{"id":"https://openalex.org/W4224326591","doi":"https://doi.org/10.3390/sym14050864","title":"Analytical Solutions of Nonlocal Thermoelastic Interaction on Semi-Infinite Mediums Induced by Ramp-Type Heating","display_name":"Analytical Solutions of Nonlocal Thermoelastic Interaction on Semi-Infinite Mediums Induced by Ramp-Type Heating","publication_year":2022,"publication_date":"2022-04-22","ids":{"openalex":"https://openalex.org/W4224326591","doi":"https://doi.org/10.3390/sym14050864"},"language":"en","primary_location":{"id":"doi:10.3390/sym14050864","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14050864","pdf_url":"https://www.mdpi.com/2073-8994/14/5/864/pdf?version=1650625561","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/5/864/pdf?version=1650625561","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080246924","display_name":"Aatef Hobiny","orcid":"https://orcid.org/0000-0001-9407-9650"},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Aatef Hobiny","raw_affiliation_strings":["Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Mathematics Department, King Abdulaziz University, Jeddah 21577, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-9407-9650","affiliations":[{"raw_affiliation_string":"Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Mathematics Department, King Abdulaziz University, Jeddah 21577, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045553984","display_name":"Ibrahim A. Abbas","orcid":null},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]},{"id":"https://openalex.org/I97455420","display_name":"Sohag University","ror":"https://ror.org/02wgx3e98","country_code":"EG","type":"education","lineage":["https://openalex.org/I97455420"]}],"countries":["EG","SA"],"is_corresponding":true,"raw_author_name":"Ibrahim Abbas","raw_affiliation_strings":["Mathematics Department, Faculty of Science, Sohag University, Sohag 82511, Egypt","Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Mathematics Department, King Abdulaziz University, Jeddah 21577, Saudi Arabia"],"raw_orcid":"https://orcid.org/0000-0001-9595-439X","affiliations":[{"raw_affiliation_string":"Mathematics Department, Faculty of Science, Sohag University, Sohag 82511, Egypt","institution_ids":["https://openalex.org/I97455420"]},{"raw_affiliation_string":"Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Mathematics Department, King Abdulaziz University, Jeddah 21577, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045924981","display_name":"Hashim M. Alshehri","orcid":"https://orcid.org/0009-0001-2659-0155"},"institutions":[{"id":"https://openalex.org/I185163786","display_name":"King Abdulaziz University","ror":"https://ror.org/02ma4wv74","country_code":"SA","type":"education","lineage":["https://openalex.org/I185163786"]}],"countries":["SA"],"is_corresponding":false,"raw_author_name":"Hashim Alshehri","raw_affiliation_strings":["Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Mathematics Department, King Abdulaziz University, Jeddah 21577, Saudi Arabia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Nonlinear Analysis and Applied Mathematics Research Group (NAAM), Mathematics Department, King Abdulaziz University, Jeddah 21577, Saudi Arabia","institution_ids":["https://openalex.org/I185163786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015681053","display_name":"Mar\u00edn Mar\u00edn","orcid":"https://orcid.org/0000-0003-1552-3763"},"institutions":[{"id":"https://openalex.org/I3123573182","display_name":"Transylvania University of Bra\u0219ov","ror":"https://ror.org/01cg9ws23","country_code":"RO","type":"education","lineage":["https://openalex.org/I3123573182"]}],"countries":["RO"],"is_corresponding":true,"raw_author_name":"Marin Marin","raw_affiliation_strings":["Department of Mathematics and Computer Science, Transilvania University of Brasov, 500093 Brasov, Romania"],"raw_orcid":"https://orcid.org/0000-0003-1552-3763","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, Transilvania University of Brasov, 500093 Brasov, Romania","institution_ids":["https://openalex.org/I3123573182"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5015681053","https://openalex.org/A5045553984"],"corresponding_institution_ids":["https://openalex.org/I185163786","https://openalex.org/I3123573182","https://openalex.org/I97455420"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":1.0505,"has_fulltext":false,"cited_by_count":9,"citation_normalized_percentile":{"value":0.69833676,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"14","issue":"5","first_page":"864","last_page":"864"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11565","display_name":"Thermoelastic and Magnetoelastic Phenomena","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11565","display_name":"Thermoelastic and Magnetoelastic Phenomena","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11646","display_name":"Nonlocal and gradient elasticity in micro/nano structures","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/thermoelastic-damping","display_name":"Thermoelastic damping","score":0.9743860960006714},{"id":"https://openalex.org/keywords/laplace-transform","display_name":"Laplace transform","score":0.7973953485488892},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6626457571983337},{"id":"https://openalex.org/keywords/displacement","display_name":"Displacement (psychology)","score":0.5526672601699829},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5281505584716797},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.5249664187431335},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.5039612650871277},{"id":"https://openalex.org/keywords/thermal","display_name":"Thermal","score":0.4875730872154236},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.44575172662734985},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.4178786873817444},{"id":"https://openalex.org/keywords/wave-propagation","display_name":"Wave propagation","score":0.416896790266037},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41079920530319214},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.26948195695877075},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.19568365812301636},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.10955995321273804},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08358648419380188}],"concepts":[{"id":"https://openalex.org/C92458943","wikidata":"https://www.wikidata.org/wiki/Q7783171","display_name":"Thermoelastic