{"id":"https://openalex.org/W4290039999","doi":"https://doi.org/10.1155/2022/4637716","title":"Nonlinear Vibrations of an Axially Moving Beam with Fractional Viscoelastic Damping","display_name":"Nonlinear Vibrations of an Axially Moving Beam with Fractional Viscoelastic Damping","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W4290039999","doi":"https://doi.org/10.1155/2022/4637716"},"language":"en","primary_location":{"id":"doi:10.1155/2022/4637716","doi":"https://doi.org/10.1155/2022/4637716","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/4637716","pdf_url":"https://downloads.hindawi.com/journals/ace/2022/4637716.pdf","source":{"id":"https://openalex.org/S86499044","display_name":"Advances in Civil Engineering","issn_l":"1687-8086","issn":["1687-8086","1687-8094"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","jufo-1","ki-jl-1","norway-1","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Civil Engineering","raw_type":"journal-article"},"parent_works":[],"lineage":["https://openalex.org/W4290039999"],"child_works_count":0,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/ace/2022/4637716.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100612140","display_name":"Zhe Zhang","orcid":"https://orcid.org/0000-0002-4736-2338","observed_orcids":["https://orcid.org/0000-0002-4736-2338"]},"institutions":[{"id":"https://openalex.org/I49934816","display_name":"Hunan University of Technology","ror":"https://ror.org/04j3vr751","country_code":"CN","type":"education","lineage":["https://openalex.org/I49934816"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhe Zhang","raw_affiliation_strings":["College of Civil Engineering , Hunan University of Technology , Zhuzhou , Hunan 412007 , China","College of Civil Engineering, Hunan University of Technology, Zhuzhou, Hunan 412007"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Civil Engineering , Hunan University of Technology , Zhuzhou , Hunan 412007 , China","institution_ids":["https://openalex.org/I49934816"]},{"raw_affiliation_string":"College of Civil Engineering, Hunan University of Technology, Zhuzhou, Hunan 412007","institution_ids":["https://openalex.org/I49934816"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075688487","display_name":"Hongxiang Yang","orcid":"https://orcid.org/0000-0001-7373-1726","observed_orcids":["https://orcid.org/0000-0001-7373-1726"]},"institutions":[{"id":"https://openalex.org/I4210118050","display_name":"Taishan University","ror":"https://ror.org/02bpnkx55","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210118050"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Hongxiang Yang","raw_affiliation_strings":["School of Information Science and Technology , Taishan University , Taian , Shandong , China","School of Information Science and Technology, Taishan University, Taian, Shandong"],"raw_orcid":"https://orcid.org/0000-0001-7373-1726","affiliations":[{"raw_affiliation_string":"School of Information Science and Technology , Taishan University , Taian , Shandong , China","institution_ids":["https://openalex.org/I4210118050"]},{"raw_affiliation_string":"School of Information Science and Technology, Taishan University, Taian, Shandong","institution_ids":["https://openalex.org/I4210118050"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100835784","display_name":"Zhongjin Guo","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210118050","display_name":"Taishan University","ror":"https://ror.org/02bpnkx55","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210118050"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhongjin Guo","raw_affiliation_strings":["School of Mathematics and Statics , Taishan University , Taian , Shandong , China","School of Mathematics and Statics, Taishan University, Taian, Shandong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statics , Taishan University , Taian , Shandong , China","institution_ids":["https://openalex.org/I4210118050"]},{"raw_affiliation_string":"School of Mathematics and Statics, Taishan University, Taian, Shandong","institution_ids":["https://openalex.org/I4210118050"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Lili Zhu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210118050","display_name":"Taishan University","ror":"https://ror.org/02bpnkx55","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210118050"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lili Zhu","raw_affiliation_strings":["School of Information Science and Technology , Taishan University , Taian , Shandong , China","School of Information Science and Technology, Taishan University, Taian, Shandong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Information Science and Technology , Taishan University , Taian , Shandong , China","institution_ids":["https://openalex.org/I4210118050"]},{"raw_affiliation_string":"School of Information Science and Technology, Taishan University, Taian, Shandong","institution_ids":["https://openalex.org/I4210118050"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101943154","display_name":"Weiyan Liu","orcid":"https://orcid.org/0000-0001-9910-7382","observed_orcids":["https://orcid.org/0000-0001-9910-7382"]},"institutions":[{"id":"https://openalex.org/I4210118050","display_name":"Taishan University","ror":"https://ror.org/02bpnkx55","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210118050"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Weiyan Liu","raw_affiliation_strings":["School