{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T22:00:13Z","timestamp":1773093613247,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2021,6,21]],"date-time":"2021-06-21T00:00:00Z","timestamp":1624233600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Beijing major science and technology projects","award":["Z191100008019002"],"award-info":[{"award-number":["Z191100008019002"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Natural vibration characteristics serve as one of the crucial references for bridge monitoring. However, temperature-induced changes in the natural vibration characteristics of bridge structures may exceed the impact of structural damage, thus causing some interference in damage identification. This study analyzed the influence of temperature on the natural vibration characteristics of simply supported beams, which is the most widely used bridge structure. The theoretical formula for the variation of the natural frequency of simply supported beams with temperature was proposed. The elastic modulus of simply supported beams in the range of \u221240 \u00b0C to 60 \u00b0C was acquired by means of the falling ball test and the theoretical formula and was compared with the elastic modulus obtained by the three-point bending test at room temperature (20 \u00b0C). In addition, the Midas\/Civil finite-element simulation was carried out for the natural frequency of simply supported beams at different temperatures. The results showed that temperature was the main factor causing the variation of the natural frequency of simply supported beams. The linear negative correlation between the natural frequency of simply supported beams and their temperature were observed. The natural frequency of simply supported beams decreased by 0.148% for every 1 \u00b0C increase. This research contributed to the further understanding of the natural vibration characteristics of simply supported beams under the influence of temperature so as to provide references for natural frequency monitoring and damage identification of beam bridges.<\/jats:p>","DOI":"10.3390\/s21124242","type":"journal-article","created":{"date-parts":[[2021,6,21]],"date-time":"2021-06-21T13:29:58Z","timestamp":1624282198000},"page":"4242","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":36,"title":["Influence of Temperature on the Natural Vibration Characteristics of Simply Supported Reinforced Concrete Beam"],"prefix":"10.3390","volume":"21","author":[{"given":"Yanxia","family":"Cai","sequence":"first","affiliation":[{"name":"Beijing Zhonglu Gaoke Highway Technology Co., Ltd., Beijing 100088, China"},{"name":"Research and Development Center of Transport Industry of New Materials, Technologies Application for Highway Construction and Maintenance, Beijing 100088, China"},{"name":"Research Institute of Highway Ministry of Transport, Beijing 100088, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kai","family":"Zhang","sequence":"additional","affiliation":[{"name":"China Construction Third Bureau First Engineering Co., Ltd., Wuhan 430040, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8115-1780","authenticated-orcid":false,"given":"Zhoujing","family":"Ye","sequence":"additional","affiliation":[{"name":"National Center for Materials Service Safety, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chang","family":"Liu","sequence":"additional","affiliation":[{"name":"National Center for Materials Service Safety, University of Science and Technology Beijing, Beijing 100083, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kaiji","family":"Lu","sequence":"additional","affiliation":[{"name":"Beijing Zhonglu Gaoke Highway Technology Co., Ltd., Beijing 100088, China"},{"name":"Research and Development Center of Transport Industry of New Materials, Technologies Application for Highway Construction and Maintenance, Beijing 100088, China"},{"name":"Research Institute of Highway Ministry of Transport, Beijing 100088, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Linbing","family":"Wang","sequence":"additional","affiliation":[{"name":"National Center for Materials Service Safety, University of Science and Technology Beijing, Beijing 100083, China"},{"name":"Virginia Tech, Blacksburg, VA 24061, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,6,21]]},"reference":[{"key":"ref_1","first-page":"147","article-title":"Load-carrying capacity assessment methods of existing bridges","volume":"25","author":"Zong","year":"2005","journal-title":"Earthq. Eng. Eng. Dyn."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1016\/j.ymssp.2018.05.037","article-title":"A robust damage detection method based on multi-modal analysis in variable temperature conditions","volume":"115","author":"Gillich","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Hu, W.-H., Tang, D.-H., Teng, J., Said, S., and Rohrmann, R.G. (2018). Structural Health Monitoring of a Prestressed Concrete Bridge Based on Statistical Pattern Recognition of Continuous Dynamic Measurements over 14 years. Sensors, 18.","DOI":"10.3390\/s18124117"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Wang, X., Gao, Q., and Liu, Y. (2020). Damage Detection of Bridges under Environmental Temperature Changes Using a Hybrid Method. Sensors, 20.","DOI":"10.3390\/s20143999"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2016\/7974090","article-title":"Effect of Temperature Variation on Modal Frequency of Reinforced Concrete Slab and Beam in Cold Regions","volume":"2016","author":"Liu","year":"2016","journal-title":"Shock. Vib."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2018\/8072843","article-title":"Modeling of Temperature Effect on Modal Frequency of Concrete Beam Based on Field Monitoring Data","volume":"2018","author":"Shan","year":"2018","journal-title":"Shock. Vib."