{"id":"https://openalex.org/W2071293666","doi":"https://doi.org/10.1080/00207170601100904","title":"Riesz basis property of serially connected Timoshenko beams","display_name":"Riesz basis property of serially connected Timoshenko beams","publication_year":2007,"publication_date":"2007-03-01","ids":{"openalex":"https://openalex.org/W2071293666","doi":"https://doi.org/10.1080/00207170601100904","mag":"2071293666"},"language":"en","primary_location":{"id":"doi:10.1080/00207170601100904","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207170601100904","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"},"type":"article","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/A5029838563","display_name":"Genqi Xu","orcid":"https://orcid.org/0000-0001-8120-0490"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"G. Q. Xu","raw_affiliation_strings":["\n Department of Mathematics, Tianjin University, Tianjin, 300072, China","Department of mathematics, Tianjin University, Tianjin, 300072 China"],"affiliations":[{"raw_affiliation_string":"\n Department of Mathematics, Tianjin University, Tianjin, 300072, China","institution_ids":["https://openalex.org/I162868743"]},{"raw_affiliation_string":"Department of mathematics, Tianjin University, Tianjin, 300072 China","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5080512986","display_name":"Zhong\u2010Jie Han","orcid":"https://orcid.org/0000-0001-6114-6976"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Z. J. Han","raw_affiliation_strings":["\n Department of Mathematics, Tianjin University, Tianjin, 300072, China","Department of mathematics, Tianjin University, Tianjin, 300072 China"],"affiliations":[{"raw_affiliation_string":"\n Department of Mathematics, Tianjin University, Tianjin, 300072, China","institution_ids":["https://openalex.org/I162868743"]},{"raw_affiliation_string":"Department of mathematics, Tianjin University, Tianjin, 300072 China","institution_ids":["https://openalex.org/I162868743"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111976261","display_name":"Siu Pang Yung","orcid":"https://orcid.org/0000-0003-1583-2953"},"institutions":[{"id":"https://openalex.org/I162868743","display_name":"Tianjin University","ror":"https://ror.org/012tb2g32","country_code":"CN","type":"education","lineage":["https://openalex.org/I162868743"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"S. P. Yung","raw_affiliation_strings":["\n Department of Mathematics, Tianjin University, Tianjin, 300072, China","Department of mathematics, Tianjin University, Tianjin, 300072 China"],"affiliations":[{"raw_affiliation_string":"\n Department of Mathematics, Tianjin University, Tianjin, 300072, China","institution_ids":["https://openalex.org/I162868743"]},{"raw_affiliation_string":"Department of mathematics, Tianjin University, Tianjin, 300072 China","institution_ids":["https://openalex.org/I162868743"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5029838563"],"corresponding_institution_ids":["https://openalex.org/I162868743"],"apc_list":null,"apc_paid":null,"fwci":16.7004,"has_fulltext":false,"cited_by_count":55,"citation_normalized_percentile":{"value":0.99040079,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"80","issue":"3","first_page":"470","last_page":"485"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9998999834060669,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9876999855041504,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11366","display_name":"Elasticity and Material Modeling","score":0.9842000007629395,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6605289578437805},{"id":"https://openalex.org/keywords/hilbert-space","display_name":"Hilbert space","score":0.5448054075241089},{"id":"https://openalex.org/keywords/resolvent","display_name":"Resolvent","score":0.5173079967498779},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.4727678596973419},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.4596767723560333},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.45046350359916687},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.42679816484451294},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.23652538657188416},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.14778992533683777}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6605289578437805},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.5448054075241089},{"id":"https://openalex.org/C196267783","wikidata":"https://www.wikidata.org/wiki/Q4392490","display_name":"Resolvent","level":2,"score":