{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T21:11:25Z","timestamp":1774473085416,"version":"3.50.1"},"reference-count":58,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,4,22]],"date-time":"2022-04-22T00:00:00Z","timestamp":1650585600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>A novel nonlocal model with one thermal relaxation time is presented to investigate the propagation of waves in a thermoelastic semi-infinite medium. We used Eringen\u2019s theory of the nonlocal continuum to develop these models. Analytical solutions in all physical quantities are provided by using Laplace transforms and eigenvalue techniques. All physical quantities are presented as symmetric and asymmetric tensors. The temperature, the displacement, and the stress variations in semi-infinite materials have been calculated. The effects of nonlocal parameters, ramp type heating, and the thermal relaxation times on the wave propagation distribution of physical fields for mediums are graphically displayed and analyzed.<\/jats:p>","DOI":"10.3390\/sym14050864","type":"journal-article","created":{"date-parts":[[2022,4,24]],"date-time":"2022-04-24T00:45:21Z","timestamp":1650761121000},"page":"864","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Analytical Solutions of Nonlocal Thermoelastic Interaction on Semi-Infinite Mediums Induced by Ramp-Type Heating"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9407-9650","authenticated-orcid":false,"given":"Aatef","family":"Hobiny","sequence":"first","affiliation":[{"name":"Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Mathematics Department, King Abdulaziz University, Jeddah 21577, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9595-439X","authenticated-orcid":false,"given":"Ibrahim","family":"Abbas","sequence":"additional","affiliation":[{"name":"Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Mathematics Department, King Abdulaziz University, Jeddah 21577, Saudi Arabia"},{"name":"Mathematics Department, Faculty of Science, Sohag University, Sohag 82511, Egypt"}]},{"given":"Hashim","family":"Alshehri","sequence":"additional","affiliation":[{"name":"Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Mathematics Department, King Abdulaziz University, Jeddah 21577, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1552-3763","authenticated-orcid":false,"given":"Marin","family":"Marin","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Computer Science, Transilvania University of Brasov, 500093 Brasov, Romania"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0020-7225(72)90070-5","article-title":"Nonlocal polar elastic continua","volume":"10","author":"Eringen","year":"1972","journal-title":"Int. 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