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2489","DOI":"10.1002\/stc.2489","article-title":"Data-driven models for temperature distribution effects on natural frequencies and thermal prestress modeling","volume":"27","author":"Jang","year":"2020","journal-title":"Struct. Control Health Monit."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Teng, J., Tang, D.-H., Zhang, X., Hu, W.-H., Said, S., and Rohrmann, R.G. (2019). Automated Modal Analysis for Tracking Structural Change during Construction and Operation Phases. Sensors, 19.","DOI":"10.3390\/s19040927"},{"key":"ref_9","first-page":"57","article-title":"Advances of Vibration-based Damage Identification Methods","volume":"43","author":"Liu","year":"2004","journal-title":"Acta Sci. Nat. Univ. Sunyatseni"},{"key":"ref_10","unstructured":"Farrar, C.R., Doebling, S.W., Cornwell, P.J., and Straser, E.G. (1997). Variability of Modal Parameters Measured on the Alamosa Canyon Bridge."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1742","DOI":"10.1061\/(ASCE)0733-9445(2007)133:12(1742)","article-title":"Effect of Temperature on Modal Variability of a Curved Concrete Bridge under Ambient Loads","volume":"133","author":"Liu","year":"2007","journal-title":"J. Struct. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1850155","DOI":"10.1142\/S0219455418501559","article-title":"Experimental Study on the Effect of Temperature on Modal Frequencies of Bridges","volume":"18","author":"Sun","year":"2018","journal-title":"Int. J. Struct. Stab. Dyn."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1016\/j.ymssp.2019.05.063","article-title":"Effects of environmental and operational actions on the modal frequency variations of a sea-crossing bridge: A periodicity perspective","volume":"131","author":"Zhou","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1002\/1096-9845(200102)30:2<149::AID-EQE1>3.0.CO;2-Z","article-title":"One-year monitoring of the Z24-Bridge: Environmental effects versus damage events","volume":"30","author":"Peeters","year":"2001","journal-title":"Earthq. Eng. Struct. Dyn."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"441","DOI":"10.1016\/j.engstruct.2005.09.001","article-title":"Long term vibration monitoring of an RC slab: Temperature and humidity effect","volume":"28","author":"Xia","year":"2006","journal-title":"Eng. Struct."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1354","DOI":"10.1016\/j.engstruct.2006.07.024","article-title":"Vibration-based damage monitoring in model plate-girder bridges under uncertain temperature conditions","volume":"29","author":"Kim","year":"2007","journal-title":"Eng. Struct."},{"key":"ref_17","unstructured":"Hu, T. (2018). The Influence of Temperature on the Self Vibration Characteristics of Cfst Deck Arch Bridge and Seismic Response Analysis, Southwest Jiaotong University."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Teng, J., Tang, D.-H., Hu, W.-H., Lu, W., Feng, Z.-W., Ao, C.-F., and Liao, M.-H. (2020). Mechanism of the effect of temperature on frequency based on long-term monitoring of an arch bridge. Struct. Health Monit.","DOI":"10.1177\/1475921720931370"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1111\/j.1747-1567.1999.tb01320.x","article-title":"Environmental Variability of Modal Properties","volume":"23","author":"Cornwell","year":"1999","journal-title":"Exp. Tech."},{"key":"ref_20","first-page":"119","article-title":"Experimental study on effects of environmental temperature on dynamic characteristics of bridge structures","volume":"27","author":"Xu","year":"2007","journal-title":"Earthq. Eng. Eng. Dyn."},{"key":"ref_21","first-page":"16","article-title":"Regression analysis of environmental temperature and humidity and the natural frequencies of composite beam","volume":"29","author":"Zhang","year":"2012","journal-title":"J. Hebei Univ. Eng. (Nat. Sci. Ed.)"},{"key":"ref_22","first-page":"138","article-title":"Influence of temperature on modal parameters of bridge","volume":"40","author":"Li","year":"2012","journal-title":"J. South China Univ. Technol. (Nat. Sci. Ed.)"},{"key":"ref_23","unstructured":"Wang, J. (2012). Research on Natural Frequency of Simply Supported Beam Basis on Multiple Temperature Fields, Jilin University."},{"key":"ref_24","unstructured":"Yang, M. (2014). Evolvement of Nature Vibration Characteriscs of Concrete Girder Bridge Considering Environmental Temperature and Time-Depended Performance of Concrete, Beijing Jiaotong University."},{"key":"ref_25","unstructured":"Li, Y. (2016). Influence of the Temperature to the Evolvement of Dynamic Characteriscs of Concrete Girder Bridge, Beijing Jiaotong University."},{"key":"ref_26","unstructured":"CEB-FIP (2010). Model Code 2010. Fib Special Activity Group 5, The International Federation for Structural Concrete."},{"key":"ref_27","unstructured":"CCCC Highway Consultants Co., Ltd. (2015). General Specifications for Design of Highway Bridges and Culverts, China Communications Press. [1st ed.]."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1016\/j.apacoust.2019.04.031","article-title":"Directivity based control of acoustic radiation","volume":"154","author":"Sharma","year":"2019","journal-title":"Appl. Acoust."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1850012","DOI":"10.1142\/S2591728518500123","article-title":"Directivity-Based Passive Barrier for Local Control of Low-Frequency Noise","volume":"26","author":"Sharma","year":"2017","journal-title":"J. Comput. Acoust."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/12\/4242\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:20:19Z","timestamp":1760163619000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/21\/12\/4242"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,21]]},"references-count":29,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2021,6]]}},"alternative-id":["s21124242"],"URL":"https:\/\/doi.org\/10.3390\/s21124242","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,21]]}}}