{“id”:“https://openalex.org/W2992643917“,”doi“:”https://doi.org/10.1155/2019/9234586“,”title“:”基于分数勒让德函数的分数绘制自激振动模型的振动位移数值解“,”display_name“:”基于分数勒让德函数的分数绘制自激振动模型的振动位移数值解“,”publication_year“:2019,”publication_date“:”2019-12-06“,”ids“:{”openalex“:”https://openalex.org/W2992643917“,”doi“:”https://doi.org/10.1155/2019/9234586“,”mag“:”2992643917“},”language“:”en“,”primary_location“:{”is_oa“:true,”landing_page_url“:”https://doi.org/10.1155/2019/9234586,“pdf_url”:https://downloads.hindawi.com/journals/complexity/2019/9234586.pdf,“源”:{“id”:https://openalex.org/S207319443“,”display_name“:”Complexity“,”issn_l“:”1076-2787“,”isn“:[”1076-278“,”1099-0526“],”is_oa“:true,”is_ in_doaj“:true,”host_organization“:”https://openalex.org/P4310319869“,”“host_organization_name”:“Hindawi Publishing Corporation”,“host_organization_lineage”:[“https://openalex.org/P4310319869“],”host_organization_lineage_names“:[”Hindawi Publishing Corporation“],“type”:“journal”},“license”:“cc-by”,“licence_id”:“https://openalex.org/licenses/cc-by“,”version“:”publishedVersion“,”is_accepted“:true,”is_published“:true},”type“:”article“,”type_crossref“:“journal-article”,”indexed_in“:[”crossref“,”doaj“],”open_access“:{”is_oa“:true,”oa_status“:”gold“,”oa_url“:”https://downloads.hindawi.com/journals/complexity/2019/9234586.pdf“,”any_repository_has_fulltext“:false},”authorships“:[{”author_position“:”第一“,”作者“:{”id“:”https://openalex.org/A5088913520“,”display_name“:”Jiaquan Xie“,”orcid“:”https://orcid.org/0000-0002-1323-5402},“机构”:[{“id”:https://openalex.org/I9086337“,”display_name“:”太原理工大学“,”ror“:”https://ror.org/03kv08d37“,”country_code“:”CN“,”type“:“教育”,”世系“:[”https://openalex.org/I9086337“]}],”国家“:[”CN“],”is_corresponding“:false,”raw_author_name“:”Jiaquan Xie“,”raw _ afiliation_strings“:[“太原工业大学机械与车辆工程学院,山西太原030024”],”affiliations“:”太原工业大学机械与车辆工程学院,中国山西省太原市030024“,“institution_ids”:[“https://openalex.org/I9086337“]}]},{”author_position“:”middle“,”author“:{”id“:”https://openalex.org/A5054524627“,”display_name“:”于正“,”兽人“:”https://orcid.org/0000-0003-4131-8480},“机构”:[{“id”:https://openalex.org/I39333907“,”display_name“:”燕山大学“,”ror“:”https://ror.org/02txfnf15“,”country_code“:”CN“,”type“:“教育”,”世系“:[”https://openalex.org/I39333907“]}],”countries“:[”CN“],”is_corresponding“:false,”raw_author_name“:”Yongjiang Zheng“,”rau_affiliation_strings“:【”燕山大学机械工程学院,河北秦皇岛066004“】,”affiliations“:[{”raw_affiliation_string“:”燕山学院,河北省秦皇岛市066004”,“机构ID“:[”https://openalex.org/I39333907“]}]},{”author_position“:”middle“,”author“:{”id“:”https://openalex.org/A504488250“,”display_name“:”仲恺人“,”兽人“:”https://orcid.org/0000-0002-5079-6372},“机构”:[{“id”:https://openalex.org/I9086337“,”display_name“:”太原理工大学“,”ror“:”网址:https://ror.org/03kv08d37“,”country_code“:”CN“,”type“:“教育”,”世系“:[”https://openalex.org/I9086337“]}],”国家“:[”CN“],”is_corresponding“:false,”raw_author_name“:”任仲恺“,”raw _ afiliation_strings“:[“太原理工大学机械与车辆工程学院,山西太原030024”],”affiliations“:”太原工业大学机械与车辆工程学院,中国山西省太原市030024“,“institution_ids”:[“https://openalex.org/I9086337“]}]},{”author_position“:”middle“,”author“:{”id“:”https://openalex.org/A5085142676“,”display_name“:”Tao Wang“,”orcid“:”https://orcid.org/0000-0003-0951-5476},“机构”:[{“id”:https://openalex.org/I9086337“,”display_name“:”太原理工大学“,”ror“:”https://ror.org/03kv08d37“,”country_code“:”CN“,”type“:“教育”,”世系“:[”https://openalex.org/I9086337“]}],”国家“:[”CN“],”is_corresponding“:true,”raw_author_name“:”Tao