{"id":"https://openalex.org/W3164058334","doi":"https://doi.org/10.1109/access.2021.3083809","title":"Discontinuous Dynamic Analysis of a Class of 2-DOF Oscillators With Strong Nonlinearity Under a Periodic Excitation","display_name":"Discontinuous Dynamic Analysis of a Class of 2-DOF Oscillators With Strong Nonlinearity Under a Periodic Excitation","publication_year":2021,"publication_date":"2021-01-01","ids":{"openalex":"https://openalex.org/W3164058334","doi":"https://doi.org/10.1109/access.2021.3083809","mag":"3164058334"},"language":"en","primary_location":{"id":"doi:10.1109/access.2021.3083809","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3083809","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/9312710/09440959.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/9312710/09440959.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000019900","display_name":"Jinjun Fan","orcid":"https://orcid.org/0000-0002-8056-5364"},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinjun Fan","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong Normal University, Jinan, China"],"raw_orcid":"https://orcid.org/0000-0002-8056-5364","affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan, China","institution_ids":["https://openalex.org/I28006308"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100678967","display_name":"Min Gao","orcid":"https://orcid.org/0000-0003-3899-2933"},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Min Gao","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong Normal University, Jinan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan, China","institution_ids":["https://openalex.org/I28006308"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024853003","display_name":"Shoulian Chen","orcid":null},"institutions":[{"id":"https://openalex.org/I28006308","display_name":"Shandong Normal University","ror":"https://ror.org/01wy3h363","country_code":"CN","type":"education","lineage":["https://openalex.org/I28006308"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shoulian Chen","raw_affiliation_strings":["School of Mathematics and Statistics, Shandong Normal University, Jinan, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Shandong Normal University, Jinan, China","institution_ids":["https://openalex.org/I28006308"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I28006308"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.3968,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.57673028,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"9","issue":null,"first_page":"77997","last_page":"78016"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10690","display_name":"Vibration Control and Rheological Fluids","score":0.9983999729156494,"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"}},"topics":[{"id":"https://openalex.org/T10690","display_name":"Vibration Control and Rheological Fluids","score":0.9983999729156494,"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/T11394","display_name":"Dynamics and Control of Mechanical Systems","score":0.9983999729156494,"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/T12206","display_name":"Vibration and Dynamic Analysis","score":0.9983000159263611,"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/control-theory","display_name":"Control theory (sociology)","score":0.7061834931373596},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6741173267364502},{"id":"https://openalex.org/keywords/phase-plane","display_name":"Phase plane","score":0.5555802583694458},{"id":"https://openalex.org/keywords/vibration","display_name":"Vibration","score":0.5546970963478088},{"id":"https://openalex.org/keywords/frequency-domain","display_name":"Frequency domain","score":0.5117285251617432},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.4631122648715973},{"id":"https://openalex.org/keywords/excitation","display_name":"Excitation","score":0.45210832357406616},{"id":"https://openalex.org/keywords/amplitude","display_name":"Amplitude","score":0.4335963726043701},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.42960745096206665},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3332647979259491},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32627540826797485},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.27067577838897705},{"id":"https://openalex.org/keywords/acoustics","display_name":"Acoustics","score":0.13364917039871216},{"id":"https://openalex.org/keywords/optics","display_name":"Optics","score":0.091511070728302},{"id":"https://openalex.org/keywords/control","display_name":"Control (management)","score":0.08245816826820374}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7061834931373596},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6741173267364502},{"id":"https://openalex.org/C157626765","wikidata":"https://www.wikidata.org/wiki/Q2088081","display_name":"Phase plane","level":3,"score":0.5555802583694458},{"id":"https://openalex.org/C198394728","wikidata":"https://www.wikidata.org/wiki/Q3695508","display_name":"Vibration","level":2,"score":0.5546970963478088},{"id":"https://openalex.org/C19118579","wikidata":"https://www.wikidata.org/wiki/Q786423","display_name":"Frequency domain","level":2,"score":0.5117285251617432},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.4631122648715973},{"id":"https://openalex.org/C83581075","wikidata":"https://www.wikidata.org/wiki/Q1361503","display_name":"Excitation","level":2,"score":0.45210832357406616},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.4335963726043701},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.42960745096206665},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3332647979259491},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32627540826797485},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.27067577838897705},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.13364917039871216},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","level":1,"score":0.091511070728302},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.08245816826820374},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2021.3083809","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3083809","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/9312710/09440959.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:5314600cdaa04563a006585d17b79d71","is_oa":true,"landing_page_url":"https://doaj.org/article/5314600cdaa04563a006585d17b79d71","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":"IEEE Access, Vol 9, Pp 77997-78016 (2021)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2021.3083809","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2021.3083809","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/9312710/09440959.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7400000095367432,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G1035110704","display_name":null,"funder_award_id":"ZR2019MA048","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G3590388942","display_name":"\u4e0d\u8fde\u7eed\u52a8\u529b\u7cfb\u7edf\u52a8\u529b\u5b66\u95ee\u9898\u7814\u7a76","funder_award_id":"11971275","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"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}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3164058334.pdf","grobid_xml":"https://content.openalex.org/works/W3164058334.grobid-xml"},"referenced_works_count":82,"referenced_works":["https://openalex.org/W223797242","https://openalex.org/W290783162","https://openalex.org/W321907441","https://openalex.org/W651117694","https://openalex.org/W1495343868","https://openalex.org/W1542389835","https://openalex.org/W1552277675","https://openalex.org/W1558079603","https://openalex.org/W1592648094","https://openalex.org/W1605896383","https://openalex.org/W1728654233","https://openalex.org/W1964094519","https://openalex.org/W1965482992","https://openalex.org/W1968467183","https://openalex.org/W1969325903","https://openalex.org/W1973699155","https://openalex.org/W1978782086","https://openalex.org/W1980151356","https://openalex.org/W1981193694","https://openalex.org/W1982071062","https://openalex.org/W1993856825","https://openalex.org/W1998749877","https://openalex.org/W2012069094","https://openalex.org/W2015142253","https://openalex.org/W2016116229","https://openalex.org/W2016609461","https://openalex.org/W2023512626","https://openalex.org/W2032713764","https://openalex.org/W2033225924","https://openalex.org/W2053648000","https://openalex.org/W2059184951","https://openalex.org/W2065381922","https://openalex.org/W2068075556","https://openalex.org/W2072292138","https://openalex.org/W2073502901","https://openalex.org/W2074386637","https://openalex.org/W2074896974","https://openalex.org/W2080360523","https://openalex.org/W2081758200","https://openalex.org/W2089646743","https://openalex.org/W2089936922","https://openalex.org/W2091115131","https://openalex.org/W2098982596","https://openalex.org/W2100635990","https://