{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,2]],"date-time":"2025-11-02T16:55:53Z","timestamp":1762102553998,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2020,9,7]],"date-time":"2020-09-07T00:00:00Z","timestamp":1599436800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11874386"],"award-info":[{"award-number":["11874386"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Scientific and Technologial Innovation Programs of Higher Education Institutions in Shanxi","award":["20190057"],"award-info":[{"award-number":["20190057"]}]},{"name":"Nondestructive Detection and Monitoring Technology for High Speed Transportation Facilities, Key Laboratory of Ministry of Industry and Information Technology","award":["2019012"],"award-info":[{"award-number":["2019012"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, the interaction of a broadband Rayleigh wave generated by a laser and an artificial rectangular notch is analyzed theoretically and experimentally. For the theoretical analysis, a Gaussian function is adopted to analyze the modulation of notch depth on the frequency spectrum via reflection and transmission coefficients. By the finite element method, the Rayleigh wave generated by pulsed laser beam irradiation and its scattering waves at cracks are calculated. A curve with a slope close to 4 fitted by crack depth and critical wavelength of the threshold phenomenon is obtained by the wavelet transform and Parseval\u2019s theorem according to simulated and experimental results. Based on this relationship, the critical frequency at which the threshold phenomenon happens due to energy transformation of transmission\/reflection Rayleigh waves is adopted to determine the size of sub-wavelength surface crack. The experimental results of artificial notch depth estimation on aluminum alloy specimens consistent with theoretical analysis validates the usefulness of the critical frequency method based on a broadband Rayleigh wave generated by laser ultrasonic.<\/jats:p>","DOI":"10.3390\/s20185077","type":"journal-article","created":{"date-parts":[[2020,9,7]],"date-time":"2020-09-07T09:18:16Z","timestamp":1599470296000},"page":"5077","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["An Approach to Size Sub-Wavelength Surface Crack Measurements Using Rayleigh Waves Based on Laser Ultrasounds"],"prefix":"10.3390","volume":"20","author":[{"given":"Haiyang","family":"Li","sequence":"first","affiliation":[{"name":"Key Laboratory of Information Detection and Processing, North University of China, Taiyuan 030051, China"}]},{"given":"Qianghua","family":"Pan","sequence":"additional","affiliation":[{"name":"China Special Equipment Inspection and Research Institute, Beijing 100029, China"}]},{"given":"Xiaotong","family":"Zhang","sequence":"additional","affiliation":[{"name":"Key Laboratory of Advanced Manufacturing Technology, North University of China, Taiyuan 030051, China"}]},{"given":"Zhiwu","family":"An","sequence":"additional","affiliation":[{"name":"Institute of Acoustics of the Chinese Academy of Sciences, Beijing 100190, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2147","DOI":"10.1007\/s12206-012-0533-1","article-title":"Pitch-catch ultrasonic study on unidirectional CFRP composite laminates using Rayleigh wave transducers","volume":"26","author":"Park","year":"2012","journal-title":"J. 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