{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,30]],"date-time":"2026-09-30T04:31:29Z","timestamp":1790742689288,"version":"4.1.0"},"reference-count":33,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,5,5]],"date-time":"2023-05-05T00:00:00Z","timestamp":1683244800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"The Fundamental Research Funds for the Central Universities of China","award":["2022JBQY002"],"award-info":[{"award-number":["2022JBQY002"]}]},{"name":"The Fundamental Research Funds for the Central Universities of China","award":["GJNY-21-65"],"award-info":[{"award-number":["GJNY-21-65"]}]},{"name":"The Fundamental Research Funds for the Central Universities of China","award":["TZKY-21-16"],"award-info":[{"award-number":["TZKY-21-16"]}]},{"name":"The Technology Development Program of China Energy Investment Corporation","award":["2022JBQY002"],"award-info":[{"award-number":["2022JBQY002"]}]},{"name":"The Technology Development Program of China Energy Investment Corporation","award":["GJNY-21-65"],"award-info":[{"award-number":["GJNY-21-65"]}]},{"name":"The Technology Development Program of China Energy Investment Corporation","award":["TZKY-21-16"],"award-info":[{"award-number":["TZKY-21-16"]}]},{"name":"Research Base of China Energy Railway Equipment Co., Ltd.","award":["2022JBQY002"],"award-info":[{"award-number":["2022JBQY002"]}]},{"name":"Research Base of China Energy Railway Equipment Co., Ltd.","award":["GJNY-21-65"],"award-info":[{"award-number":["GJNY-21-65"]}]},{"name":"Research Base of China Energy Railway Equipment Co., Ltd.","award":["TZKY-21-16"],"award-info":[{"award-number":["TZKY-21-16"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Nonlinear ultrasonic guided waves have attracted increasing attention in the field of structural health monitoring due to their high sensitivity and long detection distance. In practical applications, the temperature of the tested structure will inevitably change, so it is essential to evaluate the effects of temperature on nonlinear ultrasonic guided waves. In this paper, an analytical approach is proposed to obtain the response law of nonlinear guided waves to temperature based on the semi-analytical finite element (SAFE) method. The plate structure is investigated as a demonstration example, and the corresponding simulation analysis and experimental verification are carried out. The results show that the variation trends of different cumulative second harmonic modes with temperature are distinct, and their amplitudes monotonically increase or decrease with the continuously rising temperature. Therefore, in the applications with nonlinear ultrasonic guided waves, it is necessary to predict the changing trend of selected cumulative second harmonics under the action of temperature and compensate the result for the influence of temperature. The methods and conclusions presented in this paper are also applicable to other types of structures and have general practicality.<\/jats:p>","DOI":"10.3390\/ma16093548","type":"journal-article","created":{"date-parts":[[2023,5,5]],"date-time":"2023-05-05T09:18:09Z","timestamp":1683278289000},"page":"3548","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Temperature Effects on Nonlinear Ultrasonic Guided Waves"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7396-6346","authenticated-orcid":false,"given":"Xiaochuan","family":"Niu","sequence":"first","affiliation":[{"name":"School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China"},{"name":"Key Laboratory of Vehicle Advanced Manufacturing, Measuring and Control Technology, Beijing Jiaotong University, Ministry of Education, Beijing 100044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5436-6660","authenticated-orcid":false,"given":"Liqiang","family":"Zhu","sequence":"additional","affiliation":[{"name":"School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China"},{"name":"Key Laboratory of Vehicle Advanced Manufacturing, Measuring and Control Technology, Beijing Jiaotong University, Ministry of Education, Beijing 100044, China"},{"name":"Frontiers Science Center for Smart High-Speed Railway System, Beijing 100044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wenlin","family":"Yang","sequence":"additional","affiliation":[{"name":"School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zujun","family":"Yu","sequence":"additional","affiliation":[{"name":"School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China"},{"name":"Frontiers Science Center for Smart High-Speed Railway System, Beijing 100044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Haikuo","family":"Shen","sequence":"additional","affiliation":[{"name":"School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,5,5]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Yan, X.L., Wang, H.P., and Fan, X.Z. 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