openalex.org/W2112315996","https://openalex.org/W2137239416","https://openalex.org/W2153024620","https://openalex.org/W2155538629","https://openalex.org/W2167866500","https://openalex.org/W2482596421","https://openalex.org/W2487094296","https://openalex.org/W2560127293","https://openalex.org/W2593063709","https://openalex.org/W2593468450","https://openalex.org/W2595509448","https://openalex.org/W2766719159","https://openalex.org/W2769976934","https://openalex.org/W2790389815","https://openalex.org/W2792487153","https://openalex.org/W2794628193","https://openalex.org/W2799308947","https://openalex.org/W2883595324","https://openalex.org/W2888307405","https://openalex.org/W2891367590","https://openalex.org/W2894651388","https://openalex.org/W2903032389","https://openalex.org/W2903814344","https://openalex.org/W2910997779","https://openalex.org/W2911855588","https://openalex.org/W2913969466","https://openalex.org/W2959395361","https://openalex.org/W3086239743","https://openalex.org/W3150913747","https://openalex.org/W4237806643","https://openalex.org/W4238000550","https://openalex.org/W4242981652","https://openalex.org/W4293078920","https://openalex.org/W4299825255","https://openalex.org/W4300220933","https://openalex.org/W6611126545","https://openalex.org/W6637598801","https://openalex.org/W6682373644"],"related_works":["https://openalex.org/W2364310969","https://openalex.org/W2373007135","https://openalex.org/W2004357175","https://openalex.org/W2064502186","https://openalex.org/W1990192565","https://openalex.org/W2390901883","https://openalex.org/W2012074534","https://openalex.org/W4211113703","https://openalex.org/W2383330891","https://openalex.org/W2011422850"],"abstract_inverted_index":{"Starting":[0],"from":[1],"the":[2,6,25,36,43,46,75,81,93,107,115,124,141,148,152,165,170,177,184,192,198,206,235],"car":[3],"suspension":[4,240],"system,":[5],"nonlinear":[7],"characteristics":[8],"of":[9,12,28,42,49,54,83,129,140,147,155,169,187,200,229,238],"a":[10,19,138],"class":[11],"two-degree-of-freedom":[13],"oscillators":[14],"with":[15,213,232,257],"strong":[16],"nonlinearity":[17],"under":[18,151],"periodic":[20,118,132],"excitation":[21],"are":[22,90,120,158,218],"discussed":[23],"by":[24,175,183,191],"switching":[26,96],"theory":[27,102],"flow":[29],"in":[30,65,86,252],"discontinuous":[31,37],"dynamical":[32,204],"systems.":[33,241],"Based":[34],"on":[35,203],"forces":[38,145],"and":[39,62,67,77,80,95,111,114,137,167,208,234],"different":[40,88],"motions":[41,79,119,133],"two":[44,87,127,149,153],"masses,":[45],"phase":[47],"plane":[48],"each":[50],"mass":[51],"is":[52,103,181],"composed":[53],"stick":[55,76,125,207],"domain,":[56],"nonstick":[57,78],"domain":[58],"(or":[59,144],"free":[60],"domain)":[61],"separation":[63],"boundary":[64],"absolute":[66],"relative":[68],"coordinates,":[69],"respectively.":[70],"The":[71,99,161],"swithching":[72],"criteria":[73],"between":[74],"conditions":[82,116,154],"grazing":[84,130,209],"motion":[85],"regions":[89],"developed":[91],"via":[92],"G-functions":[94],"control":[97,156,178,185],"laws.":[98],"mapping":[100],"dynamics":[101],"used":[104],"to":[105],"give":[106],"four-dimensional":[108,112],"transformation":[109],"set":[110],"mapping,":[113],"for":[117,134,226,249],"explored.":[121],"In":[122],"addition,":[123],"motions,":[126,131],"kinds":[128],"this":[135],"system":[136,188,201],"comparison":[139],"velocities,":[142],"accelerations":[143],"responses)":[146],"masses":[150],"force":[157],"simulated":[159],"numerically.":[160],"results":[162],"show":[163],"that":[164],"stability":[166],"comfort":[168],"vehicle":[171,239],"can":[172,222],"be":[173],"improved":[174],"adjusting":[176],"force,":[179],"which":[180,221],"generated":[182],"unit":[186],"or":[189,216,255],"exerted":[190],"external":[193],"excitation.":[194],"For":[195],"further":[196],"investigating":[197],"influence":[199],"parameters":[202],"behaviors,":[205],"bifurcation":[210],"scenarios":[211],"varying":[212],"driving":[214],"frequency":[215],"amplitude":[217],"also":[219,244],"developed,":[220],"provide":[223],"useful":[224],"information":[225],"parameter":[227],"selection":[228],"vibration":[230],"systems":[231],"clearance":[233],"optimal":[236],"design":[237],"This":[242],"paper":[243],"has":[245],"important":[246],"reference":[247],"value":[248],"practical":[250],"applications":[251],"other":[253],"industries":[254],"machinery":[256],"elastic":[258],"impacts.":[259]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}