Wang“,”rau_affiliation_strings“:[“太原工业大学机械与车辆工程学院,山西太原030024”],”affiliations“:”太原工业大学机械与车辆工程学院,中国山西省太原市030024“,“institution_ids”:[“https://openalex.org/I9086337“]}]},{”author_position“:”last“,”author“:{”id“:”https://openalex.org/A5057885631“,”display_name“:”Guangxian Shen“,”orcid“:null},”institutions“:[{”id“:”https://openalex.org/I39333907“,”display_name“:”燕山大学“,”ror“:”https://ror.org/02txfnf15“,”country_code“:”CN“,”type“:“教育”,”世系“:[”https://openalex.org/I39333907“]}],”countries“:[”CN“],”is_corresponding“:false,”raw_author_name“:”Guangxian Shen“,”rau_affiliation_strings“:【”燕山大学机械工程学院,秦皇岛066004,中国“】,“affiliations”:[{“raw_affilition_string”:“燕山大学力学工程学院,河北秦皇岛,066004”,“机构ID“:[”https://openalex.org/I39333907“]}]}],”countries_disticont_count“:1,”institutions_disticent_count”:2,”corresponding_author_ids“:[”https://openalex.org/A5085142676“],”对应的机构ID“:[”https://openalex.org/I9086337“],”apc_list“:{“value”:2300,”currency“:”USD“,”value_USD“:2300、”provenance“:”doaj“}、”apc_payed“:”{“value”:230、”current“:”美元“、”value_USD“:230、“provenance”:“doaj”}、“fwci”:0.31、“has_fulltext_origin”:“pdf”、“cited_by_count”:4、“citted_by_percentile_year”:{”min“:80,“max”:82},“biblio”:{“volume”:“2019”,“issue”:null,“first_page”:“1”,“last_page“:”10“},”is_retracted“:false,”is_paratext“:fase,”primary_topic“:{”id“:”https://openalex.org/T12206“,”display_name“:”轴向运动动力学分析与控制“,”score“:0.9993,”subfield“:{”id“:”https://openalex.org/subfields/2207“,”display_name“:”控制与系统工程“},”字段“:{”id“:”https://openalex.org/fields/22“,”display_name“:”Engineering“},”domain“:{”id“:”https://openalex.org/domains/3“,”display_name“:”物理科学“}},”主题“:[{”id“:”https://openalex.org/T12206“,”display_name“:”轴向运动动力学分析与控制“,”score“:0.9993,”subfield“:{”id“:”https://openalex.org/subfields/2207“,”display_name“:”控制与系统工程“},”字段“:{”id“:”https://openalex.org/fields/22“,”display_name“:”Engineering“},”domain“:{”id“:”https://openalex.org/domains/3“,”display_name“:”物理科学“}},{”id“:”https://openalex.org/T10288“,”“display_name”:“异常扩散建模与分析”,“score”:0.9972,“subfield”:{“id”:“https://openalex.org/subfields/2611“,”display_name“:”建模与仿真“},”字段“:{”id“:”https://openalex.org/fields/26“,”display_name“:”Mathematics“},”domain“:{”id“:”https://openalex.org/domains/3“,”display_name“:”物理科学“}},{”id“:”https://openalex.org/T12197“,”“display_name”:“汽车制动摩擦材料的摩擦学研究”,“score”:0.9945,“subfield”:{“id”:“https://openalex.org/subfields/2203“,”display_name“:”汽车工程“},”字段“:{”id“:”https://openalex.org/fields/22“,”display_name“:”Engineering“},”domain“:{”id“:”https://openalex.org/domains/3“,”display_name“:”物理科学“}}],”关键词“:[{”id“:”https://openalex.org/keywords/vibration分析“,”display_name“:”振动分析“,”score“:0.554501},{”id“:”https://openalex.org/keywords/摩擦诱导振动“,”display_name“:”摩擦诱发振动“,”score“:0.527674},{”id“:”https://openalex.org/keywords/fractional-derivatives网站“,”display_name“:”分数导数“,”score“:0.519101},{”id“:”https://openalex.org/keywords/fractional-calculus“,”display_name“:”分数微积分“,”score“:0.512851}],”concepts“:[{”id“:”https://openalex.org/C111458787,“wikidata”:https://www.wikidata.org/wiki/Q215405“,”display_name“:”勒让德多项式“,”level“:2,”score“:0.81514657},{”id“:”https://openalex.org/C198394728,“wikidata”:https://www.wikidata.org/wiki/Q3695508“,”display