{"id":"https://openalex.org/W3158734873","doi":"https://doi.org/10.1080/00207160.2021.1924367","title":"Numerical analysis of axially non-linear viscoelastic string with the variable fractional order model by using Bernstein polynomials algorithm","display_name":"Numerical analysis of axially non-linear viscoelastic string with the variable fractional order model by using Bernstein polynomials algorithm","publication_year":2021,"publication_date":"2021-04-29","ids":{"openalex":"https://openalex.org/W3158734873","doi":"https://doi.org/10.1080/00207160.2021.1924367","mag":"3158734873"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2021.1924367","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2021.1924367","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5109576111","display_name":"Cundi Han","orcid":null},"institutions":[{"id":"https://openalex.org/I39333907","display_name":"Yanshan University","ror":"https://ror.org/02txfnf15","country_code":"CN","type":"education","lineage":["https://openalex.org/I39333907"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Cundi Han","raw_affiliation_strings":["School of Science, Yanshan University, Qinhuangdao, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Yanshan University, Qinhuangdao, People's Republic of China","institution_ids":["https://openalex.org/I39333907"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100333349","display_name":"Yiming Chen","orcid":"https://orcid.org/0000-0001-7040-8050"},"institutions":[{"id":"https://openalex.org/I39333907","display_name":"Yanshan University","ror":"https://ror.org/02txfnf15","country_code":"CN","type":"education","lineage":["https://openalex.org/I39333907"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Yiming Chen","raw_affiliation_strings":["School of Science, Yanshan University, Qinhuangdao, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Yanshan University, Qinhuangdao, People's Republic of China","institution_ids":["https://openalex.org/I39333907"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058038850","display_name":"Gang Cheng","orcid":"https://orcid.org/0000-0002-1242-8739"},"institutions":[{"id":"https://openalex.org/I12449238","display_name":"Universit\u00e9 d'Orl\u00e9ans","ror":"https://ror.org/014zrew76","country_code":"FR","type":"education","lineage":["https://openalex.org/I12449238"]},{"id":"https://openalex.org/I4210129154","display_name":"Centre Val de Loire","ror":"https://ror.org/03ntmtb29","country_code":"FR","type":"facility","lineage":["https://openalex.org/I4210088668","https://openalex.org/I4210129154"]},{"id":"https://openalex.org/I110017253","display_name":"Universit\u00e9 de Tours","ror":"https://ror.org/02wwzvj46","country_code":"FR","type":"education","lineage":["https://openalex.org/I110017253"]},{"id":"https://openalex.org/I4210143826","display_name":"Institut National des Sciences Appliqu\u00e9es Centre Val de Loire","ror":"https://ror.org/03y0qc033","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210143826"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Gang Cheng","raw_affiliation_strings":["INSA Centre Val de Loire, Univ. Tours, Univ. Orl\u00e9ans, LaM\u00e9, Blois, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INSA Centre Val de Loire, Univ. Tours, Univ. Orl\u00e9ans, LaM\u00e9, Blois, France","institution_ids":["https://openalex.org/I4210129154","https://openalex.org/I4210143826","https://openalex.org/I110017253","https://openalex.org/I12449238"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079534937","display_name":"Roger Serra","orcid":"https://orcid.org/0000-0001-5805-4149"},"institutions":[{"id":"https://openalex.org/I110017253","display_name":"Universit\u00e9 de Tours","ror":"https://ror.org/02wwzvj46","country_code":"FR","type":"education","lineage":["https://openalex.org/I110017253"]},{"id":"https://openalex.org/I12449238","display_name":"Universit\u00e9 d'Orl\u00e9ans","ror":"https://ror.org/014zrew76","country_code":"FR","type":"education","lineage":["https://openalex.org/I12449238"]},{"id":"https://openalex.org/I4210143826","display_name":"Institut National des Sciences Appliqu\u00e9es Centre Val de Loire","ror":"https://ror.org/03y0qc033","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210143826"]},{"id":"https://openalex.org/I4210129154","display_name":"Centre Val de Loire","ror":"https://ror.org/03ntmtb29","country_code":"FR","type":"facility","lineage":["https://openalex.org/I4210088668","https://openalex.org/I4210129154"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Roger Serra","raw_affiliation_strings":["INSA Centre Val de