{"id":"https://openalex.org/W4414769799","doi":"https://doi.org/10.1007/s11071-025-11848-z","title":"Internal resonance analysis and parameter optimization of the fractional SD oscillator system","display_name":"Internal resonance analysis and parameter optimization of the fractional SD oscillator system","publication_year":2025,"publication_date":"2025-10-02","ids":{"openalex":"https://openalex.org/W4414769799","doi":"https://doi.org/10.1007/s11071-025-11848-z"},"language":"en","primary_location":{"id":"doi:10.1007/s11071-025-11848-z","doi":"https://doi.org/10.1007/s11071-025-11848-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11071-025-11848-z","pdf_url":null,"source":{"id":"https://openalex.org/S138681734","display_name":"Nonlinear Dynamics","issn_l":"0924-090X","issn":["0924-090X","1573-269X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nonlinear Dynamics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063850144","display_name":"Xuan Luo","orcid":"https://orcid.org/0000-0002-0137-7681","observed_orcids":["https://orcid.org/0000-0002-0137-7681"]},"institutions":[{"id":"https://openalex.org/I174104030","display_name":"Taiyuan Normal University","ror":"https://ror.org/051k00p03","country_code":"CN","type":"education","lineage":["https://openalex.org/I174104030"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xuan Luo","raw_affiliation_strings":["College of Computer Science and Technology, Taiyuan Normal University, Jinzhong, 030619, China","School of Mathematics and Statistics, Taiyuan Normal University, Jinzhong, 030619, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Computer Science and Technology, Taiyuan Normal University, Jinzhong, 030619, China","institution_ids":["https://openalex.org/I174104030"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Taiyuan Normal University, Jinzhong, 030619, China","institution_ids":["https://openalex.org/I174104030"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088913520","display_name":"Jiaquan Xie","orcid":"https://orcid.org/0000-0002-1323-5402","observed_orcids":["https://orcid.org/0000-0002-1323-5402"]},"institutions":[{"id":"https://openalex.org/I174104030","display_name":"Taiyuan Normal University","ror":"https://ror.org/051k00p03","country_code":"CN","type":"education","lineage":["https://openalex.org/I174104030"]},{"id":"https://openalex.org/I4405273379","display_name":"Shanxi Provincial Education Department","ror":"https://ror.org/05r16bb17","country_code":"CN","type":"government","lineage":["https://openalex.org/I4405273379"]},{"id":"https://openalex.org/I9086337","display_name":"Taiyuan University of Technology","ror":"https://ror.org/03kv08d37","country_code":"CN","type":"education","lineage":["https://openalex.org/I9086337"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jiaquan Xie","raw_affiliation_strings":["Engineering Research Center of Advanced Metal Composites Forming Technology and Equipment, Ministry of Education, Taiyuan University of Technology, Taiyuan, 030024, China","Intelligent Optimization Computing and Blockchain Technology Shanxi Provincial Key Laboratory, Shanxi Provincial Department of Education, Taiyuan Normal University, Jinzhong, 030619, China","School of Mathematics and Statistics, Taiyuan Normal University, Jinzhong, 030619, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Engineering Research Center of Advanced Metal Composites Forming Technology and Equipment, Ministry of Education, Taiyuan University of Technology, Taiyuan, 030024, China","institution_ids":["https://openalex.org/I9086337"]},{"raw_affiliation_string":"Intelligent Optimization Computing and Blockchain Technology Shanxi Provincial Key Laboratory, Shanxi Provincial Department of Education, Taiyuan Normal University, Jinzhong, 030619, China","institution_ids":["https://openalex.org/I174104030","https://openalex.org/I4405273379"]},{"raw_affiliation_string":"School of Mathematics and Statistics, Taiyuan Normal University, Jinzhong, 030619, China","institution_ids":["https://openalex.org/I174104030"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5053120680","display_name":"Wei Shi","orcid":"https://orcid.org/0000-0003-0040-557X","observed_orcids":["https://orcid.org/0000-0003-0040-557X"]},"institutions":[{"id":"https://openalex.org/I174104030","display_name":"Taiyuan Normal University","ror":"https://ror.org/051k00p03","country_code":"CN","type":"education","lineage":["https://openalex.org/I174104030"]},{"id":"https://openalex.org/I4405273379","display_name":"Shanxi Provincial Education Department","ror":"https://ror.org/05r16bb17","country_code":"CN","type":"government","lineage":["https://openalex.org/I4405273379"]},{"id":"https://openalex.org/I9086337","display_name":"Taiyuan University of Technology","ror":"https://ror.org/03kv08d37","country_code":"CN","type":"education","lineage":["https://openalex.org/I9086337"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei Shi","raw_affiliation_strings":["Engineering Research Center of Advanced Metal Composites Forming Technology and Equipment, Ministry of Education, Taiyuan University of Technology, Taiyuan, 030024, China","Intelligent Optimization Computing and Blockchain Technology Shanxi Provincial Key Laboratory, Shanxi Provincial Department of Education, Taiyuan Normal University, Jinzhong, 