_name“:”Vibration“,”level“:2,”score“:0.7854026},{”id“:”https://openalex.org/C107551265,“wikidata”:https://www.wikidata.org/wiki/Q1458245“,”display_name“:”置换(心理学)“,”level“:2,”score“:0.653263},{”id“:”https://openalex.org/C154249771,“wikidata”:https://www.wikidata.org/wiki/Q1339058“,”display_name“:”分数微积分“,”level“:2,”score“:0.61584353},{”id“:”https://openalex.org/C198082294,“wikidata”:https://www.wikidata.org/wiki/Q3399648“,”display_name“:”职位(财务)“,”级别“:2,”分数“:0.5033375},{”id“:”https://openalex.org/C33923547,“wikidata”:https://www.wikidata.org/wiki/Q395“,”display_name“:”数学“,”等级“:0,”分数“:0.45770052},{”id“:”https://openalex.org/C134306372,“wikidata”:https://www.wikidata.org/wiki/Q7754“,”display_name“:”数学分析“,”level“:1,”score“:0.42493534},{”id“:”https://openalex.org/C78045399,“wikidata”:https://www.wikidata.org/wiki/Q11214“,”display_name“:”微分方程“,”level“:2,”score“:0.4235947},{”id“:”https://openalex.org/C121332964,“wikidata”:https://www.wikidata.org/wiki/Q413“,”display_name“:”物理“,”级别“:0,”分数“:0.27756286},{”id“:”https://openalex.org/C24890656,“wikidata”:https://www.wikidata.org/wiki/Q82811“,”display_name“:”Acoustics“,”level“:1,”score“:0.13470504},{”id“:”https://openalex.org/C15744967,“wikidata”:https://www.wikidata.org/wiki/Q9418“,”display_name“:”心理学“,”等级“:0,”分数“:0.0},{”id“:”https://openalex.org/C10138342,“wikidata”:https://www.wikidata.org/wiki/Q43015“,”display_name“:”Finance“,”level“:1,”score“:0.0},{”id“:”https://openalex.org/C162324750,“wikidata”:https://www.wikidata.org/wiki/Q8134“,”display_name“:”经济学“,”level“:0,”score“:0.0},{”id“:”https://openalex.org/C542102704,“wikidata”:https://www.wikidata.org/wiki/Q183257“,”display_name“:”心理治疗师“,”level“:1,”score“:0.0}],”mesh“:[],”locations_count“:2,”location“:[{”is_oa“:true,”landing_page_url“:”https://doi.org/10.1155/2019/9234586,“pdf_url”:https://downloads.hindawi.com/journals/complexity/2019/9234586.pdf,“源”:{“id”:https://openalex.org/S207319443“,”display_name“:”Complexity“,”issn_l“:”1076-2787“,”isn“:[”1076-278“,”1099-0526“],”is_oa“:true,”is_ in_doaj“:true,”host_organization“:”https://openalex.org/P4310319869“,”“host_organization_name”:“Hindawi Publishing Corporation”,“host_organization_lineage”:[“https://openalex.org/P4310319869“],”host_organization_lineage_names“:[”Hindawi Publishing Corporation“],“type”:“journal”},“license”:“cc-by”,“licence_id”:“https://openalex.org/licenses/cc-by“,”version“:”publishedVersion“,”is_accepted“:true,”is_published“:true},{”is_oa“:false,”landing_page_url“:”https://doaj.org/article/5ff78b239ea84f3b92d33f172ac0a9d2“,”pdf_url“:空,”源“:{”id“:”https://openalex.org/S4306401280“,”display_name“:”DOAJ(DOAJ:开放存取期刊目录)“,”issn_l“:null,”issn“:null:”is_oa“:true,”is_in_DOAJ“:false,”host_organization“:null,”host_organization_name“:null,“host_orgganization_lineage”:[],“host_orgganization _lineage_names”:[[],“type”:“repository”},“license”:null、“license_id”:null、“version”:null.