{"id":"https://openalex.org/W3108420409","doi":"https://doi.org/10.3390/sym12121933","title":"Dynamics of Nonlocal Rod by Means of Fractional Laplacian","display_name":"Dynamics of Nonlocal Rod by Means of Fractional Laplacian","publication_year":2020,"publication_date":"2020-11-24","ids":{"openalex":"https://openalex.org/W3108420409","doi":"https://doi.org/10.3390/sym12121933","mag":"3108420409"},"language":"en","primary_location":{"id":"doi:10.3390/sym12121933","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12121933","pdf_url":"https://www.mdpi.com/2073-8994/12/12/1933/pdf?version=1606199855","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/2073-8994/12/12/1933/pdf?version=1606199855","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015428805","display_name":"Vittorio Gusella","orcid":"https://orcid.org/0000-0003-0203-5349"},"institutions":[{"id":"https://openalex.org/I27483092","display_name":"University of Perugia","ror":"https://ror.org/00x27da85","country_code":"IT","type":"education","lineage":["https://openalex.org/I27483092"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Vittorio Gusella","raw_affiliation_strings":["Department of Civil and Environmental Engineering, University of Perugia, Via G. Duranti 93, 06125 Perugia, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Civil and Environmental Engineering, University of Perugia, Via G. Duranti 93, 06125 Perugia, Italy","institution_ids":["https://openalex.org/I27483092"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5048726322","display_name":"Giuseppina Autuori","orcid":null},"institutions":[{"id":"https://openalex.org/I27483092","display_name":"University of Perugia","ror":"https://ror.org/00x27da85","country_code":"IT","type":"education","lineage":["https://openalex.org/I27483092"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Giuseppina Autuori","raw_affiliation_strings":["Department of Mathematics and Informatics, University of Perugia, Via Vanvitelli 1, 06123 Perugia, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Informatics, University of Perugia, Via Vanvitelli 1, 06123 Perugia, Italy","institution_ids":["https://openalex.org/I27483092"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030813497","display_name":"Patrizia Pucci","orcid":"https://orcid.org/0000-0001-7242-8485"},"institutions":[{"id":"https://openalex.org/I27483092","display_name":"University of Perugia","ror":"https://ror.org/00x27da85","country_code":"IT","type":"education","lineage":["https://openalex.org/I27483092"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Patrizia Pucci","raw_affiliation_strings":["Department of Mathematics and Informatics, University of Perugia, Via Vanvitelli 1, 06123 Perugia, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Informatics, University of Perugia, Via Vanvitelli 1, 06123 Perugia, Italy","institution_ids":["https://openalex.org/I27483092"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024674319","display_name":"Federico Cluni","orcid":"https://orcid.org/0000-0003-4204-2324"},"institutions":[{"id":"https://openalex.org/I27483092","display_name":"University of Perugia","ror":"https://ror.org/00x27da85","country_code":"IT","type":"education","lineage":["https://openalex.org/I27483092"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Federico Cluni","raw_affiliation_strings":["Department of Civil and Environmental Engineering, University of Perugia, Via G. Duranti 93, 06125 Perugia, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Civil and Environmental Engineering, University of Perugia, Via G. Duranti 93, 06125 Perugia, Italy","institution_ids":["https://openalex.org/I27483092"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5024674319"],"corresponding_institution_ids":["https://openalex.org/I27483092"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.1622,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.42289112,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"12","issue":"12","first_page":"1933","last_page":"1933"},"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":0.9998000264167786,"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":0.9998000264167786,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9986000061035156,"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/T10514","display_name":"Numerical methods in engineering","score":0.9983000159263611,"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/discretization","display_name":"Discretization","score":0.754051685333252},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.6123818755149841},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5297770500183105},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5152485966682434},{"id":"https://openalex.org/keywords/dynamics","display_name":"Dynamics (music)","score":0.5134216547012329},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5066088438034058},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.432783842086792},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42956095933914185},{"id":"https://openalex.org/keywords/vibration","display_name":"Vibration","score":0.41894298791885376},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.21729111671447754}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.754051685333252},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.6123818755149841},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5297770500183105},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5152485966682434},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.5134216547012329},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5066088438034058},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.432783842086792},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42956095933914185},{"id":"https://openalex.org/C198394728","wikidata":"https://www.wikidata.org/wiki/Q3695508","display_name":"Vibration","level":2,"score":0.41894298791885376},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.21729111671447754},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym12121933","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12121933","pdf_url":"https://www.mdpi.com/2073-8994/12/12/1933/pdf?version=1606199855","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:d6045b9dee6849ec8133b290b35e81ff","is_oa":true,"landing_page_url":"https://doaj.org/article/d6045b9dee6849ec8133b290b35e81ff","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 12, Iss 12, p 1933 (2020)","raw_type":"article"},{"id":"pmh:oai:iris.univpm.it:11566/301571","is_oa":true,"landing_page_url":"http://hdl.handle.net/11566/301571","pdf_url":null,"source":{"id":"https://openalex.org/S4306402571","display_name":"Universit\u00e0 Politecnica delle Marche (Universit\u00e0 Politecnica delle Marche)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I122534668","host_organization_name":"Marche Polytechnic University","host_organization_lineage":["https://openalex.org/I122534668"],"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":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:mdpi.com:/2073-8994/12/12/1933/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym12121933","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/sym12121933","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12121933","pdf_url":"https://www.mdpi.com/2073-8994/12/12/1933/pdf?version=1606199855","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/W3108420409.pdf","grobid_xml":"https://content.openalex.org/works/W3108420409.grobid-xml"},"referenced_works_count":39,"referenced_works":["https://openalex.org/W173148493","https://openalex.org/W585482815","https://openalex.org/W1966286680","https://openalex.org/W1979016111","https://openalex.org/W1984898295","https://openalex.org/W1998819932","https://openalex.org/W2000009742","https://openalex.org/W2016912043","https://openalex.org/W2085220819","https://openalex.org/W2122023988","https://openalex.org/W2124797616","https://openalex.org/W2138533896","https://openalex.org/W2149909672","https://openalex.org/W2164948270","https://openalex.org/W2165529896","https://openalex.org/W2289299075","https://openalex.org/W2339644767","https://openalex.org/W2417863416","https://openalex.org/W2519148381","https://openalex.org/W2519211304","https://openalex.org/W2551592702","https://openalex.org/W2554048137","https://openalex.org/W2577673691","https://openalex.org/W2613570595","https://openalex.org/W2617998068","https://openalex.org/W2767075836","https://openalex.org/W2782974711","https://openalex.org/W2806237015","https://openalex.org/W2825855291","https://openalex.org/W2896065171","https://openalex.org/W2933432860","https://openalex.org/W2935937455","https://openalex.org/W2988072344","https://openalex.org/W3005151958","https://openalex.org/W3005470114","https://openalex.org/W3087534202","https://openalex.org/W3101522421","https://openalex.org/W3104791390","https://openalex.org/W6786001461"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W2793786119","https://openalex.org/W1507702947","https://openalex.org/W2067306155"],"abstract_inverted_index":{"The":[0,18,45,107,164],"use":[1],"of":[2,9,20,42,51,101,116,154,180],"fractional":[3,31,92],"models":[4],"to":[5,24,35,68,76,129,145,176,185],"analyse":[6],"nonlocal":[7,43,162,182],"behaviour":[8,155],"solids":[10],"has":[11],"acquired":[12],"great":[13],"importance":[14],"in":[15,33,57,89,112,119],"recent":[16],"years.":[17],"aim":[19],"this":[21],"paper":[22],"is":[23,47,66,105,109],"propose":[25],"a":[26,55,69,117],"model":[27,65,70,93,103,108,171],"that":[28,71,168],"uses":[29,72],"the":[30,37,40,58,63,78,82,86,90,98,102,120,127,152,157,161,169,178,181],"Laplacian":[32],"order":[34],"obtain":[36],"equation":[38,80],"ruling":[39,81],"dynamics":[41,113],"rods.":[44],"solution":[46],"found":[48],"by":[49,114],"means":[50,115],"numerical":[52],"techniques":[53],"with":[54,139],"discretisation":[56,118],"space":[59],"domain.":[60],"At":[61],"first,":[62],"proposed":[64,91,170],"compared":[67],"Eringen\u2019s":[73],"classical":[74],"approach":[75],"derive":[77],"differential":[79],"problem,":[83],"showing":[84,151],"how":[85],"parameters":[87,104],"used":[88,174],"can":[94,172],"be":[95,173],"estimated.":[96],"Moreover,":[97],"physical":[99],"meaning":[100],"assessed.":[106],"then":[110],"extended":[111],"time":[121,140],"domain":[122],"using":[123],"Newmark\u2019s":[124],"method,":[125],"and":[126,141,160,187],"responses":[128],"different":[130],"dynamic":[131,188],"conditions,":[132],"such":[133],"as":[134],"an":[135,146],"external":[136],"load":[137],"varying":[138],"free":[142],"vibrations":[143],"due":[144],"initial":[147],"deformation,":[148],"are":[149],"estimated,":[150],"difference":[153],"between":[156],"local":[158],"response":[159,179],"response.":[163],"obtained":[165],"results":[166],"show":[167],"efficiently":[175],"estimate":[177],"rod":[183],"both":[184],"static":[186],"loads.":[189]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}