{"id":"https://openalex.org/W4280545947","doi":"https://doi.org/10.3390/sym14051030","title":"Longitudinal Wave Locally Resonant Band Gaps in Metamaterial-Based Elastic Rods Comprising Multi-Degree-of-Freedom DAVI Resonators","display_name":"Longitudinal Wave Locally Resonant Band Gaps in Metamaterial-Based Elastic Rods Comprising Multi-Degree-of-Freedom DAVI Resonators","publication_year":2022,"publication_date":"2022-05-18","ids":{"openalex":"https://openalex.org/W4280545947","doi":"https://doi.org/10.3390/sym14051030"},"language":"en","primary_location":{"id":"doi:10.3390/sym14051030","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14051030","pdf_url":"https://www.mdpi.com/2073-8994/14/5/1030/pdf?version=1652846965","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/2073-8994/14/5/1030/pdf?version=1652846965","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5075726995","display_name":"Niuniu Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I80947539","display_name":"Fuzhou University","ror":"https://ror.org/011xvna82","country_code":"CN","type":"education","lineage":["https://openalex.org/I80947539"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Niuniu Liu","raw_affiliation_strings":["School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350116, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350116, China","institution_ids":["https://openalex.org/I80947539"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047995650","display_name":"Xianliang Lei","orcid":null},"institutions":[{"id":"https://openalex.org/I80947539","display_name":"Fuzhou University","ror":"https://ror.org/011xvna82","country_code":"CN","type":"education","lineage":["https://openalex.org/I80947539"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xianliang Lei","raw_affiliation_strings":["School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350116, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350116, China","institution_ids":["https://openalex.org/I80947539"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003261045","display_name":"Fuqiang Lai","orcid":"https://orcid.org/0009-0001-0562-6171"},"institutions":[{"id":"https://openalex.org/I80947539","display_name":"Fuzhou University","ror":"https://ror.org/011xvna82","country_code":"CN","type":"education","lineage":["https://openalex.org/I80947539"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Fuqiang Lai","raw_affiliation_strings":["School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350116, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350116, China","institution_ids":["https://openalex.org/I80947539"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5028315721","display_name":"Xin Xue","orcid":"https://orcid.org/0000-0001-8021-6685"},"institutions":[{"id":"https://openalex.org/I80947539","display_name":"Fuzhou University","ror":"https://ror.org/011xvna82","country_code":"CN","type":"education","lineage":["https://openalex.org/I80947539"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xin Xue","raw_affiliation_strings":["School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350116, China"],"raw_orcid":"https://orcid.org/0000-0001-8021-6685","affiliations":[{"raw_affiliation_string":"School of Mechanical Engineering and Automation, Fuzhou University, Fuzhou 350116, China","institution_ids":["https://openalex.org/I80947539"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5003261045"],"corresponding_institution_ids":["https://openalex.org/I80947539"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.2452,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.46006756,"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":"1030","last_page":"1030"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10822","display_name":"Acoustic Wave Phenomena Research","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T10822","display_name":"Acoustic Wave Phenomena Research","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T10160","display_name":"Seismic Performance and Analysis","score":0.9609000086784363,"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"}},{"id":"https://openalex.org/T10690","display_name":"Vibration Control and Rheological Fluids","score":0.9553999900817871,"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/resonator","display_name":"Resonator","score":0.8800479173660278},{"id":"https://openalex.org/keywords/metamaterial","display_name":"Metamaterial","score":0.7099210023880005},{"id":"https://openalex.org/keywords/band-gap","display_name":"Band gap","score":0.5854858756065369},{"id":"https://openalex.org/keywords/rod","display_name":"Rod","score":0.5650599002838135},{"id":"https://openalex.org/keywords/materials-science","display_name":"Materials science","score":0.5119796991348267},{"id":"https://openalex.org/keywords/vibration","display_name":"Vibration","score":0.49399787187576294},{"id":"https://openalex.org/keywords/resonance","display_name":"Resonance (particle physics)","score":0.43879106640815735},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4203585982322693},{"id":"https://openalex.org/keywords/transfer-matrix-method","display_name":"Transfer-matrix method (optics)","score":0.41228196024894714},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.3071483373641968},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.30507686734199524},{"id":"https://openalex.org/keywords/optoelectronics","display_name":"Optoelectronics","score":0.18570032715797424}],"concepts":[{"id":"https://openalex.org/C97126364","wikidata":"https://www.wikidata.org/wiki/Q349669","display_name":"Resonator","level":2,"score":0.8800479173660278},{"id":"https://openalex.org/C110367647","wikidata":"https://www.wikidata.org/wiki/Q497166","display_name":"Metamaterial","level":2,"score":0.7099210023880005},{"id":"https://openalex.org/C181966813","wikidata":"https://www.wikidata.org/wiki/Q806352","display_name":"Band gap","level":2,"score":0.5854858756065369},{"id":"https://openalex.org/C162184086","wikidata":"https://www.wikidata.org/wiki/Q505544","display_name":"Rod","level":3,"score":0.5650599002838135},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.5119796991348267},{"id":"https://openalex.org/C198394728","wikidata":"https://www.wikidata.org/wiki/Q3695508","display_name":"Vibration","level":2,"score":0.49399787187576294},{"id":"https://openalex.org/C139210041","wikidata":"https://www.wikidata.org/wiki/Q2145840","display_name":"Resonance (particle physics)","level":2,"score":0.43879106640815735},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4203585982322693},{"id":"https://openalex.org/C156005064","wikidata":"https://www.wikidata.org/wiki/Q7833984","display_name":"Transfer-matrix method (optics)","level":2,"score":0.41228196024894714},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.3071483373641968},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.30507686734199524},{"id":"https://openalex.org/C49040817","wikidata":"https://www.wikidata.org/wiki/Q193091","display_name":"Optoelectronics","level":1,"score":0.18570032715797424},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C142724271","wikidata":"https://www.wikidata.org/wiki/Q7208","display_name":"Pathology","level":1,"score":0.0},{"id":"https://openalex.org/C204787440","wikidata":"https://www.wikidata.org/wiki/Q188504","display_name":"Alternative medicine","level":2,"score":0.0},{"id":"https://openalex.org/C109214941","wikidata":"https://www.wikidata.org/wiki/Q18334","display_name":"Particle physics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym14051030","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14051030","pdf_url":"https://www.mdpi.com/2073-8994/14/5/1030/pdf?version=1652846965","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:1e3a982f593f4c4094d2aef77ef932db","is_oa":true,"landing_page_url":"https://doaj.org/article/1e3a982f593f4c4094d2aef77ef932db","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 1030 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/14/5/1030/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym14051030","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/sym14051030","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14051030","pdf_url":"https://www.mdpi.com/2073-8994/14/5/1030/pdf?version=1652846965","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":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.8299999833106995}],"awards":[{"id":"https://openalex.org/G1366797637","display_name":null,"funder_award_id":"JAT190009","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G137744388","display_name":null,"funder_award_id":"GXRC-20018","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1686610842","display_name":null,"funder_award_id":"52105091","funder_id":"https://openalex.org/F4320325408","funder_display_name":"Fuzhou University"},{"id":"https://openalex.org/G1711852425","display_name":null,"funder_award_id":"2021J05115","funder_id":"https://openalex.org/F4320321878","funder_display_name":"Natural Science Foundation of Fujian Province"},{"id":"https://openalex.org/G225264981","display_name":null,"funder_award_id":"GXRC-20018","funder_id":"https://openalex.org/F4320321878","funder_display_name":"Natural Science Foundation of Fujian Province"},{"id":"https://openalex.org/G2753656647","display_name":null,"funder_award_id":"VSN202103","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3117129248","display_name":null,"funder_award_id":"GXRC-20014","funder_id":"https://openalex.org/F4320325408","funder_display_name":"Fuzhou University"},{"id":"https://openalex.org/G3600993856","display_name":null,"funder_award_id":"52105091","funder_id":"https://openalex.org/F4320321878","funder_display_name":"Natural Science Foundation of Fujian Province"},{"id":"https://openalex.org/G3651534257","display_name":null,"funder_award_id":"VSN202103","funder_id":"https://openalex.org/F4320325408","funder_display_name":"Fuzhou University"},{"id":"https://openalex.org/G4200931083","display_name":null,"funder_award_id":"GXRC-20014","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4897045097","display_name":null,"funder_award_id":"JAT190009","funder_id":"https://openalex.org/F4320321878","funder_display_name":"Natural Science Foundation of Fujian Province"},{"id":"https://openalex.org/G5230673458","display_name":null,"funder_award_id":"52105091","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6090439127","display_name":null,"funder_award_id":"GXRC-20014","funder_id":"https://openalex.org/F4320321878","funder_display_name":"Natural