{"id":"https://openalex.org/W4383878497","doi":"https://doi.org/10.3390/axioms12070676","title":"Review of Nonlocal-in-Time Damping Models in the Dynamics of Structures","display_name":"Review of Nonlocal-in-Time Damping Models in the Dynamics of Structures","publication_year":2023,"publication_date":"2023-07-10","ids":{"openalex":"https://openalex.org/W4383878497","doi":"https://doi.org/10.3390/axioms12070676"},"language":"en","primary_location":{"id":"doi:10.3390/axioms12070676","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12070676","pdf_url":"https://www.mdpi.com/2075-1680/12/7/676/pdf?version=1688996208","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/12/7/676/pdf?version=1688996208","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5069344441","display_name":"Vladimir N. Sidorov","orcid":"https://orcid.org/0000-0001-8812-8022"},"institutions":[{"id":"https://openalex.org/I134694890","display_name":"Russian University of Transport","ror":"https://ror.org/05gba0366","country_code":"RU","type":"education","lineage":["https://openalex.org/I134694890"]},{"id":"https://openalex.org/I4210086057","display_name":"Moscow State University of Civil Engineering","ror":"https://ror.org/00em04n91","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210086057"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Vladimir Sidorov","raw_affiliation_strings":["Department of Systems\u2019 Automation Design, Russian University of Transport (RUT) (MIIT), 127994 Moscow, Russia","Research and Education Center after Zolotov, Moscow State University of Civil Engineering, 129337 Moscow, Russia","Department of Systems' Automation Design, Russian University of Transport (RUT) (MIIT), 127994 Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Department of Systems\u2019 Automation Design, Russian University of Transport (RUT) (MIIT), 127994 Moscow, Russia","institution_ids":["https://openalex.org/I134694890"]},{"raw_affiliation_string":"Research and Education Center after Zolotov, Moscow State University of Civil Engineering, 129337 Moscow, Russia","institution_ids":["https://openalex.org/I4210086057"]},{"raw_affiliation_string":"Department of Systems' Automation Design, Russian University of Transport (RUT) (MIIT), 127994 Moscow, Russia","institution_ids":["https://openalex.org/I134694890"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071952948","display_name":"Marina V. Shitikova","orcid":"https://orcid.org/0000-0003-2186-1881"},"institutions":[{"id":"https://openalex.org/I4210086057","display_name":"Moscow State University of Civil Engineering","ror":"https://ror.org/00em04n91","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210086057"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"Marina Shitikova","raw_affiliation_strings":["Research and Education Center after Zolotov, Moscow State University of Civil Engineering, 129337 Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Research and Education Center after Zolotov, Moscow State University of Civil Engineering, 129337 Moscow, Russia","institution_ids":["https://openalex.org/I4210086057"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034355862","display_name":"Elena Badina","orcid":"https://orcid.org/0009-0007-0461-5087"},"institutions":[{"id":"https://openalex.org/I4210086057","display_name":"Moscow State University of Civil Engineering","ror":"https://ror.org/00em04n91","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210086057"]},{"id":"https://openalex.org/I4210137967","display_name":"Institute of Applied Mechanics","ror":"https://ror.org/04jjns303","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210137967","https://openalex.org/I4210164537"]},{"id":"https://openalex.org/I134694890","display_name":"Russian University of Transport","ror":"https://ror.org/05gba0366","country_code":"RU","type":"education","lineage":["https://openalex.org/I134694890"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Elena Badina","raw_affiliation_strings":["Department of Systems\u2019 Automation Design, Russian University of Transport (RUT) (MIIT), 127994 Moscow, Russia","Institute of Applied Mechanics, Russian Academy of Sciences, 125040 Moscow, Russia","Research and Education Center after Zolotov, Moscow State University of Civil Engineering, 129337 Moscow, Russia","Department of Systems' Automation Design, Russian University of Transport (RUT) (MIIT), 127994 Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Department of Systems\u2019 Automation Design, Russian University of Transport (RUT) (MIIT), 127994 Moscow, Russia","institution_ids":["https://openalex.org/I134694890"]},{"raw_affiliation_string":"Institute of Applied Mechanics, Russian Academy of Sciences, 125040 Moscow, Russia","institution_ids":["https://openalex.org/I4210137967"]},{"raw_affiliation_string":"Research and Education Center after Zolotov, Moscow State University of Civil Engineering, 129337 Moscow, Russia","institution_ids":["https://openalex.org/I4210086057"]},{"raw_affiliation_string":"Department of Systems' Automation Design, Russian University of Transport (RUT) (MIIT), 127994 Moscow, Russia","institution_ids":["https://openalex.org/I134694890"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023196937","display_name":"Elena Detina","orcid":null},"institutions":[{"id":"https://openalex.org/I4210086057","display_name":"Moscow State University of Civil