Loire, Univ. Tours, Univ. Orl\u00e9ans, LaM\u00e9, Blois, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"INSA Centre Val de Loire, Univ. Tours, Univ. Orl\u00e9ans, LaM\u00e9, Blois, France","institution_ids":["https://openalex.org/I4210129154","https://openalex.org/I4210143826","https://openalex.org/I110017253","https://openalex.org/I12449238"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100435892","display_name":"Lei Wang","orcid":"https://orcid.org/0000-0002-3090-1921"},"institutions":[{"id":"https://openalex.org/I39333907","display_name":"Yanshan University","ror":"https://ror.org/02txfnf15","country_code":"CN","type":"education","lineage":["https://openalex.org/I39333907"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lei Wang","raw_affiliation_strings":["School of Science, Yanshan University, Qinhuangdao, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Yanshan University, Qinhuangdao, People's Republic of China","institution_ids":["https://openalex.org/I39333907"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027037598","display_name":"Junyao Feng","orcid":null},"institutions":[{"id":"https://openalex.org/I39333907","display_name":"Yanshan University","ror":"https://ror.org/02txfnf15","country_code":"CN","type":"education","lineage":["https://openalex.org/I39333907"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Junyao Feng","raw_affiliation_strings":["School of Science, Yanshan University, Qinhuangdao, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Science, Yanshan University, Qinhuangdao, People's Republic of China","institution_ids":["https://openalex.org/I39333907"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5079534937","https://openalex.org/A5100333349"],"corresponding_institution_ids":["https://openalex.org/I110017253","https://openalex.org/I12449238","https://openalex.org/I39333907","https://openalex.org/I4210129154","https://openalex.org/I4210143826"],"apc_list":null,"apc_paid":null,"fwci":0.2775,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.52763062,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":96},"biblio":{"volume":"99","issue":"3","first_page":"537","last_page":"552"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12206","display_name":"Vibration and Dynamic Analysis","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T12206","display_name":"Vibration and Dynamic Analysis","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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/T11254","display_name":"Fluid Dynamics and Vibration Analysis","score":0.9976000189781189,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T10690","display_name":"Vibration Control and Rheological Fluids","score":0.9898999929428101,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7029672861099243},{"id":"https://openalex.org/keywords/constitutive-equation","display_name":"Constitutive equation","score":0.5820530652999878},{"id":"https://openalex.org/keywords/viscoelasticity","display_name":"Viscoelasticity","score":0.5792918801307678},{"id":"https://openalex.org/keywords/string","display_name":"String (physics)","score":0.5706671476364136},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5407434105873108},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5002114772796631},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.4788651168346405},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.45165950059890747},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.42415738105773926},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.41569432616233826},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36537089943885803},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.1924867033958435},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.16937875747680664}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7029672861099243},{"id":"https://openalex.org/C202973686","wikidata":"https://www.wikidata.org/wiki/Q1937401","display_name":"Constitutive equation","level":3,"score":0.5820530652999878},{"id":"https://openalex.org/C186541917","wikidata":"https://www.wikidata.org/wiki/Q910483","display_name":"Viscoelasticity","level":2,"score":0.5792918801307678},{"id":"https://openalex.org/C157486923","wikidata":"https://www.wikidata.org/wiki/Q1376436","display_name":"String (physics)","level":2,"score":0.5706671476364136},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5407434105873108},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5002114772796631},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.4788651168346405},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.45165950059890747},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.42415738105773926},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.41569432616233826},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36537089943885803},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.1924867033958435},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.16937875747680664},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1080/00207160.2021.1924367","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2021.1924367","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03621326v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03621326","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"International Journal of Computer Mathematics, 2022, 99 (3), pp.537-552. ⟨10.1080/00207160.2021.1924367⟩","raw_type":"Journal articles"},{"id":"pmh:oai:HAL:hal-04444411v1","is_oa":false,"landing_page_url":"https://hal.science/hal-04444411","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 0020-7160","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4850625604","display_name":null,"funder_award_id":"A2017203100","funder_id":"https://openalex.org/F4320322163","funder_display_name":"Natural Science Foundation of Hebei Province"}],"funders":[{"id":"https://openalex.org/F4320322163","display_name":"Natural Science Foundation of Hebei Province","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W808066179","https://openalex.org/W1963636474","https://openalex.org/W1979149559","https://openalex.org/W2003897150","https://openalex.org/W2016443935","https://openalex.org/W2017663693","https://openalex.org/W2022275678","https://openalex.org/W2050923536","https://openalex.org/W2054593596","https://openalex.org/W2056194922","https://openalex.org/W2068601892","https://openalex.org/W2076575482","https://openalex.org/W2082944446","https://openalex.org/W2084137032","https://openalex.org/W2097711576","https://openalex.org/W2130840186","https://openalex.org/W2135919740","https://openalex.org/W2167781655","https://openalex.org/W2171477367","https://openalex.org/W2295179465","https://openalex.org/W2469000661","https://openalex.org/W2474984875","https://openalex.org/W2582526819","https://openalex.org/W2618430072","https://openalex.org/W2758349477","https://openalex.org/W2772507505","https://openalex.org/W2781523636","https://openalex.org/W2894413670","https://openalex.org/W2894803565","https://openalex.org/W2907542486","https://openalex.org/W2914021327","https://openalex.org/W2923505959","https://openalex.org/W2937486991","https://openalex.org/W2950708086","https://openalex.org/W2964110260","https://openalex.org/W2969811770","https://openalex.org/W2995757144","https://openalex.org/W2996352244","https://openalex.org/W3003602255","https://openalex.org/W3122020756"],"related_works":["https://openalex.org/W4221057967","https://openalex.org/W4243019676","https://openalex.org/W2517352629","https://openalex.org/W2783562378","https://openalex.org/W4293192718","https://openalex.org/W2531131539","https://openalex.org/W2089309364","https://openalex.org/W2354516437","https://openalex.org/W3162315667","https://openalex.org/W2037885462"],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"a":[3,48],"new":[4],"numerical":[5,73,76],"method":[6],"to":[7,70],"solve":[8],"the":[9,22,27,33,43,59,63,72,82,85,112,120,127],"non-linear":[10,23,39],"constitutive":[11,24,40],"equations":[12],"of":[13,26,42,78,84,122],"viscoelastic":[14,36,79],"string":[15,28,44,80],"with":[16,126],"variable":[17,34,128],"fractional":[18,35,129],"order":[19,130],"model.":[20,37,131],"Firstly,":[21],"equation":[25,41,50,65],"is":[29,45,66],"established":[30],"based":[31],"on":[32,91],"Secondly,":[38],"transformed":[46],"into":[47],"matrix":[49,64],"by":[51,106],"using":[52],"Bernstein":[53],"polynomials,":[54],"which":[55],"can":[56],"greatly":[57],"simplify":[58],"solving":[60,119],"process.":[61],"Then":[62],"discretized":[67],"and":[68,88,95],"solved":[69],"obtain":[71],"solutions.":[74],"Finally,":[75],"results":[77],"show":[81],"effect":[83],"axial":[86,89],"tension":[87],"velocity":[90,94],"its":[92],"displacement,":[93],"acceleration.":[96],"It":[97],"also":[98],"indicates":[99],"that":[100],"how":[101],"dynamic":[102],"behaviours":[103],"are":[104],"affected":[105],"external":[107],"force":[108],"excitation.":[109],"In":[110],"addition,":[111],"proposed":[113],"algorithm":[114],"shows":[115],"enormous":[116],"potentials":[117],"for":[118],"problem":[121],"high":[123],"precision":[124],"dynamics":[125]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2}],"updated_date":"2026-05-07T13:39:58.223016","created_date":"2025-10-10T00:00:00"}