{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T08:31:23Z","timestamp":1773822683859,"version":"3.50.1"},"reference-count":34,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2018,8,8]],"date-time":"2018-08-08T00:00:00Z","timestamp":1533686400000},"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":["11002017"],"award-info":[{"award-number":["11002017"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, the exact analytical solutions are developed for the thermodynamic behavior of an Euler-Bernoulli beam resting on an elastic foundation and exposed to a time decaying laser pulse that scans over the beam with a uniform velocity. The governing equations, namely the heat conduction equation and the vibration equation are solved using the Green\u2019s function approach. The temporal and special distributions of temperature, deflection, strain, and the energy absorbed by the elastic foundation are calculated. The effects of the laser motion speed, the modulus of elastic foundation reaction, and the laser pulse duration time are studied in detail.<\/jats:p>","DOI":"10.3390\/sym10080328","type":"journal-article","created":{"date-parts":[[2018,8,9]],"date-time":"2018-08-09T03:33:48Z","timestamp":1533785628000},"page":"328","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Thermodynamic Response of Beams on Winkler Foundation Irradiated by Moving Laser Pulses"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0396-0539","authenticated-orcid":false,"given":"Yuxin","family":"Sun","sequence":"first","affiliation":[{"name":"Institute of Solid Mechanics, Beihang University, Beijing 100191, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0472-0983","authenticated-orcid":false,"given":"Shoubin","family":"Liu","sequence":"additional","affiliation":[{"name":"Institute of Solid Mechanics, Beihang University, Beijing 100191, China"}]},{"given":"Zhangheng","family":"Rao","sequence":"additional","affiliation":[{"name":"Institute of Solid Mechanics, Beihang University, Beijing 100191, China"}]},{"given":"Yuhang","family":"Li","sequence":"additional","affiliation":[{"name":"Institute of Solid Mechanics, Beihang University, Beijing 100191, China"}]},{"given":"Jialing","family":"Yang","sequence":"additional","affiliation":[{"name":"Institute of Solid Mechanics, Beihang University, Beijing 100191, China"}]}],"member":"1968","published-online":{"date-parts":[[2018,8,8]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"3895","DOI":"10.1063\/1.324261","article-title":"Heat treating and melting material with a scanning laser or electron beam","volume":"48","author":"Cline","year":"1977","journal-title":"J. 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