Engineering","ror":"https://ror.org/00em04n91","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210086057"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Elena Detina","raw_affiliation_strings":["Research and Education Center after Zolotov, Moscow State University of Civil Engineering, 129337 Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Research and Education Center after Zolotov, Moscow State University of Civil Engineering, 129337 Moscow, Russia","institution_ids":["https://openalex.org/I4210086057"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5071952948"],"corresponding_institution_ids":["https://openalex.org/I4210086057"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.7825,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.65895516,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"12","issue":"7","first_page":"676","last_page":"676"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11646","display_name":"Nonlocal and gradient elasticity in micro/nano structures","score":0.9983999729156494,"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"}},"topics":[{"id":"https://openalex.org/T11646","display_name":"Nonlocal and gradient elasticity in micro/nano structures","score":0.9983999729156494,"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"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9959999918937683,"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/T12206","display_name":"Vibration and Dynamic Analysis","score":0.9934999942779541,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7134193181991577},{"id":"https://openalex.org/keywords/displacement","display_name":"Displacement (psychology)","score":0.6193377375602722},{"id":"https://openalex.org/keywords/vibration","display_name":"Vibration","score":0.5502005219459534},{"id":"https://openalex.org/keywords/damping-matrix","display_name":"Damping matrix","score":0.5501693487167358},{"id":"https://openalex.org/keywords/beam","display_name":"Beam (structure)","score":0.503924548625946},{"id":"https://openalex.org/keywords/magnitude","display_name":"Magnitude (astronomy)","score":0.48410308361053467},{"id":"https://openalex.org/keywords/damping-ratio","display_name":"Damping ratio","score":0.41822579503059387},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4171101152896881},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.39259061217308044},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.3607555627822876},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2899521589279175},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.1924389898777008},{"id":"https://openalex.org/keywords/stiffness-matrix","display_name":"Stiffness matrix","score":0.17569395899772644},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.14701929688453674}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7134193181991577},{"id":"https://openalex.org/C107551265","wikidata":"https://www.wikidata.org/wiki/Q1458245","display_name":"Displacement (psychology)","level":2,"score":0.6193377375602722},{"id":"https://openalex.org/C198394728","wikidata":"https://www.wikidata.org/wiki/Q3695508","display_name":"Vibration","level":2,"score":0.5502005219459534},{"id":"https://openalex.org/C2777256427","wikidata":"https://www.wikidata.org/wiki/Q5212949","display_name":"Damping matrix","level":4,"score":0.5501693487167358},{"id":"https://openalex.org/C168834538","wikidata":"https://www.wikidata.org/wiki/Q3705329","display_name":"Beam (structure)","level":2,"score":0.503924548625946},{"id":"https://openalex.org/C126691448","wikidata":"https://www.wikidata.org/wiki/Q2028919","display_name":"Magnitude (astronomy)","level":2,"score":0.48410308361053467},{"id":"https://openalex.org/C124139854","wikidata":"https://www.wikidata.org/wiki/Q1127660","display_name":"Damping ratio","level":3,"score":0.41822579503059387},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4171101152896881},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.39259061217308044},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.3607555627822876},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2899521589279175},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.1924389898777008},{"id":"https://openalex.org/C14198674","wikidata":"https://www.wikidata.org/wiki/Q3851930","display_name":"Stiffness matrix","level":3,"score":0.17569395899772644},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.14701929688453674},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"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/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms12070676","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12070676","pdf_url":"https://www.mdpi.com/2075-1680/12/7/676/pdf?version=1688996208","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:46c21f6d99634100af5634a2455817df","is_oa":true,"landing_page_url":"https://doaj.org/article/46c21f6d99634100af5634a2455817df","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 12, Iss 7, p 676 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/12/7/676/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms12070676","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":"Axioms; Volume 12; Issue 7; Pages: 