、“is_accepted”:false、“is_published“:false}],”最佳位置“:{”is_oa“:true,”登录页面url“:”https://doi.org/10.1155/2019/9234586,“pdf_url”:https://downloads.hindawi.com/journals/complexity/2019/9234586.pdf,“源”:{“id”:https://openalex.org/S207319443“,”display_name“:”Complexity“,”issn_l“:”1076-2787“,”isn“:[”1076-278“,”1099-0526“],”is_oa“:true,”is_ in_doaj“:true,”host_organization“:”https://openalex.org/P4310319869“,”“host_organization_name”:“Hindawi Publishing Corporation”,“host_organization_lineage”:[“https://openalex.org/P4310319869“],”host_organization_lineage_names“:[”Hindawi Publishing Corporation“],“type”:“journal”},“license”:“cc-by”,“licence_id”:“https://openalex.org/licenses/cc-by“,”version“:”publishedVersion“,”is_accepted“:true,”is_published“:true},”sustainable_development_goals“:[],”grants“:{”funder“:”https://openalex.org/F4320321001“,”funder_display_name“:”国家自然科学基金“,”award_id“:”51505417“},{”资助者“:”https://openalex.org/F4320321001“,”funder_display_name“:”国家自然科学基金“,”award_id“:”2018YFB1307902“},{”资助者“:”https://openalex.org/F4320321001“,”“funder_display_name”:“国家自然科学基金”,“award_id”:“201703D111003”},{“funder”:“https://openalex.org/F4320321001“,”“funder_display_name”:“国家自然科学基金”,“award_id”:“20181102015”},{“funder”:“https://openalex.org/F4320321001“,”“funder_display_name”:“国家自然科学基金”,“award_id”:“U1710254”},{“funder”:“https://openalex.org/F4320321001“,”funder_display_name“:”国家自然科学基金“,”award_id“:”E2016203294“}],”datasets“:[],”versions“:[],”referenced_works_count“:18,”referrenced_works“:[”https://openalex.org/W1842957613","https://openalex.org/W1989781189","https://openalex.org/W2037423068","https://openalex.org/W2042923669","https://openalex.org/W2053988539","https://openalex.org/W2083559699","https://openalex.org/W2087687656","https://openalex.org/W2295646973","https://openalex.org/W2560743047","https://openalex.org/W2766195651","https://openalex.org/W2795982376","https://openalex.org/W2796539113","https://openalex.org/W2801334908","https://openalex.org/W2808933267","https://openalex.org/W2903172934","https://openalex.org/W2919497243","https://openalex.org/W2948998906","https://openalex.org/W2963785737“],”related_works“:[”https://openalex.org/W605098443","https://openalex.org/W4320801820","https://openalex.org/W4210327724","https://openalex.org/W374314514","https://openalex.org/W3007167322","https://openalex.org/W2992643917","https://openalex.org/W2572667212","https://openalex.org/W2321342552","https://openalex.org/W2074759558","https://openalex.org/W2001662728“],”ngrams_url“:”https://api.openalex.org/works/W2992643917/ngrams网站“,”“abstract_inverted_index”:{“In”:[0,68],“practice”:[1],“due”:[2],“to”:[3,63,92],“the”:[4,7,19,23,31,38,47,66,71,78,83,85,97],“fact”:[5],“that”:[6],“phenoma”:[8,45],“of”:[9,18,22,46,74,77],“drawing”:[10,32],“self-excited”:[11,33],“vibration”:[12,34,75],“可以”:[13],“是”:[14,93],“视为”:[15],“作为”:[16],“一”:[17],“狩猎”:[20,44],“现象”:[21],“机械”:[24,48],“系统”:[25],“这个”:[26,69],“研究”:[27],“重点”:[28],“关于”:[29],“调查”:[30],“过程”:[35],“通过”:[36],“提出”:[37],“分数”:[39,51,57],“微分”:[40,58],“方程”:[41],“模型”:[42,79,87],“系统”。“:[49],”The“:[50],”Legendre“:[52],”functions“:[53],”together“:[54],”with“:55],”their“:[56],”operational“:[59],”matrix“:[60],”are“:[C1,80,90],”used“:[62],”numerically“:[64],”solve“:[65],”model。“:[67],”方式,“:[70],”数值“:[72,98],”解“:[73],”位移“:[76],”获得。“:[81],”At“:[82],”end“:[84],”提议“:[86],”and“:[8810],”算法“:[89],”证明“:[91],”有效“:[94],”通过“:[95],”分析“:[96],”结果“:[99],”相位“:[101],”位置。“:[102]},”cited_by_api_url“:”https://api.openalex.org/works?filter=cites:W2992643917“,”counts_by_year“:[{”年份“:2023,”cited_by_count“:2},{”年“:2022,”cited_by_count”:1},“{”年度“:2020,”citecd_by_count“:1}],”更新日期“:”2024-06-21T04:00:24.435374“,”创建日期“:“2019-12-13”}