{"id":"https://openalex.org/W3082430160","doi":"https://doi.org/10.1142/s0218127420501564","title":"Bifurcation Analysis of Gear Pair with Continuous and Intermittent Mesh Stiffness Using Enhanced Compliance Method","display_name":"Bifurcation Analysis of Gear Pair with Continuous and Intermittent Mesh Stiffness Using Enhanced Compliance Method","publication_year":2020,"publication_date":"2020-08-01","ids":{"openalex":"https://openalex.org/W3082430160","doi":"https://doi.org/10.1142/s0218127420501564","mag":"3082430160"},"language":"en","primary_location":{"id":"doi:10.1142/s0218127420501564","is_oa":true,"landing_page_url":"https://doi.org/10.1142/s0218127420501564","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1142/s0218127420501564","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088075975","display_name":"De\u2010Shin Liu","orcid":"https://orcid.org/0000-0002-3613-3206"},"institutions":[{"id":"https://openalex.org/I148099254","display_name":"National Chung Cheng University","ror":"https://ror.org/0028v3876","country_code":"TW","type":"education","lineage":["https://openalex.org/I148099254"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"De-Shin Liu","raw_affiliation_strings":["Department of Mechanical Engineering, National Chung Cheng University, Chia-Yi, 621, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, National Chung Cheng University, Chia-Yi, 621, Taiwan","institution_ids":["https://openalex.org/I148099254"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065091261","display_name":"Chuen-Ren Wang","orcid":"https://orcid.org/0000-0002-7356-8583"},"institutions":[{"id":"https://openalex.org/I148099254","display_name":"National Chung Cheng University","ror":"https://ror.org/0028v3876","country_code":"TW","type":"education","lineage":["https://openalex.org/I148099254"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Chuen-Ren Wang","raw_affiliation_strings":["Department of Mechanical Engineering, National Chung Cheng University, Chia-Yi, 621, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, National Chung Cheng University, Chia-Yi, 621, Taiwan","institution_ids":["https://openalex.org/I148099254"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108553392","display_name":"Ting-Nung Shiau","orcid":null},"institutions":[{"id":"https://openalex.org/I148099254","display_name":"National Chung Cheng University","ror":"https://ror.org/0028v3876","country_code":"TW","type":"education","lineage":["https://openalex.org/I148099254"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Ting-Nung Shiau","raw_affiliation_strings":["Department of Mechanical Engineering, National Chung Cheng University, Chia-Yi, 621, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, National Chung Cheng University, Chia-Yi, 621, Taiwan","institution_ids":["https://openalex.org/I148099254"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112561431","display_name":"K. H. Huang","orcid":null},"institutions":[{"id":"https://openalex.org/I148099254","display_name":"National Chung Cheng University","ror":"https://ror.org/0028v3876","country_code":"TW","type":"education","lineage":["https://openalex.org/I148099254"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Kuo-Hsuan Huang","raw_affiliation_strings":["Department of Mechanical Engineering, National Chung Cheng University, Chia-Yi, 621, Taiwan"],"raw_orcid":"https://orcid.org/0000-0002-8910-5233","affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, National Chung Cheng University, Chia-Yi, 621, Taiwan","institution_ids":["https://openalex.org/I148099254"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5038753623","display_name":"Wei-Chun Hsu","orcid":null},"institutions":[{"id":"https://openalex.org/I162521676","display_name":"WuFeng University","ror":"https://ror.org/05d293n36","country_code":"TW","type":"education","lineage":["https://openalex.org/I162521676"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Wei-Chun Hsu","raw_affiliation_strings":["Department of Mechanical Engineering, Wu Feng University, Chia-Yi, 621, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, Wu Feng University, Chia-Yi, 621, Taiwan","institution_ids":["https://openalex.org/I162521676"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5088075975"],"corresponding_institution_ids":["https://openalex.org/I148099254"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.10260326,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"30","issue":"10","first_page":"2050156","last_page":"2050156"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11062","display_name":"Gear and Bearing Dynamics Analysis","score":0.9998999834060669,"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/T11062","display_name":"Gear and Bearing Dynamics Analysis","score":0.9998999834060669,"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/T11138","display_name":"Tribology and Lubrication Engineering","score":0.9912999868392944,"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/T12907","display_name":"Mechanical Engineering and Vibrations Research","score":0.9872000217437744,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/lyapunov-exponent","display_name":"Lyapunov exponent","score":0.6705442070960999},{"id":"https://openalex.org/keywords/sine","display_name":"Sine","score":0.6599104404449463},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5354706645011902},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.510464072227478},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.5011003017425537},{"id":"https://openalex.org/keywords/stiffness","display_name":"Stiffness","score":0.4981977939605713},{"id":"https://openalex.org/keywords/bifurcation","display_name":"Bifurcation","score":0.4876900911331177},{"id":"https://openalex.org/keywords/aperiodic-graph","display_name":"Aperiodic graph","score":0.4784529209136963},{"id":"https://openalex.org/keywords/periodic-function","display_name":"Periodic