676","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms12070676","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms12070676","pdf_url":"https://www.mdpi.com/2075-1680/12/7/676/pdf?version=1688996208","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"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":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3432891969","display_name":null,"funder_award_id":"21-19-00634","funder_id":"https://openalex.org/F4320324099","funder_display_name":"Russian Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320324099","display_name":"Russian Science Foundation","ror":"https://ror.org/03y2gwe85"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4383878497.pdf"},"referenced_works_count":62,"referenced_works":["https://openalex.org/W362676439","https://openalex.org/W1572302960","https://openalex.org/W1577093815","https://openalex.org/W1993991424","https://openalex.org/W2007631710","https://openalex.org/W2011832794","https://openalex.org/W2033790696","https://openalex.org/W2035618239","https://openalex.org/W2064785350","https://openalex.org/W2072865257","https://openalex.org/W2076510756","https://openalex.org/W2079651294","https://openalex.org/W2079929453","https://openalex.org/W2080296395","https://openalex.org/W2083690060","https://openalex.org/W2085220819","https://openalex.org/W2090818568","https://openalex.org/W2102656083","https://openalex.org/W2111254323","https://openalex.org/W2118415307","https://openalex.org/W2120968945","https://openalex.org/W2125104127","https://openalex.org/W2128462944","https://openalex.org/W2143943794","https://openalex.org/W2152081806","https://openalex.org/W2211280137","https://openalex.org/W2329594468","https://openalex.org/W2501456448","https://openalex.org/W2502737846","https://openalex.org/W2580588034","https://openalex.org/W2731467166","https://openalex.org/W2903867513","https://openalex.org/W2907571581","https://openalex.org/W2910187746","https://openalex.org/W2929025994","https://openalex.org/W2947412119","https://openalex.org/W2963254199","https://openalex.org/W2985325590","https://openalex.org/W2992240192","https://openalex.org/W3033007961","https://openalex.org/W3034586745","https://openalex.org/W3092056877","https://openalex.org/W3093205766","https://openalex.org/W3164878010","https://openalex.org/W3200740916","https://openalex.org/W4200111179","https://openalex.org/W4200218947","https://openalex.org/W4206522304","https://openalex.org/W4236172687","https://openalex.org/W4237051098","https://openalex.org/W4242712695","https://openalex.org/W4248675155","https://openalex.org/W4285185597","https://openalex.org/W4311183346","https://openalex.org/W4323024766","https://openalex.org/W4386864329","https://openalex.org/W6623192766","https://openalex.org/W6634563255","https://openalex.org/W6653366778","https://openalex.org/W6771239883","https://openalex.org/W6805149221","https://openalex.org/W6805254076"],"related_works":["https://openalex.org/W2146707597","https://openalex.org/W1965527087","https://openalex.org/W4386843935","https://openalex.org/W2122348662","https://openalex.org/W3102915582","https://openalex.org/W2074077196","https://openalex.org/W1964206125","https://openalex.org/W2081866650","https://openalex.org/W2387488188","https://openalex.org/W2287416708"],"abstract_inverted_index":{"In":[0],"the":[1,4,19,22,30,43,48,57,64,75,85,91,97,100,104,106,114,127,136,143,160,169,173,181,194],"present":[2],"paper,":[3],"nonlocal-in-time":[5],"damping":[6,59,124],"models,":[7,10,56],"called":[8],"\u201cdamping-with-memory\u201d":[9],"are":[11,26,186],"reviewed.":[12],"Since":[13],"such":[14],"models":[15,148],"do":[16],"not":[17,72],"involve":[18],"distribution":[20],"along":[21,90],"longitudinal":[23],"coordinate,":[24],"they":[25],"easily":[27],"adjustable":[28],"for":[29],"FEM":[31,46],"(Finite":[32],"Element":[33],"Model)":[34],"algorithm,":[35],"which":[36],"is":[37,47,67],"a":[38,61,118,132,176],"big":[39],"advantage":[40],"due":[41],"to":[42,69],"fact":[44],"that":[45,108,168],"most-used":[49],"method":[50],"in":[51,135,187],"engineering":[52],"calculations.":[53],"Within":[54],"damping-with-memory":[55,178],"internal":[58],"of":[60,110,129,131,175],"structure":[62,133],"at":[63],"current":[65],"time,":[66],"assumed":[68],"be":[70,140,151],"dependent":[71],"only":[73],"on":[74,84,113,154],"instant":[76],"strain-rate":[77,86],"magnitude":[78,81],"or":[79,87],"displacement-velocity":[80],"but":[82],"also":[83],"velocity":[88],"values":[89],"previous":[92],"time":[93,102],"history.":[94],"The":[95,147],"greater":[96],"gap":[98],"between":[99],"two":[101],"points,":[103],"lower":[105],"influence":[107],"one":[109],"them":[111],"has":[112,165],"other.":[115],"To":[116],"implement":[117],"composite":[119],"beam":[120,184],"vibration":[121],"simulation":[122,157,197],"involving":[123],"with":[125,159,190],"memory,":[126],"equation":[128],"motion":[130],"written":[134],"matrix":[137],"form":[138],"could":[139,150],"solved":[141],"using":[142,172],"central":[144],"difference":[145],"method.":[146,163],"constructed":[149],"calibrated":[152,177],"based":[153],"3D":[155],"numerical":[156,196],"data":[158],"least":[161],"squares":[162],"It":[164],"been":[166],"shown":[167],"results":[170],"obtained":[171],"implementation":[174],"model":[179],"within":[180],"1D":[182],"finite-element":[183],"algorithm":[185],"good":[188],"correlation":[189],"those":[191],"given":[192],"by":[193],"3D-FEM":[195],"data.":[198]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1}],"updated_date":"2026-02-28T09:26:25.869077","created_date":"2025-10-10T00:00:00"}