2006","journal-title":"J. Sound Vib."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1080\/00423114.2016.1267371","article-title":"Effect of temperature- and frequency-dependent dynamic properties of rail pads on high-speed vehicle\u2013track coupled vibrations","volume":"55","author":"Wei","year":"2017","journal-title":"Veh. Syst. Dyn."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1006\/jsvi.1998.1492","article-title":"Developments of the indirect method for measuring the high frequency dynamic stiffness of resilient elements","volume":"213","author":"Thompson","year":"1998","journal-title":"J. Sound Vib."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"460","DOI":"10.1016\/j.jsv.2015.11.009","article-title":"Obtaining railpad properties via dynamic mechanical analysis","volume":"363","author":"Oregui","year":"2016","journal-title":"J. Sound Vib."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Liu, L.Y., Zuo, Z.Y., Zhou, Y.L., and Qin, J.L. (2020). Insights into the Effect of WJ-7 Fastener Rubber Pad to Vehicle-Rail-Viaduct Coupled Dynamics. Appl. Sci., 10.","DOI":"10.3390\/app10051889"},{"key":"ref_26","unstructured":"Wang, P., Dou, Y., Wang, S., Wang, F., and Wei, K. (2020). Influence of the temperature- and frequency-dependent dynamic properties of rail pads on the vibration characteristics of rails at low temperature. J. Rail Rapid Transit."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"103505","DOI":"10.1016\/j.mechmat.2020.103505","article-title":"Influence of the operational conditions on static and dynamic stiffness of rail pads","volume":"148","author":"Carrascal","year":"2020","journal-title":"Mech. Mater."},{"key":"ref_28","unstructured":"Koroma, S., Hussein, M., and Owen, J. (2013, January 13). The effects of railpad nonlinearity on the dynamic behaviour of railway track. Proceedings of the Institute of Acoustics Spring Conference, Nottingham, UK."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1260\/0263-0923.34.3.289","article-title":"Influence of preload and nonlinearity of railpads on vibration of railway tracks under stationary and moving harmonic loads","volume":"34","author":"Koroma","year":"2015","journal-title":"J. Low Freq. Noise Vib. Act. Control"},{"key":"ref_30","unstructured":"TJ\/GW 121-2014 (2014). Provisional Technical Regulations for Floating Slab Track of Rubber Vibration Isolation Mat in Beijing Underground Diameter Line Project, China Railway Corporation."},{"key":"ref_31","unstructured":"DIN 45673-7 (2008). 2010-08 Mechanical Vibration. Resilient Elements Used in Railway Tracks. Part 7: Laboratory Test Procedures for Resilient Elements of Floating Slab Track Systems, Acoustics, Noise Control and Vibration Engineering Standards Committee."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"848","DOI":"10.1016\/j.conbuildmat.2017.06.044","article-title":"Experimental investigation into temperature- and frequency-dependent dynamic properties of high-speed rail pads","volume":"151","author":"Wei","year":"2017","journal-title":"Constr. Build. Mater."},{"key":"ref_33","unstructured":"Podlubny, I. (1999). Fractional Differential Equations, Mathematics in Science and Engineering."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1016\/j.ijmecsci.2013.02.007","article-title":"Non-linear problems of fractional calculus in modeling of mechanical systems","volume":"70","author":"Grzesikiewicz","year":"2013","journal-title":"Int. J. Mech. Sci."},{"key":"ref_35","unstructured":"ISO 18437-6-2017 (2017). Mechanical Vibration and Shock\u2014Characterization of the Dynamic Mechanical Properties of Visco-Elastic Materials\u2014Part6: Time-Temperature Superposition, British Standard Institute."},{"key":"ref_36","unstructured":"ISO 4664-1-2011 Rubber (2011). Vulcanized or Thermoplastic\u2014Determination of Dynamic Properties, The International Organization for Standardization."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1080\/00423119308969544","article-title":"A detailed model for investigating vertical interactions between railway vehicle and track","volume":"23","author":"Zhai","year":"1994","journal-title":"Veh. Syst. Dyn."},{"key":"ref_38","unstructured":"ISO 2631-1:1997 (1997). Mechanical Vibration and Shock\u2014Evaluation of Human Exposure to Whole-body Vibration\u2014Part 1: General Requirements, Human Exposure to Mechanical Vibration and Shock."},{"key":"ref_39","unstructured":"CJJ\/T 191-2012 (2012). Technical Code for Floating Slab Track."},{"key":"ref_40","first-page":"2","article-title":"The effect of track and vehicle parameters on wheel\/rail vertical dynamic loads","volume":"3","author":"Jenkins","year":"1974","journal-title":"Railw. Eng. J."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1080\/00423119308969027","article-title":"Modelling of railway track and vehicle track interaction at high frequencies","volume":"22","author":"Knothe","year":"1993","journal-title":"Veh. Syst. Dyn."},{"key":"ref_42","first-page":"79","article-title":"Study on Vertical Natural Vibrations of Steel Rail Considering Frequency-dependent Stiffness of Rail Pads","volume":"38","author":"Wei","year":"2016","journal-title":"J. China Railw. Soc."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/14\/2\/452\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T05:12:34Z","timestamp":1760159554000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/14\/2\/452"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,1,18]]},"references-count":42,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2021,1]]}},"alternative-id":["ma14020452"],"URL":"https:\/\/doi.org\/10.3390\/ma14020452","relation":{},"ISSN":["1996-1944"],"issn-type":[{"value":"1996-1944","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,1,18]]}}}