030619, China","Shanxi Economic Construction Investment Group Co.,Ltd., Huayuan International Land Port Group Co., Ltd., Taiyuan, 030021, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Engineering Research Center of Advanced Metal Composites Forming Technology and Equipment, Ministry of Education, Taiyuan University of Technology, Taiyuan, 030024, China","institution_ids":["https://openalex.org/I9086337"]},{"raw_affiliation_string":"Intelligent Optimization Computing and Blockchain Technology Shanxi Provincial Key Laboratory, Shanxi Provincial Department of Education, Taiyuan Normal University, Jinzhong, 030619, China","institution_ids":["https://openalex.org/I174104030","https://openalex.org/I4405273379"]},{"raw_affiliation_string":"Shanxi Economic Construction Investment Group Co.,Ltd., Huayuan International Land Port Group Co., Ltd., Taiyuan, 030021, China","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101341569","display_name":"Shuai Zhu","orcid":"https://orcid.org/0000-0002-4782-9110","observed_orcids":["https://orcid.org/0000-0002-4782-9110"]},"institutions":[{"id":"https://openalex.org/I5422934","display_name":"Shanxi Datong University","ror":"https://ror.org/03s8xc553","country_code":"CN","type":"education","lineage":["https://openalex.org/I5422934"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shuai Zhu","raw_affiliation_strings":["College of Mathematics and Statistics, Shanxi Datong University, Datong, 037009, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Statistics, Shanxi Datong University, Datong, 037009, China","institution_ids":["https://openalex.org/I5422934"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5088913520"],"corresponding_institution_ids":["https://openalex.org/I174104030","https://openalex.org/I4405273379","https://openalex.org/I9086337"],"apc_list":{"value":4790,"currency":"USD","value_usd":4790},"apc_paid":null,"fwci":0.308,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.45803919,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"113","issue":"25","first_page":"34843","last_page":"34869"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10690","display_name":"Vibration Control and Rheological Fluids","score":0.8115000128746033,"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":0.8115000128746033,"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/T12206","display_name":"Vibration and Dynamic Analysis","score":0.16030000150203705,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.009200000204145908,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/internal-resonance","display_name":"internal resonance","score":0.9620000123977661},{"id":"https://openalex.org/keywords/fractional-order-oscillators","display_name":"fractional-order oscillators","score":0.7630000114440918},{"id":"https://openalex.org/keywords/nonlinear-vibration-isolation","display_name":"nonlinear vibration isolation","score":0.7450000047683716},{"id":"https://openalex.org/keywords/metal-rubber","display_name":"metal rubber","score":0.6710000038146973},{"id":"https://openalex.org/keywords/amplitude-frequency-response","display_name":"amplitude-frequency response","score":0.6460000276565552},{"id":"https://openalex.org/keywords/basins-of-attraction","display_name":"basins of attraction","score":0.984000027179718},{"id":"https://openalex.org/keywords/stability-region","display_name":"stability region","score":0.6690000295639038},{"id":"https://openalex.org/keywords/multiscale-methods","display_name":"multiscale methods","score":0.6010000109672546},{"id":"https://openalex.org/keywords/routh-hurwitz-criterion","display_name":"Routh-Hurwitz criterion","score":0.8029999732971191}],"concepts":[{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.7774999737739563},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6550999879837036},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5109000205993652},{"id":"https://openalex.org/C28427503","wikidata":"https://www.wikidata.org/wiki/Q13580300","display_name":"Internal model","level":3,"score":0.4674000144004822},{"id":"https://openalex.org/C207821765","wikidata":"https://www.wikidata.org/wiki/Q405372","display_name":"Instability","level":2,"score":0.4596000015735626},{"id":"https://openalex.org/C40678858","wikidata":"https://www.wikidata.org/wiki/Q6934874","display_name":"Multiple-scale analysis","level":3,"score":0.454800009727478},{"id":"https://openalex.org/C139210041","wikidata":"https://www.wikidata.org/wiki/Q2145840","display_name":"Resonance (particle physics)","level":2,"score":0.43290001153945923},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.41200000047683716},{"id":"https://openalex.org/C198394728","wikidata":"https://www.wikidata.org/wiki/Q3695508","display_name":"Vibration","level":2,"score":0.40369999408721924},{"id":"https://openalex.org/C180205008","wikidata":"https://www.wikidata.org/wiki/Q159190","display_name":"Amplitude","level":2,"score":0.4034000039100647},{"id":"https://openalex.org/C19118579","wikidata":"https://www.wikidata.org/wiki/Q786423","display_name":"Frequency domain","level":2,"score":0.3910999894142151},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.36390000581741333},{"id":"https://openalex.org/C83581075","wikidata":"https://www.wikidata.org/wiki/Q1361503","display_name":"Excitation","level":2,"score":0.353300005197525},{"id":"https://openalex.org/C49240428","wikidata":"https://www.wikidata.org/wiki/Q3305953","display_name":"Vibration