0.5173079967498779},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4727678596973419},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.4596767723560333},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.45046350359916687},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.42679816484451294},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.23652538657188416},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.14778992533683777},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00207170601100904","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207170601100904","pdf_url":null,"source":{"id":"https://openalex.org/S88061139","display_name":"International Journal of Control","issn_l":"0020-7179","issn":["0020-7179","1366-5820"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Control","raw_type":"journal-article"},{"id":"pmh:oai:hub.hku.hk:10722/75325","is_oa":false,"landing_page_url":"http://hdl.handle.net/10722/75325","pdf_url":null,"source":{"id":"https://openalex.org/S4377196271","display_name":"The HKU Scholars Hub (University of Hong Kong)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I889458895","host_organization_name":"University of Hong Kong","host_organization_lineage":["https://openalex.org/I889458895"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W130219908","https://openalex.org/W593634829","https://openalex.org/W621672655","https://openalex.org/W1248197218","https://openalex.org/W1486874193","https://openalex.org/W1527296550","https://openalex.org/W1642453465","https://openalex.org/W1863321137","https://openalex.org/W1964932009","https://openalex.org/W1998639858","https://openalex.org/W2001864220","https://openalex.org/W2003412775","https://openalex.org/W2007624157","https://openalex.org/W2015567437","https://openalex.org/W2026730079","https://openalex.org/W2041701305","https://openalex.org/W2043650549","https://openalex.org/W2053390926","https://openalex.org/W2069116532","https://openalex.org/W2073366798","https://openalex.org/W2094951808","https://openalex.org/W2106418667","https://openalex.org/W2117600869","https://openalex.org/W2121248553","https://openalex.org/W2126403089","https://openalex.org/W2130606767","https://openalex.org/W2133122555","https://openalex.org/W2316005905"],"related_works":["https://openalex.org/W2350866827","https://openalex.org/W2963600173","https://openalex.org/W2951761543","https://openalex.org/W4327812601","https://openalex.org/W2795788140","https://openalex.org/W2100603772","https://openalex.org/W4239624332","https://openalex.org/W2949463090","https://openalex.org/W4299800520","https://openalex.org/W2594888460"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,153],"study":[4],"the":[5,22,26,32,40,50,64,70,77,82,86,112,116,126,134,142,145,169],"Riesz":[6,121],"basis":[7,122],"property":[8],"of":[9,25,45,63,111,115,141],"serially":[10,170],"connected":[11,171],"Timoshenko":[12,172],"beams":[13,46,65],"with":[14,123],"joint":[15],"and":[16,31,42,53,69,93],"boundary":[17],"feedback":[18,62],"controls.":[19],"Suppose":[20],"that":[21,81,106,118,160],"left":[23],"end":[24,34,72],"whole":[27],"beam":[28],"is":[29,35,108,137,149],"clamped":[30],"right":[33,71],"free.":[36],"At":[37],"intermediate":[38,67],"nodes,":[39],"displacement":[41],"rotational":[43],"angle":[44],"are":[47,73],"continuous":[48],"but":[49],"shearing":[51],"force":[52],"bending":[54],"moment":[55],"could":[56],"be":[57,164],"discontinuous.":[58],"The":[59],"collocated":[60],"velocity":[61],"at":[66],"nodes":[68],"used":[74],"to":[75,158],"stabilize":[76],"system.":[78],"We":[79,103],"prove":[80],"operator":[83,117],"determined":[84,128],"by":[85],"closed":[87,146],"loop":[88,147],"system":[89,148],"has":[90],"compact":[91],"resolvent":[92],"generates":[94],"a":[95,109,120,155],"C0":[96],"semigroup":[97],"in":[98],"an":[99,139],"appropriate":[100],"Hilbert":[101],"space.":[102],"also":[104],"show":[105],"there":[107],"sequence":[110],"generalized":[113],"eigenvectors":[114],"forms":[119],"parentheses.":[124],"Hence":[125],"spectrum":[127],"growth":[129],"condition":[130],"holds.":[131],"Therefore":[132],"if":[133],"imaginary":[135],"axis":[136],"not":[138,166],"asymptote":[140],"spectrum,":[143],"then":[144],"exponentially":[150],"stable.":[151],"Finally,":[152],"give":[154],"conclusion":[156],"remark":[157],"explain":[159],"our":[161],"result":[162],"can":[163],"applied":[165],"only":[167],"on":[168],"beams.":[173]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":2}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}