Science Foundation of Fujian Province"},{"id":"https://openalex.org/G6202089580","display_name":null,"funder_award_id":"2021J05115","funder_id":"https://openalex.org/F4320325408","funder_display_name":"Fuzhou University"},{"id":"https://openalex.org/G6556975126","display_name":null,"funder_award_id":"VSN202103","funder_id":"https://openalex.org/F4320321878","funder_display_name":"Natural Science Foundation of Fujian Province"},{"id":"https://openalex.org/G6825495131","display_name":null,"funder_award_id":"JAT190009","funder_id":"https://openalex.org/F4320325408","funder_display_name":"Fuzhou University"},{"id":"https://openalex.org/G6890953653","display_name":null,"funder_award_id":"2021J05115","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8997638633","display_name":null,"funder_award_id":"GXRC-20018","funder_id":"https://openalex.org/F4320325408","funder_display_name":"Fuzhou University"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321878","display_name":"Natural Science Foundation of Fujian Province","ror":null},{"id":"https://openalex.org/F4320325408","display_name":"Fuzhou University","ror":"https://ror.org/011xvna82"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4280545947.pdf","grobid_xml":"https://content.openalex.org/works/W4280545947.grobid-xml"},"referenced_works_count":35,"referenced_works":["https://openalex.org/W1967180432","https://openalex.org/W1990731446","https://openalex.org/W1994982755","https://openalex.org/W1996091678","https://openalex.org/W1996535703","https://openalex.org/W2005030381","https://openalex.org/W2007180834","https://openalex.org/W2008279176","https://openalex.org/W2010288322","https://openalex.org/W2017305992","https://openalex.org/W2021209075","https://openalex.org/W2026078581","https://openalex.org/W2029130410","https://openalex.org/W2037761271","https://openalex.org/W2040701462","https://openalex.org/W2041047547","https://openalex.org/W2067051496","https://openalex.org/W2075053184","https://openalex.org/W2076460617","https://openalex.org/W2088676195","https://openalex.org/W2091039113","https://openalex.org/W2152873637","https://openalex.org/W2622413833","https://openalex.org/W2746277395","https://openalex.org/W2911320049","https://openalex.org/W2914729639","https://openalex.org/W2999881002","https://openalex.org/W3007616443","https://openalex.org/W3099829450","https://openalex.org/W3124443531","https://openalex.org/W3178116658","https://openalex.org/W3215239610","https://openalex.org/W4206824787","https://openalex.org/W4230420206","https://openalex.org/W6785564777"],"related_works":["https://openalex.org/W1570806970","https://openalex.org/W2174268617","https://openalex.org/W4390331329","https://openalex.org/W2951552468","https://openalex.org/W2045305845","https://openalex.org/W2545051477","https://openalex.org/W2166662560","https://openalex.org/W3021878631","https://openalex.org/W4386932413","https://openalex.org/W2090780666"],"abstract_inverted_index":{"The":[0,51,110,162,181],"wave":[1],"propagation":[2],"and":[3,35,64],"vibration":[4,17],"transmission":[5],"in":[6,106,128],"metamaterial-based":[7,88],"elastic":[8,89],"rods":[9],"with":[10,59,124,186,206],"periodically":[11,84],"attached":[12],"multi-degree-of-freedom":[13],"(MDOF)":[14],"dynamic":[15,138],"anti-resonant":[16],"isolator":[18],"(DAVI)":[19],"resonators":[20,63,68,83,116,127],"are":[21,69,169],"investigated.":[22],"A":[23,72],"methodology":[24],"based":[25],"on":[26,86],"a":[27,141,149,197],"combination":[28],"of":[29,54,80,140,147,164,177],"the":[30,36,46,55,77,87,103,107,121,136,144,165,173,178,187,192,207,210],"transfer":[31],"matrix":[32],"(TM)":[33],"method":[34],"Bloch":[37],"theorem":[38],"is":[39,160],"developed,":[40],"yielding":[41],"an":[42,93,118],"explicit":[43],"formulation":[44],"for":[45],"complex":[47],"band":[48,97,132,154,175,203],"structure":[49,57,78,112,123,159,194],"calculation.":[50],"bandgap":[52],"behavior":[53],"periodic":[56,111,122,158,179,193],"arrayed":[58],"single-degree-of-freedom":[60],"(SDOF)":[61],"DAVI":[62,67,82,115,126,142,167,190],"two-degree-of-freedom":[65],"(2DOF)":[66],"investigated,":[70],"respectively.":[71],"comparative":[73],"study":[74],"indicates":[75],"that":[76],"consisting":[79],"SDOF":[81,125],"jointed":[85],"rod":[90],"can":[91,195],"obtain":[92,172],"initial":[94,151,200],"locally":[95,152,201],"resonant":[96,153,202],"gap":[98,155,176,204],"500":[99],"Hz":[100],"smaller":[101],"than":[102],"one":[104],"given":[105],"published":[108],"literature.":[109],"containing":[113],"2DOF":[114,166,189],"has":[117],"advantage":[119],"over":[120],"achieving":[129,148],"two":[130],"resonance":[131],"gaps.":[133],"By":[134],"analyzing":[135],"equivalent":[137],"mass":[139],"resonator,":[143],"underlying":[145],"mechanism":[146],"lower":[150,199],"by":[156],"this":[157],"revealed.":[161],"parameters":[163],"resonator":[168],"optimized":[170],"to":[171],"lowest":[174],"structure.":[180],"numerical":[182],"results":[183],"show":[184],"that,":[185],"optimal":[188],"parameters,":[191],"generate":[196],"much":[198],"compared":[205],"case":[208],"before":[209],"optimization.":[211]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}