of Mathematics and Statics , Taishan University , Taian , Shandong , China","School of Mathematics and Statics, Taishan University, Taian, Shandong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statics , Taishan University , Taian , Shandong , China","institution_ids":["https://openalex.org/I4210118050"]},{"raw_affiliation_string":"School of Mathematics and Statics, Taishan University, Taian, Shandong","institution_ids":["https://openalex.org/I4210118050"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5075688487"],"corresponding_institution_ids":["https://openalex.org/I4210118050"],"apc_list":{"value":2760,"currency":"USD","value_usd":2760},"apc_paid":{"value":2760,"currency":"USD","value_usd":2760},"fwci":1.131,"has_fulltext":true,"cited_by_count":12,"citation_normalized_percentile":{"value":0.71770143,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":98},"biblio":{"volume":"2022","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12206","display_name":"Vibration and Dynamic Analysis","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.0015999999595806003,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11565","display_name":"Thermoelastic and Magnetoelastic Phenomena","score":0.00039999998989515007,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/nonlinear-vibration","display_name":"nonlinear vibration","score":0.7129999995231628},{"id":"https://openalex.org/keywords/axially-moving-beam","display_name":"axially moving beam","score":0.9919999837875366},{"id":"https://openalex.org/keywords/viscoelastic-damping","display_name":"viscoelastic damping","score":0.8669999837875366},{"id":"https://openalex.org/keywords/fractional-derivatives","display_name":"fractional derivatives","score":0.8019999861717224},{"id":"https://openalex.org/keywords/duffing-system","display_name":"Duffing system","score":0.7440000176429749},{"id":"https://openalex.org/keywords/fractional-kelvin-voigt-model","display_name":"fractional Kelvin-Voigt model","score":0.9559999704360962},{"id":"https://openalex.org/keywords/caputo-fractional-derivative","display_name":"Caputo fractional derivative","score":0.8629999756813049},{"id":"https://openalex.org/keywords/primary-resonance","display_name":"primary resonance","score":0.9789999723434448},{"id":"https://openalex.org/keywords/steady-state-response","display_name":"steady-state response","score":0.7950000166893005},{"id":"https://openalex.org/keywords/routh-hurwitz-stability-criterion","display_name":"Routh-Hurwitz stability","score":0.7149999737739563},{"id":"https://openalex.org/keywords/vibration-reduction","display_name":"vibration suppression","score":0.6959999799728394},{"id":"https://openalex.org/keywords/fractional-order","display_name":"fractional order","score":0.7889999747276306}],"concepts":[{"id":"https://openalex.org/C186541917","wikidata":"https://www.wikidata.org/wiki/Q910483","display_name":"Viscoelasticity","level":2,"score":0.7907835245132446},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6763483285903931},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.6539427042007446},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.6463529467582703},{"id":"https://openalex.org/C35377427","wikidata":"https://www.wikidata.org/wiki/Q3886264","display_name":"Axial symmetry","level":2,"score":0.621733546257019},{"id":"https://openalex.org/C168834538","wikidata":"https://www.wikidata.org/wiki/Q3705329","display_name":"Beam (structure)","level":2,"score":0.5921546816825867},{"id":"https://openalex.org/C198394728","wikidata":"https://www.wikidata.org/wiki/Q3695508","display_name":"Vibration","level":2,"score":0.5607810020446777},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.49154624342918396},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.48737412691116333},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.47952723503112793},{"id":"https://openalex.org/C121758426","wikidata":"https://www.wikidata.org/wiki/Q5659248","display_name":"Harmonic balance","level":3,"score":0.4725075662136078},{"id":"https://openalex.org/C127934551","wikidata":"https://www.wikidata.org/wiki/Q1148098","display_name":"Harmonic","level":2,"score":0.4648066759109497},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.46100208163261414},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.45841169357299805},{"id":"https://openalex.org/C132323500","wikidata":"https://www.wikidata.org/wiki/Q675387","display_name":"Duffing equation","level":3,"score":0.4191761016845703},{"id":"https://openalex.org/C178270690","wikidata":"https://www.wikidata.org/wiki/Q3048149","display_name":"Kelvin\u2013Voigt material","level":3,"score":0.4169686734676361},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38229793310165405},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.13146153092384338},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.11389711499214172},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.09561905264854431},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.07564455270767212},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1155/2022/4637716","doi":"https://doi.org/10.1155/2022/4637716","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/4637716","pdf_url":"https://downloads.hindawi.com/journals/ace/2022/4637716.pdf","source":{"id":"https://openalex.org/S86499044","display_name":"Advances in Civil