control","level":3,"score":0.3499000072479248},{"id":"https://openalex.org/C500300565","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Computer simulation","level":2,"score":0.34209999442100525},{"id":"https://openalex.org/C17500928","wikidata":"https://www.wikidata.org/wiki/Q959968","display_name":"Control system","level":2,"score":0.34200000762939453},{"id":"https://openalex.org/C103824480","wikidata":"https://www.wikidata.org/wiki/Q185889","display_name":"Time domain","level":2,"score":0.3395000100135803},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3375999927520752},{"id":"https://openalex.org/C45799244","wikidata":"https://www.wikidata.org/wiki/Q109968206","display_name":"Vibration isolation","level":3,"score":0.33000001311302185},{"id":"https://openalex.org/C147317941","wikidata":"https://www.wikidata.org/wiki/Q1925419","display_name":"Describing function","level":3,"score":0.319599986076355},{"id":"https://openalex.org/C8590192","wikidata":"https://www.wikidata.org/wiki/Q1054694","display_name":"Frequency response","level":2,"score":0.2985999882221222},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.2921000123023987},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.29159998893737793},{"id":"https://openalex.org/C167020490","wikidata":"https://www.wikidata.org/wiki/Q3457902","display_name":"Nonlinear resonance","level":3,"score":0.290800005197525},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.2906999886035919},{"id":"https://openalex.org/C172707124","wikidata":"https://www.wikidata.org/wiki/Q423488","display_name":"Actuator","level":2,"score":0.28679999709129333},{"id":"https://openalex.org/C126980161","wikidata":"https://www.wikidata.org/wiki/Q863783","display_name":"Simulated annealing","level":2,"score":0.28049999475479126},{"id":"https://openalex.org/C81299745","wikidata":"https://www.wikidata.org/wiki/Q334269","display_name":"Transfer function","level":2,"score":0.2685999870300293},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.26669999957084656},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2597000002861023},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.2529999911785126},{"id":"https://openalex.org/C2779728712","wikidata":"https://www.wikidata.org/wiki/Q17014617","display_name":"Fractional-order system","level":3,"score":0.25200000405311584},{"id":"https://openalex.org/C529865628","wikidata":"https://www.wikidata.org/wiki/Q1790740","display_name":"Manifold (fluid mechanics)","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11071-025-11848-z","doi":"https://doi.org/10.1007/s11071-025-11848-z","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11071-025-11848-z","pdf_url":null,"source":{"id":"https://openalex.org/S138681734","display_name":"Nonlinear Dynamics","issn_l":"0924-090X","issn":["0924-090X","1573-269X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","cwts-core","dongbi-b","jufo-2","norway-1","poland-140","russia-white-list-1"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Nonlinear Dynamics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4581628350","display_name":null,"funder_award_id":"202203021221148","funder_id":"https://openalex.org/F4320327913","funder_display_name":"ShanXi Science and Technology Department"},{"id":"https://openalex.org/G5262973780","display_name":null,"funder_award_id":"52005360","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/F4320327913","display_name":"ShanXi Science and Technology Department","ror":"https://ror.org/05vp4an32"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W2016397694","https://openalex.org/W2024561775","https://openalex.org/W2026718235","https://openalex.org/W2046210296","https://openalex.org/W2049249211","https://openalex.org/W2066639428","https://openalex.org/W2077707516","https://openalex.org/W2736293831","https://openalex.org/W2747321678","https://openalex.org/W2808360835","https://openalex.org/W3015085916","https://openalex.org/W3097485879","https://openalex.org/W3210379366","https://openalex.org/W4205251459","https://openalex.org/W4284962788","https://openalex.org/W4291184679","https://openalex.org/W4293217354","https://openalex.org/W4310744554","https://openalex.org/W4312062988","https://openalex.org/W4313399356","https://openalex.org/W4313441937","https://openalex.org/W4315798116","https://openalex.org/W4327814056","https://openalex.org/W4366608397","https://openalex.org/W4389461424","https://openalex.org/W4390442939","https://openalex.org/W4394813545","https://openalex.org/W4394947808","https://openalex.org/W4400363990","https://openalex.org/W4401991336","https://openalex.org/W4403005649","https://openalex.org/W4403749521","https://openalex.org/W4408090970"],"related_works":["https://openalex.org/W7205015389","https://openalex.org/W4410733194","https://openalex.org/W4309336594","https://openalex.org/W4390790992","https://openalex.org/W4313250637","https://openalex.org/W7168427906","https://openalex.org/W4413932487","https://openalex.org/W2461175888","https://openalex.org/W7126274941","https://openalex.org/W2144915690"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-09-24T07:57:37.273135","created_date":"2025-10-10T00:00:00"}