damping","level":3,"score":0.9743860960006714},{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.7973953485488892},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6626457571983337},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.5526672601699829},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5281505584716797},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.5249664187431335},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.5039612650871277},{"id":"https://openalex.org/C204530211","wikidata":"https://www.wikidata.org/wiki/Q752823","display_name":"Thermal","level":2,"score":0.4875730872154236},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.44575172662734985},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.4178786873817444},{"id":"https://openalex.org/C44886760","wikidata":"https://www.wikidata.org/wiki/Q1758425","display_name":"Wave propagation","level":2,"score":0.416896790266037},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41079920530319214},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.26948195695877075},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.19568365812301636},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.10955995321273804},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08358648419380188},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C542102704","wikidata":"https://www.wikidata.org/wiki/Q183257","display_name":"Psychotherapist","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14050864","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14050864","pdf_url":"https://www.mdpi.com/2073-8994/14/5/864/pdf?version=1650625561","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:28565dfb5c2741e48dfc3636e91a8e65","is_oa":true,"landing_page_url":"https://doaj.org/article/28565dfb5c2741e48dfc3636e91a8e65","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 14, Iss 5, p 864 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/5/864/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14050864","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym14050864","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14050864","pdf_url":"https://www.mdpi.com/2073-8994/14/5/864/pdf?version=1650625561","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4224326591.pdf","grobid_xml":"https://content.openalex.org/works/W4224326591.grobid-xml"},"referenced_works_count":57,"referenced_works":["https://openalex.org/W97123318","https://openalex.org/W1524809726","https://openalex.org/W1589465642","https://openalex.org/W1963548782","https://openalex.org/W1965313232","https://openalex.org/W1973038067","https://openalex.org/W1973343968","https://openalex.org/W1974745964","https://openalex.org/W1986009128","https://openalex.org/W1995379804","https://openalex.org/W2000761434","https://openalex.org/W2010018064","https://openalex.org/W2045499649","https://openalex.org/W2046344013","https://openalex.org/W2057342974","https://openalex.org/W2061360760","https://openalex.org/W2062885352","https://openalex.org/W2065670728","https://openalex.org/W2069344959","https://openalex.org/W2074331260","https://openalex.org/W2082721200","https://openalex.org/W2090084036","https://openalex.org/W2121105689","https://openalex.org/W2123737083","https://openalex.org/W2129085700","https://openalex.org/W2138533896","https://openalex.org/W2167882337","https://openalex.org/W2417293072","https://openalex.org/W2420237543","https://openalex.org/W2508462075","https://openalex.org/W2513316610","https://openalex.org/W2537609436","https://openalex.org/W2555827219","https://openalex.org/W2604415127","https://openalex.org/W2618393903","https://openalex.org/W2790396594","https://openalex.org/W2795804611","https://openalex.org/W2796699721","https://openalex.org/W2810272749","https://openalex.org/W2810888449","https://openalex.org/W2967592093","https://openalex.org/W3011115649","https://openalex.org/W3013111500","https://openalex.org/W3016234513","https://openalex.org/W3016753807","https://openalex.org/W3025108249","https://openalex.org/W3027340946","https://openalex.org/W3036791425","https://openalex.org/W3087907962","https://openalex.org/W3093014180","https://openalex.org/W3116705297","https://openalex.org/W3159211235","https://openalex.org/W3198277292","https://openalex.org/W3199552234","https://openalex.org/W3207893211","https://openalex.org/W6631342704","https://openalex.org/W6801032921"],"related_works":["https://openalex.org/W2054919018","https://openalex.org/W2001550513","https://openalex.org/W2090764544","https://openalex.org/W2128585177","https://openalex.org/W3208881875","https://openalex.org/W2016092895","https://openalex.org/W2325690970","https://openalex.org/W2944231641","https://openalex.org/W2059631326","https://openalex.org/W4388101082"],"abstract_inverted_index":{"A":[0],"novel":[1],"nonlocal":[2,28,76],"model":[3],"with":[4],"one":[5],"thermal":[6,83],"relaxation":[7,84],"time":[8],"is":[9],"presented":[10,53],"to":[11,30],"investigate":[12],"the":[13,27,61,64,82,87],"propagation":[14,89],"of":[15,26,75,91],"waves":[16],"in":[17,36,67],"a":[18],"thermoelastic":[19],"semi-infinite":[20,68],"medium.":[21],"We":[22],"used":[23],"Eringen\u2019s":[24],"theory":[25],"continuum":[29],"develop":[31],"these":[32],"models.":[33],"Analytical":[34],"solutions":[35],"all":[37],"physical":[38,50,92],"quantities":[39,51],"are":[40,52,96],"provided":[41],"by":[42],"using":[43],"Laplace":[44],"transforms":[45],"and":[46,56,63,81,99],"eigenvalue":[47],"techniques.":[48],"All":[49],"as":[54],"symmetric":[55],"asymmetric":[57],"tensors.":[58],"The":[59,73],"temperature,":[60],"displacement,":[62],"stress":[65],"variations":[66],"materials":[69],"have":[70],"been":[71],"calculated.":[72],"effects":[74],"parameters,":[77],"ramp":[78],"type":[79],"heating,":[80],"times":[85],"on":[86],"wave":[88],"distribution":[90],"fields":[93],"for":[94],"mediums":[95],"graphically":[97],"displayed":[98],"analyzed.":[100]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