Engineering","issn_l":"1687-8086","issn":["1687-8086","1687-8094"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","jufo-1","ki-jl-1","norway-1","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Civil Engineering","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:b72e3e03a15f41b88536caec105fee5e","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/b72e3e03a15f41b88536caec105fee5e","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,"listed_in":[],"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":"Advances in Civil Engineering, Vol 2022 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2022/4637716","doi":"https://doi.org/10.1155/2022/4637716","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2022/4637716","pdf_url":"https://downloads.hindawi.com/journals/ace/2022/4637716.pdf","source":{"id":"https://openalex.org/S86499044","display_name":"Advances in Civil Engineering","issn_l":"1687-8086","issn":["1687-8086","1687-8094"],"is_oa":true,"is_in_doaj":true,"is_core":true,"listed_in":["cwts-core","doaj","dongbi-c","jufo-1","ki-jl-1","norway-1","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Civil Engineering","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2281192211","display_name":null,"funder_award_id":"11502160","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G31153007","display_name":null,"funder_award_id":"51808212","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5566053284","display_name":null,"funder_award_id":"ZR2019MA017","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G7205514249","display_name":null,"funder_award_id":"Y2014-01-18","funder_id":"https://openalex.org/F4320329341","funder_display_name":"Taishan University"},{"id":"https://openalex.org/G7720287010","display_name":null,"funder_award_id":"51708205","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8582741125","display_name":null,"funder_award_id":"ZR2021MA086","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null},{"id":"https://openalex.org/F4320329341","display_name":"Taishan University","ror":"https://ror.org/02bpnkx55"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4290039999.pdf","grobid_xml":"https://content.openalex.org/works/W4290039999.grobid-xml"},"referenced_works_count":34,"referenced_works":["https://openalex.org/W617206983","https://openalex.org/W803899340","https://openalex.org/W1600794312","https://openalex.org/W1979149559","https://openalex.org/W2000600982","https://openalex.org/W2003655765","https://openalex.org/W2014315504","https://openalex.org/W2016443935","https://openalex.org/W2023719405","https://openalex.org/W2023789853","https://openalex.org/W2025564363","https://openalex.org/W2030947086","https://openalex.org/W2043646514","https://openalex.org/W2046930844","https://openalex.org/W2050923536","https://openalex.org/W2058153478","https://openalex.org/W2064771119","https://openalex.org/W2069165340","https://openalex.org/W2078558877","https://openalex.org/W2080296395","https://openalex.org/W2110062126","https://openalex.org/W2115927302","https://openalex.org/W2149598428","https://openalex.org/W2150866422","https://openalex.org/W2259227674","https://openalex.org/W2520413966","https://openalex.org/W2525631261","https://openalex.org/W2605190690","https://openalex.org/W2624937967","https://openalex.org/W2724416890","https://openalex.org/W2769197569","https://openalex.org/W2789530646","https://openalex.org/W4231409469","https://openalex.org/W4241976930"],"related_works":["https://openalex.org/W4241976930","https://openalex.org/W2963611335","https://openalex.org/W4205251459","https://openalex.org/W4246183760","https://openalex.org/W4396977834","https://openalex.org/W4396917414","https://openalex.org/W3135409488","https://openalex.org/W2971563694","https://openalex.org/W2062949694","https://openalex.org/W2605190690"],"abstract_inverted_index":{"The":[0,16,38,56,92],"nonlinear":[1,32],"vibrations":[2],"of":[3,19,21,40,69,81,94,111,125,135],"an":[4],"axially":[5],"moving":[6,42],"viscoelastic":[7,23],"beam":[8,24,43],"under":[9],"the":[10,22,41,47,53,63,67,79,82,86,102,109,112,117,133,136],"transverse":[11],"harmonic":[12],"excitation":[13],"are":[14,97],"examined.":[15],"governing":[17],"equation":[18],"motion":[20],"is":[25,44,59,75,114,121],"discretized":[26],"into":[27],"a":[28,72],"Duffing":[29],"system":[30],"with":[31],"fractional":[33,48,83],"derivative":[34],"using":[35],"Galerkin\u2019s":[36],"method.":[37,65],"viscoelasticity":[39],"described":[45],"by":[46,62,116],"Kelvin\u2013Voigt":[49],"model":[50],"based":[51],"on":[52,89],"Caputo":[54],"definition.":[55],"primary":[57],"resonance":[58],"analytically":[60],"investigated":[61],"averaging":[64],"With":[66],"aid":[68],"response":[70],"curves,":[71],"parametric":[73],"study":[74,96],"conducted":[76],"to":[77],"display":[78],"influences":[80],"order":[84],"and":[85,105],"viscosity":[87,134],"coefficient":[88],"steady\u2010state":[90],"responses.":[91],"validations":[93],"this":[95],"given":[98],"through":[99],"comparisons":[100],"between":[101],"analytical":[103],"solutions":[104,113],"numerical":[106],"ones,":[107],"where":[108],"stability":[110],"determined":[115],"Routh\u2013Hurwitz":[118],"criterion.":[119],"It":[120],"found":[122],"that":[123],"suppression":[124],"undesirable":[126],"responses":[127],"can":[128],"be":[129],"achieved":[130],"via":[131],"changing":[132],"system.":[137]},"counts_by_year":[{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":1}],"updated_date":"2026-09-07T09:17:50.787605","created_date":"2022-08-06T00:00:00"}