function","score":0.4699026942253113},{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"Trigonometric functions","score":0.44914793968200684},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4382585287094116},{"id":"https://openalex.org/keywords/bifurcation-diagram","display_name":"Bifurcation diagram","score":0.42085200548171997},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2709215581417084},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.17244726419448853},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14800643920898438}],"concepts":[{"id":"https://openalex.org/C191544260","wikidata":"https://www.wikidata.org/wiki/Q1238630","display_name":"Lyapunov exponent","level":3,"score":0.6705442070960999},{"id":"https://openalex.org/C186661526","wikidata":"https://www.wikidata.org/wiki/Q13647261","display_name":"Sine","level":2,"score":0.6599104404449463},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5354706645011902},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.510464072227478},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.5011003017425537},{"id":"https://openalex.org/C2779372316","wikidata":"https://www.wikidata.org/wiki/Q569057","display_name":"Stiffness","level":2,"score":0.4981977939605713},{"id":"https://openalex.org/C2781349735","wikidata":"https://www.wikidata.org/wiki/Q4904824","display_name":"Bifurcation","level":3,"score":0.4876900911331177},{"id":"https://openalex.org/C104247578","wikidata":"https://www.wikidata.org/wiki/Q4779368","display_name":"Aperiodic graph","level":2,"score":0.4784529209136963},{"id":"https://openalex.org/C98644592","wikidata":"https://www.wikidata.org/wiki/Q184743","display_name":"Periodic function","level":2,"score":0.4699026942253113},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.44914793968200684},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4382585287094116},{"id":"https://openalex.org/C86243350","wikidata":"https://www.wikidata.org/wiki/Q2595915","display_name":"Bifurcation diagram","level":4,"score":0.42085200548171997},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2709215581417084},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.17244726419448853},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14800643920898438},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","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},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218127420501564","is_oa":true,"landing_page_url":"https://doi.org/10.1142/s0218127420501564","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1142/s0218127420501564","is_oa":true,"landing_page_url":"https://doi.org/10.1142/s0218127420501564","pdf_url":null,"source":{"id":"https://openalex.org/S81011612","display_name":"International Journal of Bifurcation and Chaos","issn_l":"0218-1274","issn":["0218-1274","1793-6551"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Bifurcation and Chaos","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1555266762","display_name":null,"funder_award_id":"CCNU19TS030","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G3560172809","display_name":null,"funder_award_id":"11771168","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8483412","display_name":null,"funder_award_id":"11871235","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/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1968800475","https://openalex.org/W1975215659","https://openalex.org/W1990948624","https://openalex.org/W2010449232","https://openalex.org/W2017263301","https://openalex.org/W2033641397","https://openalex.org/W2046216954","https://openalex.org/W2047069904","https://openalex.org/W2047125371","https://openalex.org/W2047720174","https://openalex.org/W2052800408","https://openalex.org/W2076801548","https://openalex.org/W2108726035","https://openalex.org/W2276527129","https://openalex.org/W2525153292","https://openalex.org/W4247685643"],"related_works":["https://openalex.org/W2063166054","https://openalex.org/W2358475213","https://openalex.org/W2028663913","https://openalex.org/W3142213391","https://openalex.org/W1775321609","https://openalex.org/W4385749744","https://openalex.org/W4316092752","https://openalex.org/W2588864086","https://openalex.org/W1511441395","https://openalex.org/W2092000673"],"abstract_inverted_index":{"The":[0,55],"nonlinear":[1],"dynamics":[2],"of":[3,35,37,49,63,84,105,118,135],"a":[4],"multigear":[5,39,65],"pair":[6,40,66],"with":[7,69],"the":[8,21,33,38,50,60,64,85,106,112,116,132],"time-varying":[9,86],"gear":[10,51,87,107],"mesh":[11,52,88,108],"stiffness":[12],"are":[13,29,67,100],"investigated":[14],"using":[15,73],"an":[16],"enhanced":[17],"compliance-based":[18],"methodology.":[19],"In":[20,110],"proposed":[22],"approach,":[23],"Lagrangian":[24],"theory":[25],"and":[26,41,77,81,97,122,126],"Runge\u2013Kutta":[27],"method":[28],"used":[30],"to":[31],"derive":[32],"equation":[34],"motion":[36,121],"solve":[42],"its":[43],"dynamic":[44,61],"response":[45],"for":[46,59],"various":[47],"values":[48,104],"frequency,":[53],"respectively.":[54],"simulation":[56],"results":[57],"obtained":[58,71],"behavior":[62],"compared":[68],"those":[70],"by":[72],"continuous":[74],"(cosine,":[75],"sine":[76,79],"offset":[78],"function)":[80],"intermittent":[82],"representations":[83],"stiffness.":[89],"It":[90],"is":[91],"shown":[92],"that":[93],"periodic,":[94],"quasi-periodic,":[95],"aperiodic":[96],"chaos":[98,133],"motions":[99],"induced":[101],"at":[102],"different":[103],"frequency.":[109],"addition,":[111],"bifurcation":[113],"diagram":[114],"reveals":[115],"occurrence":[117],"both":[119],"nonimpact":[120],"single-sided":[123],"impact":[124],"motion,":[125],"Lyapunov":[127],"exponent":[128],"can":[129],"easily":[130],"diagnose":[131],"phenomenon":[134],"system.":[136]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
